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COURSE MANUAL

Operations Management in Educational Practices

EME 302

University of Ibadan Distance Learning Centre

Open and Distance Learning Course Series Development

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Copyright © 2015 by Distance Learning Centre, University of Ibadan, Ibadan.

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ISBN 978-021-899-8

General Editor: Prof. Bayo Okunade

University of Ibadan Distance Learning Centre

University of Ibadan, Nigeria

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Tel: +234 (80775935727) E-mail: [email protected]

Website: www.dlc.ui.edu.ng

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Vice-Chancellor’s Message The Distance Learning Centre is building on a solid tradition of over two decades of

service in the provision of External Studies Programme and now Distance Learning

Education in Nigeria and beyond. The Distance Learning mode to which we are

committed is providing access to many deserving Nigerians in having access to higher

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of full time education. Recently, it is contributing in no small measure to providing places

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These course materials have been written by writers specially trained in ODL course

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It is our hope that you will put these course materials to the best use.

Prof. Abel Idowu Olayinka

Vice-Chancellor

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Foreword As part of its vision of providing education for “Liberty and Development” for Nigerians

and the International Community, the University of Ibadan, Distance Learning Centre has

recently embarked on a vigorous repositioning agenda which aimed at embracing a

holistic and all encompassing approach to the delivery of its Open Distance Learning

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The development of the materials which is on-going also had input from experienced

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It is important to note that, for a distance learner to excel there is the need to source and

read relevant materials apart from this course material. Therefore, adequate

supplementary reading materials as well as other information sources are suggested in the

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Apart from the responsibility for you to read this course material with others, you are also

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during your study even before the interactive session which is by design for revision.

Your academic advisors will assist you using convenient technology including Google

Hang Out, You Tube, Talk Fusion, etc. but you have to take advantage of these. It is also

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The implication of the above is that, a distance learner has a responsibility to develop

requisite distance learning culture which includes diligent and disciplined self-study,

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skills by availing yourself the opportunity of training that the Centre’s provide and put

these into use.

In conclusion, it is envisaged that the course materials would also be useful for the

regular students of tertiary institutions in Nigeria who are faced with a dearth of high

quality textbooks. We are therefore, delighted to present these titles to both our distance

learning students and the university’s regular students. We are confident that the

materials will be an invaluable resource to all.

We would like to thank all our authors, reviewers and production staff for the high

quality of work.

Best wishes.

Professor Bayo Okunade

Director

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Course Development Team Content Authoring Prof. Emunemu B.O. & Isuku, E.J

Content Editor

Production Editor

Learning Design/Assessment Authoring

Managing Editor

General Editor

Prof. Remi Raji-Oyelade

Ogundele Olumuyiwa Caleb

Tolulope Famaye

Ogunmefun Oladele Abiodun

Prof. Bayo Okunade

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Table of Contents

Course Overview .................................................................................................................................... xii

Course Objectives ................................................................................................................................... xii

Study Session One The Development of Modern Management Principles ................................. 1

Introduction ............................................................................................................................................... 1

Learning Outcomes for Study Session 1 ................................................................................................... 1

1.1. The Origin and Evolution of Management ................................................................................... 2

1.1.1. Origin of Management .......................................................................................................... 2

1.1.2. The Evolution of Management ............................................................................................. 3

1.2. Modern Management Era.............................................................................................................. 7

1.2.1. Empirical School ................................................................................................................... 7

1.2.2. SocialSchool System ............................................................................................................. 7

1.2.3. Decision Theory School ........................................................................................................ 9

Summary of Session 1 ............................................................................................................................ 10

Self-Assessment Questions (SAQs) for Session 1 .................................................................................. 10

References ............................................................................................................................................... 11

Study Session Two: Programme Evaluation and Review Technique (PERT) .......................... 12

Introduction ............................................................................................................................................. 12

Learning Outcomes for Study Session 2 ................................................................................................. 12

2.1. Meaning and Analysis of Program Evaluation and Review Technique (PERT) ............................. 12

2.1.1. Meaning of Program Evaluation and Review Technique ......................................................... 12

2.1.2. Pert Analysis ............................................................................................................................. 15

2.2. Critical Path Analysis, and Critical Path Method ....................................................................... 16



References ............................................................................................................................................... 18

Study Session Three: Critical Path Method (CPM) ...................................................................... 19

Introduction ............................................................................................................................................. 19

Learning Outcomes for StudySession 3 .................................................................................................. 19

3.1. Meaning, Steps, and Merits, and Demerits of Critical Path Method (CPM) ................................... 19

3.1.1. Meaning of Critical Path Method .............................................................................................. 20

3.1.2. Key Steps in Critical Path Method ............................................................................................ 22

3.1.3 Merits of Critical Path Method .................................................................................................. 24

3.1.4 Demerits of Critical Path Method .............................................................................................. 24

3.2. Critical Chain Project Management (CCPM) .................................................................................. 25


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References ............................................................................................................................................... 27

Study Session Four: Inventory Policy........................................................................................... 29

Introduction ............................................................................................................................................. 29


4.1. Meaning, Methods, and Types of Inventory Policies ...................................................................... 29

4.1.1. Meaning of Inventory Policy .................................................................................................... 29

4.1.2. Inventory Methods best for Organisation ................................................................................. 31

4.1.3. Types of Inventory Policies ...................................................................................................... 31

4.2. Meaning of Stock and Types ........................................................................................................... 34

4.2.1. Stock Reduction ........................................................................................................................ 34

4.2.2. Why the need for Stock? ........................................................................................................... 34

4.3. Economic Order Quantity (EOQ) model ......................................................................................... 36



References ............................................................................................................................................... 42

Study Session Five: Equipment Replacement Policies ................................................................. 43

(Individual and Mass/Group Techniques for Non-Durable Items, Npv and Least Cost Methods

for Durable Items) ......................................................................................................................... 43

Introduction ............................................................................................................................................. 43


5.1. Replacement Theory, Maintenance, and Models in Operation Research ........................................ 44

5.1.1. Replacement Theory inOperation Research .............................................................................. 44

5.1.2. Replacement and Maintenance ................................................................................................. 46

5.1.3. Reasons for Equipment Replacement ....................................................................................... 47

5.1.4. Models in Replacement and Maintenance .......................................................................... 49

5.2. Net Present Value (Npv) and Least Cost Methods .......................................................................... 50

5.2.1. Net Present Value...................................................................................................................... 50

5.2.2. Advantages of Net Present Value (NPV) .................................................................................. 51

5.2.3. Disadvantages of NPV .............................................................................................................. 51

5.2.4.Least Cost Method ..................................................................................................................... 52



References ............................................................................................................................................... 55

Study Session Six: Queuing Theory ............................................................................................. 56

Introduction ............................................................................................................................................. 56

Learning Outcomes for StudySession 6 .................................................................................................. 56

6.1. Meaning and Definition of Terms in Queuing Theory .................................................................... 56

6.1.1. Meaning of Queuing Theory ..................................................................................................... 56

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6.1.2. Definition of Terms inQueuing Model ..................................................................................... 57



References ............................................................................................................................................... 65

Study Session Seven: Total Quality Management in Education .................................................. 66

Introduction ............................................................................................................................................. 66


7.1. Origin, Meaning, and Principles of Total Quality Management ...................................................... 66

7.1.1. The Origin of Total Quality Management ................................................................................ 67

7.1.2. Meaning of Total Quality Management (TQM) ....................................................................... 68

7.1.3. Total Quality Management (TQM)Principles ........................................................................... 71

7.2. The Elements, Generic Model, and Building Blocks of Total Quality Management (TQM) .......... 72

7.2.1. The Primary Elements of TQM ................................................................................................ 72

7.2.2. Generic Model for Implementing TQM .............................................................................. 74

7.2.3. The Buildingblocks of TQM ..................................................................................................... 75



References ............................................................................................................................................... 79

Study Session Eight: Resource Allocation/Assignment: Hungarian Method ............................... 80

Introduction ............................................................................................................................................. 80


8.1. Meaning and Hungarian Method of Resource Allocation ............................................................... 81

8.1.1. Meaning of Resource Allocation .............................................................................................. 81

8.1.2. Hungarian Method for Solving Assignment Problem ............................................................... 81



References ............................................................................................................................................... 89

Study Session Nine: Resource Allocation/Assignment: ........................................................... 90

Transportation Problem I (Simplex and Transportation Method) ................................................ 90

Introduction ............................................................................................................................................. 90


9.1. Meaning of Transportation Problem ................................................................................................ 91

9.2. Variants of the Simplex Method ...................................................................................................... 95

9.2.1. Simplex Method ........................................................................................................................ 95

9.2.2. Transportation Method .............................................................................................................. 97

9.2.3. Methods for Obtaining Basic Feasible Solution for Transportation Problem ........................... 97



References ............................................................................................................................................... 98

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Study Session Ten: Resource Allocation/Assignment: Transportation Problem II (North-West

Rule Model) .................................................................................................................................. 99

Introduction ............................................................................................................................................. 99

Learning Outcomes for Study Session 10 ............................................................................................... 99

10.1. Overview and Meaning of the North-West Rule Model (NWRM) ............................................... 99

10.1.1. Overview of the North-West Rule Model .............................................................................. 99

10.1.2. North-West Corner Method (NWCM) .................................................................................... 99

Summary of Session 10 ........................................................................................................................ 103

Self-Assessment Questions (SAQs) for Session 10 .............................................................................. 104

References ............................................................................................................................................. 104

Study Session Eleven: Resource Allocation/Assignment: Least-Cost Method ....................... 106

Introduction ........................................................................................................................................... 106

Learning Outcomes for Study Session 11 ............................................................................................. 106

11.1. Least Cost Method in Resource Allocation ................................................................................. 106

11.1.1. Minimum Cell-Cost Method ................................................................................................. 107

11.1.2. MODI Method (for obtaining reduced costs) ........................................................................ 108



Study SessionTwelve: Resource Allocation/Assignment: .......................................................... 115

(Vogel’s Approximation Method) .............................................................................................. 115

Introduction ........................................................................................................................................... 115


12.1. Vogel’s Approximation Method in Resource Allocation ............................................................ 115

Summary ofSession 12 ......................................................................................................................... 119


References ............................................................................................................................................. 121

Study Session Thirteen: Model in Education.............................................................................. 122

Introduction ........................................................................................................................................... 122


13.1. Meaning of a Model ..................................................................................................................... 123

13.2.DerivingSolutionsfromModels...................................................................................................... 127

13.2.1. Testing the Model and the Solution ...................................................................................... 127

13.3. Model Building Process ............................................................................................................... 130

13.4. Lewin’s Change Management Model .......................................................................................... 131

13.5. McKinsey 7-S Model ................................................................................................................... 132

13.5.1. The Benefits of McKinsey 7-S Model .............................................................................. 133

13.5.2. The Disadvantages of McKinsey 7-S Model are: ................................................................. 133

13.6. Kotter’s 8 Step Change Model ..................................................................................................... 134

13.6.1. Advantages of Kotter’s 8 Step Change Model ...................................................................... 135

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13.6.2. Disadvantages of Kotter’s 8 Step Change Model ................................................................. 135



References ............................................................................................................................................. 138

Study SessionFourteen: Decision Making Process: PPBS ......................................................... 139

Introduction ........................................................................................................................................... 139


14.1. Meaning of Decision Making and Types of Decisions ................................................................ 139

14.1.1. Meaning of Decision Making ............................................................................................... 140

14.1.2. Types of Decisions .................................................................................................................... 141

14.2. Planning, Programming, Budgeting System (PPBS) ................................................................... 141

14.2.1. Decision-Making under states of Certainty, Uncertainty and Risk ....................................... 142

14.2.2. Proactive and Reactive Decisions ......................................................................................... 142

14.2.3. The Rational Decision Making Process ................................................................................ 143

14.2.4. Individual Decision Making .................................................................................................. 145

14.2.5. A Group Decision-Making .................................................................................................... 146

14.3. Decision Making Techniques....................................................................................................... 148

14.3.1. Brainstorming ....................................................................................................................... 149

14.3.2. The Delphi Technique ........................................................................................................... 149

14.3.3. The Nominal Group Technique (NGT) ................................................................................. 150

14.3.4. Marginal Analysis ................................................................................................................. 150

14.3.5. Cost Benefit or Cost Effectiveness Analysis ........................................................................ 151

14.3.6. Decision Trees....................................................................................................................... 151

Summary of Unit 14 .............................................................................................................................. 153


References ............................................................................................................................................. 155

Study Session Fifteen: Management by Objectives (MBO) ....................................................... 156

Introduction ........................................................................................................................................... 156


15.1. Meaning, Strengths and Weaknesses of Management by Objectives .......................................... 156

15.1.1. Meaning of Management by Objectives ............................................................................... 156

15.1.2. Strengths of Management by Objectives .............................................................................. 159

15.1.3. Weaknesses of Management by Objectives .......................................................................... 159

15.2. Activities in Management by Objectives (MBO) ........................................................................ 160



References ............................................................................................................................................. 164

Study Session Sixteen: Linear Programming ............................................................................. 165

Introduction ........................................................................................................................................... 165

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16.1. Meaning, Formulation, and Structureof Linear Programming ..................................................... 165

16.1.1. Meaning of Linear Programming .......................................................................................... 165

16.1.2. Formulation of the Linear Programming Problem ................................................................ 169

16.1.3. Structure of Linear Programming model .............................................................................. 170

16.2. Assumptions of Linear Programming Certainty .......................................................................... 171

16.2.1. General Mathematical Model of an LPP ............................................................................... 171

16.2.2. Guidelines for Formulating Linear Programming Model ..................................................... 172



References ............................................................................................................................................. 175

APPENDIX ........................................................................................................................................... 176

Notes to the Self-Assessment Questions (SAQs) for Session 1 ............................................................ 176









Notes to the Self-Assessment Questions (SAQs) for Session 10 .......................................................... 184







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Course Overview

Operations Management in Educational Practice (EME 302) is a course that has been

designed for your understanding of the concept. In defining Operations Management, it

deals with the application of scientific methods to the management and administration of

organizations such as: education, military, governmental, commercial, and industrial

processes. It has the basic aspects as operations research which attempts to provide those

who manage organized systems with an objective and quantitative basis for

decision.Operations research is not a science itself but rather the application of science to

the solution of managerial and administrative problems. You also need to note that this

course focuses on the performance of organized systems treated wholly. It is usually

concerned with systems in which human behaviour plays an important part. Operations

research was originally concerned with improving the operations of existing systems

rather than developing new ones.The subject matter consists of decisions that control the

operations of systems. Hence, it is concerned with how managerial decisions are and

should be made, how to acquire and process data and information required to make

decisions effectively, how to monitor decisions once they are implemented, and how to

organize the decision-making and decision-implementation process. Extensive use is

made of older disciplines such as logic, mathematics, andstatistics, as well as more recent

scientific developments such as communications theory, decision theory, cybernetics,

organization theory, the behavioral sciences, and general systems theory. Owing to the

complexities of the educational system, operation Management becomes an important

instrument for achieving efficiency in the system, hence the need for you to pay a rapt

attention as you go through the lectures in this course.

Course Objectives

This course is aimed at intimating you with the following:

1. The roots from which modern management sprang.

2. The principles which guide human behaviour and performance organizations with

special reference to educational institutions; and

3. Techniques which are available to the managers in the absence of an enabling

environment.

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Study Session One The Development of Modern Management

Principles

Expected duration: 1 week or 2 contact hours

Introduction

I’m welcoming you to the first lecture in EME 302 which will be focusing on how

modern management principles evolved. You would agree with me that we are all born in

an organisation (a family), we live in organisations (society) and at the same time work in

organizations (Business, Government, Army, School, College etc.). Each one of these

organisations is a group of persons working together to achieve some common

objectives. The organisations can be successful only when the efforts of various

individuals in the groups are integrated into team work. The central agency which

performs this task is known as management. Another interesting thing you need to note is

that management plays the same role in an organization as the brain does in human body.

All these activities are what sums up in the development of modern management

principles as it would be treated in this lecture.

Learning Outcomes for Study Session 1

At the end of this lecture, it is expected that you will be able to;

1.1. Define and use correctly keywords printed in bold. (SAQ 1.1.)

1.2. Examine a fair background of management practice as dating back to

creation of man. (SAQ 1.2)

1.3. Discuss briefly on how the study of management began.(SAQ 1.3)

1.4. Highlight the major activities that stemmed from modern management era.

(SAQ 1.4)

Key words: management and civilization

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1.1. The Origin and Evolution of Management

1.1.1. Origin of Management

As you would expect, many records and ideas relating to management date from

antiquity. Managementhas been practiced in some form or the other since the dawn of

civilisation. Ever since human beings began to live and work together in groups,

techniques of organisation and management were evolved. The pyramids of Egypt, the

Chinese civil service, the Roman Catholic Church, and military organisation offer good

examples of the application of management in ancient times. Kawtilya’s Arthashashtra,

the Bhagwat Gita, the Holy Bible and other epics contain referencesto the management of

public affairs. The early contributions to management thought came from Roman

Catholic Church, Military organizations and camera-lists. Thus, art of management has

ancient origins.

However, the science of management developed largely after the industrial Revolution

which established the factory system. Scientific Management movement laid the

foundations of Management as a science.Modern Management thought has developed

during several stages. These stages, approaches or theories to the study of Management

can be classified as follows;

1. Classical theory

2. Neo-classical theory

3. Modern Theory

Teachers are the only professionals who, like managers, are perceived on two

dimensions. To be an educational manager (manager and teacher) which therefore

subjects one to double scrutiny. In the early century, Frederick Taylor popularised the

word 'management' to describe what he had formerly and more accurately called 'work

study' or 'task study'. That aspect of management is referred to today as Industrial

Engineering. It is important for you to note that Management as a practice is not new as it

dates back to creation as every man organizes personal affairs to attain desired ends.

However, as societies became complex, there was need for harmonization of affairs to

achieve desired goals. The impact of the work of managers is felt in the development and

progress that is noticeable within the societies, groups, organizations, units, etc. This

applies to a family, a company or a nation. However, this can be linked to planning,

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organizing, deciding and implementing as Drucker (1974) observed that:

"Our society has become, within an incredibly short fifty year, a society of

institutions. It has become a pluralistic society in which every major social

task has been entrusted to large organizations - from producing economic

goods and services to health care, from social security and welfare to

education, from the search for new knowledge to the protection of the

natural environment ..., (and) it is the managers and management that

make institutions perform."

In addition to that, the degree of success attained by any society, group or organization

depends on the quality of it; administrators/managers. For management to make a

difference, three criteria must be fulfilled namely, goals, people and other resources.

While goals must be specified in quantifiable terms, resources must be limited to

necessitate efficiency of use and the people must not only be efficient and effective but

also reliable.

In-text Question

• What are those activities that offer good examples of the application of

management in ancient times?

• Such activities are; the pyramids of Egypt, the Chinese civil service, the Roman

Catholic Church, and military organization.

1.1.2. The Evolution of Management

This is another phase in this lecture which will be addressing the evolution of

Management. Management thinking and practice have evolved over the last century

because of increased understanding of human and organisational behaviour, the economic

climate and historical context and the changes in generations over time. However, if you

will be honest, you would observe that much of what we practice today is due to the

consulting industry playing on executives’ fears and aspirations by selling products and

services that cause more problems than solutions, and our own human weakness of

always looking for a quick fix even to very complex issues. It is time to rethink

Management. But before we do that, let’s take a look at the rear-view mirror and see how

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we got to where we are today with the aid of Fig 1.1.

Fig 1.1. The various trends in the Evolution of Management

Image source: http://www.bmmagazine.co.uk/in-business/advice/the-evolution-of-management/

From Fig 1.1.

1. Management Approach: the style of top management, ranging from:

a. Control (i.e. your line manager tells you what to do and how to do it).

b. Set Goals (i.e. your line manager sets goals and expectations, but you have more

freedom with regards to how you achieve them).

c. Inspire (i.e. your line manager gives you scope and freedom to innovate on both

the what and the how).

2. Approach to Innovation/Problem Solving: how leaders solve strategic problems and

develop new products and services. This ranged from:

a. Top Down (i.e. solutions are created and come from the top)

b. Top Down with Bottom Up Data (i.e. the rest of the organisation contributes

information and experiences, but solutions are still created at the top).

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c. Participatory (i.e. solutions are created collaboratively, and throughout the

organisational levels).

After a century of trying to control people, processes and information, we have come to a

point in organisational history where we need to recognise that what worked before just

simply is not enough anymore. Traditional Management is fine if you want compliance,

but if you want innovation and growth, you need to engage your people on a whole new

level. Top down control is a thing of the past. Succeeding in today’s environment

requires a management style that inspires and is participatory.

Now let us have a look at each of these successive periods;

a. 1910s-1940s: Management as Science

As seen in the top down level of Fig 1.1. management as Science was developed in the

early 19th century and focused on increasing productivity and efficiency through

standardisation, division of labour, centralisation and hierarchy. A very ‘top down’

management with strict control over people and processes dominated across industries.

b. 1950s-1960s: Functional Organisations

Due to growing and more complex organisations, the 1950’s and 1960’s as seen in Fig

1.1. saw the emergence of functional organisations and the Human Resource (HR)

movement. Managers began to understand the human factor in production and

productivity and tools such as goal setting, performance reviews and job descriptions

were born.

In-text Question

• You have observed that Bola who is your line manager at work always does the

following a tells you what to do and how to do it, sets goals and expectations, but

gives you scope and freedom to innovate on both the what and the how. What

approach do you think he is using?

• Clearly he is using the Management Approach: the style of top management, ranging

from: a. Control, goal setting and inspiration.

c. 1970s: Strategic Planning

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As we proceed in our discussion on evolution of management, another stage we need to

consider is the strategic planning of the 1970s. During this period, the focus was changed

from measuring function to resource allocation and tools like Strategic Planning (GE),

Growth Share Matrix (BCG) and SWOT were used to formalise strategic planning

processes. After several decades of ‘best practice’ and ‘one size fits all’ solutions,

academics began the development of contingency theories.

d. 1980s: Competitive Advantage

As the business environment grew increasingly competitive and connected, and with a

blooming management consultancy industry, Competitive Advantage became a priority

for organisations in the 1980’s. Tools like Total Quality Management (TQM), Six Sigma

and Lean were used to measure processes and improve productivity. Employees were

more involved by collecting data, but decisions were still made at the top, and goals were

used to manage people and maintain control.

e. 1990s: Process Optimisation

Benchmarking and business process reengineering became popular in the 1990’s, and by

the middle of the decade, 60% of Fortune 500 companies claimed to have plans for or

have already initiated such projects. TQM, Six Sigma and Lean remained popular and a

more holistic, organisation-wide approach and strategy implementation took the stage

with tools such as Strategy Maps and Balance Scorecards.

f. 2000s: Big Data

Looking at the present state as presented on Fig 1.1., this era is largely driven by the

consulting industry under the banner of Big Data, organisations in the 2000’s started to

focus on using technology for growth and value creation. Meanwhile, oversaturation of

existing market space drove to concepts such as Blue Ocean Strategy and Value

Innovation. You also need to note that globalisation, advances in technology, and

increased diversity have put organisational challenges into hyper drive. Despite the

inspirational stories we read about companies like Zappos, Innocent Drinks and Google,

the truth is that most of us are using out-dated management practices and failing to get

the most out of our people. How we lead our people and how we solve problems and

innovate, are some of the most important aspects of Management to get right. Through

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research, we have therefore looked specifically at two aspects of Management throughout

history, and how these will develop in the future.

Box 1.1. Stages in the Evolution of Management

The stages in the evolution of Management are;

1. Management as a science (1910s-1940s)

2. Functional organisations (1950s-1960s)

3. Strategic planning (1970s)

4. Competitive advantage (1980s)

5. Process optimization (1990s)

6. Big data (2000s)

1.2. Modern Management Era

1.2.1. Empirical School

As the heading suggests, this relates to the current Management Era. Ernest Dale, the

founder of this school, identified management as a study of experience. The intention of

studying experience is to draw generalizations and to develop means of teaching

experiences to other practitioners and students. As such, it is also called the case

approach or management experience approach. The unique features of this school are as

follows:

1. Managerial experience can be passed from one person to another.

2. Management can be taught best by the case method.

3. Theories of management can be developed by studying many experiences.

4. It is a study of success and failures in the application of management techniques

by managers in their practice.

Although the case method helps in developing diagnostic and analytical skills in

management students in classroom situations, it may not be useful in dynamic situations.

1.2.2. SocialSchool System

The social school system stems from the application of behavioural sciences to

management. Vilfredo Pareto, a sociologist is the real pioneer of the social system, i.e. a

system of cultural interrelationship. His ideas were later developed by Chester Barnard

who is regarded as the founding father of the social system school. For the adherents of

8

this school, an organization is essentially a socio-cultural system composed of groups of

people who work in cooperation with one another.

The broad features of this school are as follows:

1. An organization is a social system-a system of cultural relationship.

2. Relationships exist among the external and internal environments of the organization.

3. Cooperation among group members is necessary for the achievement of

organizational objectives.

4. For effective management, efforts should be made for establishing harmony between

the goals of the organization and the various groups functioning therein.

Barnard in his famous book, The Functions of an Executive, has identified the following

three types of functions of an executive. These are;

1. Maintenance of organizational communication through formal interaction.

2. Achieving organizational purpose by securing essential services from individuals in

the organization.

3. Formulation and definition of the organizational purpose.

Barnard has also given a new concept of authority known as the acceptance theory of

authority. In his opinion, a person will accept authority only when the following four

conditions are met simultaneously.

You can pause to consider these conditions;

1. He can understand the communication.

2. He believes that it is consistent with the organizational purpose.

3. He believes it to be compatible with his own personal interests.

4. He is mentally and physically able to comply with it.

The concept of informal organization is also a contribution of this school. The supporters

of this school advocate that efforts should be directed towards establishing harmony

between the goals of the organization and the goals of the groups and individual

members.

9

1.2.3. Decision Theory School

In another trend in modern management, Herbert Simon, Luther Gulick and Lyndall

Urwick are the major contributors to this school of thought. Decision theory concentrates

on rational approaches to decision making-the selection of a course of action from

various possible alternatives. The manager is a decision maker and the organization is a

decision-making unit. Hence the basic problem in managing is to make rational decisions.

The main features of this theory are as follows:

1. Decision making is central to the study of management.

2. The members of the organization are decision makers and problem solvers. Thus,

management is the study of the process of decision-making and the personalities

and behaviour of the decision makers.

3. The organizational effectiveness depends on the quality of decisions.

4. All factors affecting decision making are the subject matter of the study of

management.

Although the decision theory school contributes to the sharpening of managerial tools

especially for making suitable decisions in the organization, it does not take the total

view of management. As such, its scope is quite limited considering the requirements of

management. Decision-making is significant in every school of management. This

significant aspect cannot be denied, but management is more than mere decision making.

Activity 1.1. Time Allowed: 1hour

Take a moment to reflect on what you have learnt on modern management era and

highlight at least one significant activity under each era.

Activity 1.1. Feedback

1. The Empirical School: Studying experience to draw generalizations and to develop

means of teaching experiences to other practitioners and students.

2. The Social School System: This stems from the application of behavioural

sciences to management.

3. The Decision Theory School: This concentrates on rational approaches to decision

making-the selection of a course of action from various possible alternatives.

10

Summary of Session 1

In this Session, you have learned that;

1. Management has been practiced in some form or the other since the dawn of

civilisation. Ever since human beings began to live and work together in groups,

techniques of organisation and management were evolved.

2. The science of management developed largely after the industrial Revolution

which established the factory system.

3. Modern Management thought has developed during several stages. These stages or

approaches may be classified as; Classical theory; Neo-classical theory and

Modern Theory.

4. For management to make a difference, three criteria must be fulfilled namely,

goals, people and other resources. While goals must be specified in quantifiable

terms, resources must be limited to necessitate efficiency of use and the people

must not only be efficient and effective but also reliable.

5. Management thinking and practice have evolved over the last century because of

increased understanding of human and organisational behaviour, the economic

climate and historical context and the changes in generations over time.

6. In the evolution of management, there are stages involved. We have management

as a science (1910-1940); functional organisations (1950-1960); strategic planning

(1970s); competitive advantage (1980s); process optimization(1990s); and big data

(2000s).

7. In modern management era, we have; empirical school; social school system; and

decision theory school.

Self-Assessment Questions (SAQs) for Session 1

Now that you have completed this study session, you can assess how well you have

achieved its Learning Outcomes by answering these questions. You can check your

answers with the Notes on the Self-Assessment Questions at the end of this courseware.

SAQ 1.1. (tests learning outcome 1.1.)

Identify the TRUE/FALSE statements from the items provided below;

a. Managementhas been practiced in some form or the other since the dawn of

civilisation.

11

b. The science of management developed largely before the industrial Revolution

which established the factory system.


Describe the origin of management in relation to the creation of man.


In tracing the evolution of management, what major activity will you attribute to its

turnaround?


Based on what you have learnt in this lecture, what are the major activities dominating

the modern management era.

References

Bach, Stephen & Sisson, Keith (ed.) (2000); Personnel Management: A comprehensive

guide to theory and practice, Blackwell Business, Oxford.

Drucker, P. (1974): Management: Tasks, Responsibilities, Practices. New York: Harper

and Row.

George Jr, C.S. (1972): The History of Management Thought. Englewood Cliffs: Prentice

Hall

12

Study Session Two: Programme Evaluation and Review Technique

(PERT)


Introduction

Welcome to another lecture in EME 302. This lecture is meant to acquaint you with the

programme evaluation review technique(PERT). You need to understand that managers

can obtain a great deal of information by analyzing network diagrams of projects. For

example, network diagrams show the sequence of activities involved in a project. From

this sequence, managers can determine which activities must take place before others can

begin and which can occur independently of one another. Managers can also gain

valuable insight by examining paths other than the critical path. Since these paths require

less time to complete, they can often accommodate slippage without affecting the project

completion time. The difference between the length of a given path and the length of the

critical path is known as slack. Knowing where slack is located helps managers to

allocate scarce resources and direct their efforts to control activities. Your attention is

needed to assimilate the contents of this lecture.




2.2. Describe Program Evaluation Review Technique. (SAQ 2.2.)

2.3. Identify the steps involved in PERT planning.(SAQ 2.3.)

2.4. Outline project information input in PERT analysis. (SAQ 2.4)

Key words;evaluate, estimate, cost, time, planning, and coordinating.

2.1. Meaning and Analysis of Program Evaluation and Review Technique (PERT)

2.1.1. Meaning of Program Evaluation and Review Technique

Program Evaluation and Review Technique (PERT) is a technique adopted by

organizations to analyze and represent the activity in a project and to illustrate the flow of

13

events in a project. PERT is a method to evaluate and estimate the time required to

complete a task within deadlines. PERT serves as a management tool to analyze, define

and integrate events. PERT also illustrates the activities and interdependencies in a

project. The main goal of PERT is to reduce the cost and time needed to complete a

project.

This technique is a widely-used method for planning and coordinating large-scale

projects. As Harold Kerzner explained in his book Project Management, "PERT is

basically a management planning and control tool. It can be considered as a road map for

a program or project in which all the major elements (events) have been completely

identified, together with their corresponding interrelations'. You need to note that PERT

charts are often constructed from back to front because for many projects, the end date is

fixed and the contractor has front-end flexibility." A basic element of PERT-style

planning is to identify critical activities on which others depend. The technique is often

referred to as PERT/CPM, the CPM standing for "critical path method."

Let us briefly discuss the history of PERT, it was known to be developed during the

1950s through the efforts of the U.S. Navy and some of its contractors working on the

Polaris missile project. Concerned about the growing nuclear arsenal of the Soviet Union,

the U.S. government wanted to complete the Polaris project as quickly as possible. The

Navy used PERT to coordinate the efforts of some 3,000 contractors involved with the

project. Experts credited PERT with shortening the project duration by two years. Since

then, all government contractors have been required to use PERT or a similar project

analysis technique for all major government contracts. PERT was developed in 1950 by

the U.S. Navy during the Cold War and is intended for large projects, which are;

1. complex;

2. require a series of sequential tasks; and

3. performed in parallel with other projects.

Before we discuss PERT analysis, let us consider the steps in PERT planning.

Steps in PERT planning are;

14

• Identifying Tasks and Milestones: Every project involves a series of required

tasks. These tasks are listed in a table allowing additional information on sequence

and timing to be added later.

• Placing the Tasks in a Proper Sequence: The tasks are analyzed and placed in a

sequence to get the desired results.

• Network Diagramming: A network diagram is drawn using the activity sequence

data showing the sequence of serial and parallel activities.

• Time Estimating: This is the time required to carry out each activity, in three parts:

o Optimistic timing: The shortest time to complete an activity.

o Most likely timing: The completion time having the highest probability.

o Pessimistic timing: The longest time to complete an activity

• Critical Path Estimating: This determines the total time required to complete a

project.

Box 2.1. Program Evaluation and Review Technique

Please note these points;

• PERT is widely-used method for planning and coordinating large-scale projects.

• A basic element of PERT-style planning is to identify critical activities on which others depend.

• The technique is often referred to as PERT/CPM, the CPM standing for "critical path method."

• PERT was developed during the 1950s through the efforts of the U.S. Navy and some of its contractors

working on the Polaris missile project.

To round up this discussion on meaning of PERT, it is important for you to know that it

does not only determines the time to complete a specific software development activity,

but also determines the cost.PERT is a project managementtechnique that shows the time

taken by each component of a project, and the total time required for its completion.

PERT breaks down the project into events and activities, and lays down their proper

sequence, relationships, and duration in the form of a network. Lines connecting the

events are calledpaths, and the longest path resulting from connecting all events is called

the critical path. The length (duration) of the critical path is the duration of the project,

and any delay occurring along it delays the whole project. PERT is a schedulingtool, and

does not help in finding the best or the shortest way to complete a project.

15

In-text Question

• A team of school owners have come together to carry out a project they have

decided that the best way to accomplish this task is using PERT. So far, they have

carried out two steps in the entire process. They have identified tsks and

Milestones in a table. They have also gone ahead to place the tasks in a proper

sequence. Explain to them the next two steps under the PERT that they will have

to carry out.

o The next two steps are Network Diagramming and Time Estimating:

o When creating a network diagram they will use the activity sequence data

showing the sequence of serial and parallel activities. Timing estimating

involves the time required to carry out each activity, in three part.

2.1.2. Pert Analysis

We have come to another concept under PERT and this is PERT analysis. For complex

problems involving hundreds of activities, computers are used to create and analyze the

project networks. The project information input into the computer includes; the earliest

start time for each activity; earliest finish time for each activity; latest start time for each

activity; and latest finish time for each activity without delaying the project completion.

From these values, a computer algorithm can determine the expected project duration and

the activities located on the critical path. Managers can use this information to determine

where project time can be shortened by injecting additional resources, like workers or

equipment. Nonetheless, the solution of the algorithm is easy for the computer, but the

resulting information will only be as good as the estimates originally made. Thus, PERT

depends on good estimates and sometimes inspired guesses.

PERT offers several advantages and disadvantages to managers. Some of the advantages

are;

1. It forces them to organize and quantify project information and provides them with

a graphic display of the project.

2. It also helps them to identify which activities are critical to the project completion

time and should be watched closely, and which activities involve slack time and

can be delayed without affecting the project completion time.

16

Despite these advantages, you also need to note that this technique is posed with some

limitations which are;

1. Complex systems and plans, with many suppliers and channels of supply involved,

sometimes make it difficult to predict precisely what will happen.

2. The technique works best in well-understood projects where sufficient experience

exists to predict tasks accurately in advance.

Activity 2.1. Time Allowed: 1 hour

Get a cardboard paper and map out PERT planning steps in a hierarchical order.


Your sketch should follow this order; Identifying tasks and milestones; Placing the tasks

in a proper sequence; Network diagramming; Time estimating and Critical Path

estimating.

2.2. Critical Path Analysis, and Critical Path Method

As seen in Fig 2.1, the critical path analysis, method is a network map of a project,

tracing the work from a departure point to the completion objective.

Fig 2.1. Critical Path Analysis and Critical Path Method

Image source: http://www.ifm.eng.cam.ac.uk/research/dstools/critical-path-analysis/

Using Fig 2.1., any activity is represented by a line or arrow. This line or arrow connects

two events. Each event is a specific point in time, marking the beginning and/or end of an

activity.Artificial dummy events may be included to ensure that all activities have a

unique pair of event numbers. Also, network dummy activities, (shown by dashed line)

17

which take no time but indicate dependence. Dummies are particularly necessary in

computerised CPMs.The network may also include time/calendar information (including

boundaries) and hence deadline data.



1. Program Evaluation and Review Technique (PERT) is a technique adopted by

organizations to analyze and represent the activity in a project and to illustrate the

flow of events in a project.

2. PERT was developed during the 1950s through the efforts of the U.S. Navy and

some of its contractors working on the Polaris missile project.

3. PERT is a project managementtechnique that shows the time taken by each

component of a project, and the total time required for its completion.

4. PERT breaks down the project into events and activities, and lays down their

proper sequence, relationships, and duration in the form of a network. Lines

connecting the events are calledpaths, and the longest path resulting from

connecting all events is called the critical path.

5. The length (duration) of the critical path is the duration of the project, and any

delay occurring along it delays the whole project.

6. PERT is a schedulingtool, and does not help in finding the best or the shortest way

to complete a project.

7. PERT planning steps are: Identifying Tasks and Milestones, Placing the Tasks in a

Proper Sequence, Network Diagramming, Time Estimating and Critical Path

Estimating.






Fill in the blanks in the sentences provided below using the appropriate keywords.

a. PERT is a method to _________ and ________ the time required to complete a

task within deadlines.

18

b. The main goal of PERT is to reduce the _______ and _______ needed to complete

a project.

c. PERT is widely-used method for _________ and ________ large-scale projects.


Based on the knowledge you have gained in this lecture; how would you describe PERT

if you are called upon to do so?


As an expert in Educational Management, you have been given a project by the Ministry

of Education. In deciding on the technique to use, you have adopted PERT. What are the

steps that will guide you in having an effective planning for your chosen technique?


In the conduct of PERT analysis, make a list of project information inputs that are needed

for the analysis result.

References

Harold Kerzner 2003. Project Management: A Systems Approach to Planning,

Scheduling, and Controlling (8th Ed. ed.). Wiley. ISBN 0-471-22577-0.

Milosevic, Dragan Z. 2003. Project Management ToolBox: Tools and Techniques for the

Practicing Project Manager. Wiley. ISBN 978-0-471-20822-8.

Project Management Institute 2013. A Guide to the Project Management Body of

Knowledge (5th ed.). Project Management Institute. ISBN 978-1-935589-67-9.

19

Study Session Three: Critical Path Method (CPM)


Introduction

In the last lecture, critical path method was briefly mentioned and it is also a major

approach in PERT. However, this lecture is meant to dwell more on it. Before we go into

the content of this lecture, you need to know that project schedule plan is the main plan

included in any Project Management Plan. Project schedule is responsible for bringing

project time, cost and quality under control. Project schedule links resources, tasks and

time line together. Once a project manager has list of resources, work breakdown

structure (WBS) and effort estimates, it is good to go for planning project schedule.

Schedule network analysis helps project manager to prevent undesirable risks involved in

the project. This brings us to the business of this lecture which is the Critical Path

Method (CPM) and Critical Chain Project Management (CCPM) which are key elements

of schedule network analysis.

Learning Outcomes for StudySession 3



3.2. Describe the Critical Path Method used for projects. (SAQ 3.2)

3.3. Identify the 6 key steps in Critical Path Method. (SAQ 3.3.)

3.4. Highlight at least 3 merit and demerits each of CPM (SAQ 3.4)

3.5. Pinpoint the relevance of CCPM to CPM. (SAQ 3.5)

Key words; planning, scheduling, controlling, and float time

20

3.1. Meaning, Steps, and Merits, and Demerits of Critical Path Method (CPM)

3.1.1. Meaning of Critical Path Method

CPM is a method for planning, scheduling, and controlling projects.The critical path

method (CPM) is a step-by-step technique for process planning that defines critical and

non-critical tasks with the goal of preventing time-frame problems and process

bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that

interact in a complex manner.

In applying the CPM, there are several steps that can be summarized as follows:

a. define the required tasks and put them down in an ordered (sequenced) list.

b. create a flowchart or other diagram showing each task in relation to the others.

c. identify the critical and non-critical relationships (paths) among tasks.

d. determine the expected completion or execution time for each task.

e. locate or devise alternatives (backups) for the most critical paths.

CPM was developed in the 1950s by DuPont, and was first used in missile-defense

construction projects. Since that time, CPM has been adapted to other fields including

hardware and software product research and development. Various computer programs

are available to help project managers use the CPM.CPM is based on mathematical

calculations and it is used for scheduling project activities. The initial critical path

method was used for managing plant maintenance projects. Although the original method

was developed for construction work, this method can be used for any project where

there are interdependent activities. In the critical path method, the critical activities of a

program or a project are identified. These are the activities that have a direct impact on

the completion date of the project. The Critical Path Method (CPM) is a schedule

network analysis technique.Critical path determines the shortest time to complete the

project and it is the longest duration path through a network of tasks.

In-text Question

• A group of educational experts decided to come together to carry out a project in a

community the project is to last for 3months. The project centers on carrying out

adult education in a small rural community. They have decided to use CPM as

21

their approach to managing the project. Do you think this is a good choice of

method? State why

o Well, the CPM is not really the best choice of method for this project because,

CPM is ideally suited to projects consisting of numerous activities that interact

in a complex manner. There are several other approaches that can be adopted

to suit a project like this which we shall discuss as we go along.

Another important point which is crucial here is that critical tasks (activities) are tasks

(activities) on the critical path. To understand CPM further, the first thing is to

understand the nature of the task. Using the standard laid by Project Management Body

of Knowledge (PMBOK), every scheduled task can be defined by the following four

parameters.

a. Early Start (ES): Earliest possible point in time on which a task can start.

b. Early Finish (EF): Earliest possible point in time on which a task can finish.

c. Late Start (LS): Latest possible point in time on which a task can start.

d. Late Finish (LF): Latest possible point in time on which a task can finish.

Let us continue our discussion on The CPM. Early Start and finish dates are calculated by

means of Forward Pass; Late Start; and Late Finish dates are calculated by means of

Backward Pass. Many Tasks have some amount of buffer added to them referred as Slack

Time or Float. Float time is amount of time a task can sleep before it delays project

schedule. There are two common types of floats.

• Free Float: Amount of time a single task can be delayed without delaying the

early start of any successor task.

• Total Float: Amount of time a single task can be delayed without delaying project

completion.

Mathematically Float is defined as: Float = LS - ES or LF - EF. Critical path has zero or

negative Total Float. A project can have several critical paths.

In-text Question

• In the critical path method, how would you describe the critical activities of a

program or a project?

22

o These are the activities that have a direct impact on the completion date of the

project.

Fig 3.1 Shows an example of how the CPM is charted.

Figure 3.1: An example of CPM

Image source: http://www.pcoder.net/cpm-a-tough-example/#axzz4O62ADMCi

3.1.2. Key Steps in Critical Path Method

Let us have a look at how critical path method is used in practice with reference to Fig

3.1. The process of using critical path method in project planning phase has six steps. We

have;

Step 1: Activity specification

This is the first step in critical path method. You can use the Work Breakdown Structure

(WBS) to identify the activities involved in the project. This is the main input for the

critical path method. In activity specification, only the higher-level activities are selected

for critical path method. When detailed activities are used, the critical path method may

become too complex to manage and maintain.

23

Step 2: Activity sequence establishment

In this step, the correct activity sequence is established. For that, you need to ask three

questions for each task of your list.Pause to consider these questions;

i. Which tasks should take place before this task happens.

ii. Which tasks should be completed at the same time as this task.

iii. Which tasks should happen immediately after this task.

Step 3: Network diagram

Once the activity sequence is correctly identified, the network diagram can be drawn

(Figure 3.1). Although this diagram was drawn, there are several computer softwares,

such as Primavera that is being used for this purpose nowadays.

Step 4: Estimates for each activity

This could be a direct input from the WBS based estimation sheet. Most organisations

use 3-point estimation method or COCOMO based (function points based) estimation

methods for tasks estimation. You can use such estimation information for this step of the

process.

Step 5: Identification of the critical path

For this, you need to determine four parameters of each activity of the network. These

parameters are;

i. Earliest start time (ES) - The earliest time an activity can start once the previous

dependent activities are over.

ii. Earliest finish time (EF) - ES + activity duration.

iii. Latest finish time (LF) - The latest time an activity can finish without delaying the

project.

iv. Latest start time (LS) - LF - activity duration.

The float time for an activity is the time between the earliest (ES) and the latest (LS) start

time or between the earliest (EF) and latest (LF) finish times. During the float time, an

activity can be delayed without delaying the project finish date. The critical path is the

longest path of the network diagram. The activities in the critical path influence the

24

deadline of the project. If an activity of this path is delayed, the project will be delayed.

In case if the project management needs to accelerate the project, the times for critical

path activities should be reduced.

Step 6: Critical path diagram to show project progresses

This is known as the last step in CPM. Under this step, critical path diagram is a live

artifact. Therefore, this diagram should be updated with actual values once the task is

completed. This gives more realistic figure for the deadline and the project management

can know whether they are on track regarding the deliverables.

Box 3.1. Key steps in Critical Path Method

The key steps in critical path method are;

1. Activity specification

2. Activity sequence establishment

3. Network diagram

4. Estimates for each activity

5. Identification of the critical path; and

6. Critical path diagram to show project progresses.

3.1.3 Merits of Critical Path Method

Let us consider the following merits of Critical Path Method. We have;

i. Offers a visual representation of the project activities.

ii. Presents the time to complete the tasks and the overall project.

iii. Tracking of critical activities.

In the same vein, CPM is also helpful in:

a. Project Planning and control.

b. Time-cost trade-offs.

c. Cost-benefit analysis.

d. Contingency planning.

e. Reducing risk.

25

3.1.4 Demerits of Critical Path Method

Despite the advantages of CPM, it is also faced with the following limitations;

a. CPM assumes low uncertainty in schedule dates.

b. Does not consider resource dependencies.

c. Less efficient use of buffer time.

d. Less focus on non-critical tasks that can cause risk.

e. Based on only deterministic task duration.

f. Critical Path can change during execution.

Activity 3.1.

Select an educational project on your own and make a list of the steps you would embark

on in applying CPM to such project.


In applying the CPM, you need to take the following steps in your project;

a. Define the required tasks and put them down in an ordered (sequenced) list.

b. Create a flowchart or other diagram showing each task in relation to the others.

c. Identify the critical and non-critical relationships (paths) among tasks.

d. Determine the expected completion or execution time for each task.

e. Locate or devise alternatives (backups) for the most critical paths.

3.2. Critical Chain Project Management (CCPM)

You would recall in the introductory part of this lecture where CCPM was mentioned, it

is helpful in the sense that the limitations stated above for CPM could be surmounted by

Critical Chain Project Management (CCPM). According to Project Management Body of

Knowledge (PMBOK) in (PMI, 2001) Critical chain method is a schedule network

analysis technique that modifies the project schedule to account for limited resources. It

mixes deterministic and probabilistic approaches to schedule network analysis. The

critical chain concept was coined by Eliyahu Goldratt.

CCPM takes advantage of the best practices of:

• PMBOK: Planning and control processes.

• TOC (Theory of Constraints): Remove bottleneck to resolve constraints.

26

• Lean: Eliminate waste.

• Six Sigma: Reduce Variations.

CCPM can help to overcome following phenomenon. We have;

• Parkinson’s Law: Work expands to fill the available time.

• Student Syndrome: People start to work in full fledge only when deadline is near.

• Murphy's Law: What can go wrong will go wrong.

• Bad Multi-Tasking: Bad multitasking can delay start of the successor tasks.

You should also note that CCPM is based on:

- Resource constrained situations.

- Optimum use of Buffer (amount of time added to any task to prevent slippage of

schedule)

• Project Buffers (PB): Amount of buffer time at the end of the project.

• Feeding Buffers (FB): Amount of buffer time at the end of a sequence of tasks.

• Resource Buffers (RB): It is an alert that is used to indicate that resource is

needed to perform a task. This alert can be set few days before a resource is

needed.



1. CPM is a method for planning, scheduling, and controlling projects.

2. CPM was developed in the 1950s by DuPont, and was first used in missile-defense

construction projects. Since that time, CPM has been adapted to other fields

including hardware and software product research and development.

3. To understand CPM further, the first thing is to understand the nature of the task.

Using the standard laid by Project Management Body of Knowledge (PMBOK),

every scheduled task can be defined by the following four parameters: Early Start

(ES); Early Finish (EF); Late Start (LS); and Late Finish (LF).

4. Key Steps in Critical Path Method are; activity specification, activity sequence

establishment, network diagram, estimates for each activity; identification of the

critical path; and critical path diagram to show project progresses.

27

5. Float time is amount of time a task can sleep before it delays project schedule.

There are two common types of floats which are free float and total float.

6. Challenges faced by CPM can be tacked with CCPM.






In the statements provided below, fill in the blanks with the matching keywords.

i. CPM is a method for ______, _______ and _______projects.

ii. _________ is amount of time a task can sleep before it delays project schedule.


You have learnt in this lecture that CPM is a method for planning, scheduling, and

controlling projects. You can shed more light on this to show how relevant is it to any

significant project.


In adopting CPM for a project, what are the key steps you will take into consideration?


After taking the steps needed in SAQ 3.3., outline 3 things you think you would benefit

from using CPM and 3 things that might likely pose a challenge in its usage.


Based on what you have learnt in this lecture, identify the relevance of Critical Chain

Project Management (CCPM) to Critical Path Method (CPM).

28

References

Malakooti, B. 2013. Operations and Production Systems with Multiple Objectives. John

Wiley & Sons. ISBN 978-1-118-58537-5.

Project Management Institute 2013. A Guide to The Project Management Body Of

Knowledge (5th ed.). Project Management Institute. ISBN 978-1-935589-67-9.

Woolf, Murray B. 2012. CPM Mechanics: The Critical Path Method of Modeling Project

Execution Strategy. ICS-Publications. ISBN 978-0-9854091-0-4.

29

Study Session Four: Inventory Policy


Introduction

You are welcome back from our lecture on CPM. This lecture is meant to expose you to

inventory policy. Holding stock or inventory is a very expensive issue to organisation,

particularly where the goods are of high value. However even for small value items the

cost can be high if the quantities involved are large enough. The alternative to holding

stock is to operate a Just in Time (JIT) policy where stock arrives just as it is

needed.Hence the need for you to follow along in this lecture to get the most out of it.




4.2. Describe inventory policy with a highlight of methods best suited for an

organization. (SAQ 4.2)

4.3. Differentiate among the various types of inventory policies. (SAQ 4.3)

4.4. Identify at least 3 strategies in stock reduction. (SAQ 4.4.)

4.5. Determine order and storage costs for different order quantities with the

Economic Order Quality.

Key words; inventory, inventory policy, lead time, safety stocks, and stocks

4.1. Meaning, Methods, and Types of Inventory Policies

4.1.1. Meaning of Inventory Policy

Inventory is the physical stock of items held in any business for future productionor

sales. In a production shop the inventory may be in the form of raw materials. When the

itemsare in production process, we have the inventory as in-process inventory and at the

end of theproduction cycle inventory is in the form of finished goods. We shall be dealing

only with thefinished goods inventory.

30

There are very many inventory control policies which this lecture will look at. The most

important one is the Economic Order Quantity, or EOQ model. This is a model for

situations where there is little uncertainty in demand or delivery times. However, we will

also briefly consider a situation where there is some uncertainty in demand.

An inventory policy is a standard set of rules/boundaries and guidelines that provide the

framework for an organisation to make better informed and timely decisions on which

stock to purchase or manufacture, how much stock to purchase or manufacture and where

to store and distribute to customers. In the absence of any product knowledge or planning

parameters such as lead time, safety stocks, etc. A stockpolicy must be applied and

monitored regularly against future demand. By measuring the variability between

forecast demand and historical sales data by month, businesses will then be able to

implement the right planning parameter settings and improve their level investment in

stock.

Several stocking policies can be implemented to improve stock management

performance, these being: Reorder point; Min/Max; lot for lot; days of supply and item

location. The following components are essential for an effective inventory policy:

a. ABC Classification

b. Safety stock levels

c. The level of inventory at stocking points or locations

d. Number of warehouses or nodes

e. Number of stocking points or nodes

f. Order quantity and order frequency

g. Replenishment quantity and replenishment frequency

h. Lead time from suppliers

i. Stock obsolescence

j. Slow moving stock

k. Inventory Procedures

31

4.1.2. Inventory Methods best for Organisation

At this point, let us consider some of the inventory methods that are well suited for an

organization. We have;

1. Reorder Point - Fixed Replenishment point or fixed replenishment quantity is

used when the stock falls below a certain point which then triggers an order

release.

2. Min/Max is used when stock falls to or below the minimum stock levels which

triggers a replenishment or reorder quantity equal to the maximum level. Carton

rounding can apply with the reorder quantity to make the warehouse operation

more efficient with handling.

3. Lot for Lot or demand flow generates a new replenishment order for the same

quantity at the time the previous order arrives to your facility or operation.

4. Days of Supply (Historical demand based) is like the min / max above, however

this method relies on average daily sales using historical demand to calculate an

order quantity for a number of days’ supply.

5. Days of Supply (Forecast demand based) is like min / max above, however this

method relies on average daily sales using forecast demand to calculate an order

quantity for a number of days’ supply.

6. Item location which is based on the multi echelon optimisation approach that

incorporates greater emphasis on all elements of the entire end to end supply chain

where there is variability in demand, projections or service.

In-text Question

• During this lecture, you learnt that several stocking policies can be implemented to

improve stock management performance. In an educational organization, when

stock falls to or below the minimum stock levels which triggers a replenishment or

reorder quantity equal to the maximum level. What inventory method is this?

o Min/Max.

4.1.3. Types of Inventory Policies

1. Demand Flow: In Demand Flow policy, there is no strict inventory control.

Instead, every order that arrives at this site for this product will generate a request

for a replenishment order for the exact same quantity. All requests are driven by the

actual demand quantities received at this site for this product. Therefore, the

32

Reorder Point and Reorder/Order Up to Quantity fields are not used in this policy.

However, there is need to establish an initial inventory level. By establishing an

initial inventory level, the site will always replenish exactly what was consumed by

actual demand, whether it was filled immediately, or left unfilled as a back order.

Though it seems straightforward, Demand Flow can exhibit complex behaviour,

especially when combined with Review Period. Defining a Review Period can

produce batching. Batching occurs when the replenishment orders accumulate

during the Review Period ends and are then filled.

2. Days of Supply, Demand-Based Days of Supply (DOS): Demand is similar to an

s,S inventory policy except that the parameters for minimum and maximum levels

are specified in number of days rather than product quantities. This policy

computes the daily average of product by looking back at the actual demand. How

far back to look is given by the DOS window field.

3. Days of Supply, Forecast-Based DOS: - Forecast is similar to an s,S inventory

policy except that the parameters for minimum and maximum levels are specified

in number of days rather than product quantities. This policy computes the daily

average of product by looking forward and using forecasted demand. How far

forward to look is given by the DOS window field. Forecast quantities must be

entered in the forecast table. In short, DOS-Demand establishes inventory based on

what has happened; DOS-Forecast establishes inventory based on what you expect

to happen.

4. R, Q Targets: The” R, Q Targets” inventory policy allows the user to change the

Reorder Point (R) and Reorder Quantity (Q) based on a period designated by the

user (year, quarter, month, day, etc.)When using the R, Q Targets inventory policy,

the quantities and period are specified in the Forecasts input table. In other words,

R, Q is a fixed replenishment point/fixed replenishment quantity inventory policy.

When the inventory level on-hand falls below a certain replenishment point, R, the

site will generate a replenishment order for a certain quantity, Q, of this product.

When using this policy, the Reorder Point field is set as the trigger level. The

Reorder/Order Up to Quantity field will be the exact number of units reordered.

5. s,S Targets: The regular s,S policy is a minimum/maximum inventory policy that

says that when the inventory on-hand falls below a certain minimum s, the site will

33

request for a replenishment order that will restore the on-hand inventory to a

maximum number, S. When using this policy, the Reorder Point field is the

minimum, or trigger level. The Reorder/Order Up to Quantity field is the maximum,

or the number to which the inventory level is restored.”s,S Targets” inventory policy

is just like the regular s,S policy except that you can specify Reorder Point (s) and

Order up to Quantity (S) for certain periods. You can define the period as days,

weeks, months, years, quarters etc. When using the s,S Targets inventory policy, the

quantities and period are specified in the Forecasts input table.The main difference

between s,S and R,Q is that the s,S takes into account exactly how far below the

reorder level the inventory is when the request for replenishment is generated. The

behaviour of the system depends on how often inventory is checked. So, it is

important to select the appropriate Review Period.

In-text Question

• Inventory Policies are important as they provide organisations and businesses with

the needed guideline to manage their inventory. Can you identify and match where

each inventory policy goes in the table below (Note that the table is mixed up you

have to match a policy to where it fits rightly. The first one has been done for you)

Description Inventory policy

In this policy, every order that arrives at this site for this product

will generate a request for a replenishment order for the exact

same quantity.

Forecast-Based DOS

This policy computes the daily average of product by looking

back at the actual demand.

s,S Targets

This policy computes the daily average of product by looking

forward and using forecasted demand.

Demand-Based Days of

Supply

This inventory policy allows the user to change the Reorder Point

(R) and Reorder Quantity (Q) based on a period designated by

the user (year, quarter, month, day, etc.)

Demand order

This policy that says that when the inventory on-hand falls below

a certain minimum s, the site will request for a replenishment

order that will restore the on-hand inventory to a maximum

number, S.

R, Q Targets

(Remember your task is to match the right inventory policy to it’s correct description the first one has

been done for you)

34

4.2. Meaning of Stock and Types

A stockis a type of security that signifies ownership in a corporation and represents a

claim on part of the corporation's assets and earnings. The Physical stock an organisation

may store as an asset is in the following forms:

i. Raw Materials

ii. Work in Process

iii. Finished Goods

iv. Maintenance, Repair and Operating (MRO)

As we proceed in this lecture, you also need to learn about stock reduction.

4.2.1. Stock Reduction

Organisations must strive towards reducing stock levels on a regular basis and can adopt

several strategies to achieve the expected objective. These strategies are;

1. Direct deliveries of purchase products in raw material or assembly form can be

delivered to a manufacturing line or processing point and avoid double handling

through a warehouse process.

2. Just in time production by only making what is required resulting in lower WIP

inventory.

3. Direct Deliveries of finished goods by shipping direct from your source of supply

and avoiding your logistics network, if possible.

Box 4.1. Inventory Methods best for Organisations

The inventory methods best for organisations are;

1. Reorder point

2. Min/Max

3. Lot for lot

4. Days of supply

5. Item location

4.2.2. Why the need for Stock?

There are several core reasons why organisations need to keep a level of stock across

their operations. However, the challenge is to understand the total cost of your supply

35

chain and the impact stock can have to a range of functions and facilities for operation

within organisation. Depending upon the nature of your business or the strategy your

organisation is adopting to meet the needs of the market, understanding the total supply

chain cost will enable you to make better decisions on expanding your organisation or

scaling down the number of sites or warehouses and still achieve the right customer

service level at the right cost for your business.

At this point, let us consider some reasons for keeping stock:

i. Improve customer service

ii. Economies of scale for purchasing

iii. Transportation costs

iv. Variation in consumer demand

v. Economic conditions, strikes etc.

There are many costs associated with holding (or not holding) stock. Some of these are:

i. warehouse costs

ii. money tied up in stock (interest charges)

iii. damage while in storage

iv. deterioration while in storage

v. obsolescence

vi. ordering costs

vii. delivery costs

viii. cost of any ‘stock-outs’.

Warehouse costs include things like rental charges, heating and wages. Money that is tied

up in stock could be earning money (or reducing overdraft charges). A certain proportion

of goods will be damaged while in the warehouse or may be stolen and certain products

deteriorate (for example, food), while other items may become obsolete if stored too long

(last year’s computer will be worth less than the latest version). In addition to the costs

directly associated with the holding of stock, there is also the cost of ordering and

delivery. One of the models used when dealing with stock is the EOQ Model and it will

be discussed shortly.

36

4.3. Economic Order Quantity (EOQ) model

This is one off the models used when dealing with stock. The assumptions that must be

made before this model can be used are as follows:

i. Demand is known and constant

ii. Lead time is constant

iii. Only one item is involved

iv. Stock is monitored on a continuous basis and an order is made when the stock

v. level reaches a re-order point

vi. When an order arrives, the stock level is replenished instantaneously

vii. Stock-outs do not occur.

Fig 4.1. Economic Order Quantity Model

The Figure 4.1 above may help you picture the general problem. An order quantity Q

arrives and is used up at a constant rate, until the stock level reaches zero, at which point

a new order arrives. For small values of Q more frequent ordering will be necessary and

hence order costs will be high, while large values of Q will increase the quantity in store

and therefore increase the storage costs. The problem is to determine the value of Q that

minimizes the sum of the order costs and storage costs.

If the cost of placing an order is represented by the letter C, then the total order cost is

simply the number of orders multiplied by C. If D is the demand over a specified period,

then the number of orders must be:

Stock Level

Q2

Q Demand Steady

Instantaneously

Replenish

Average Stock Level

New order Arrives Time

37

��

and the order cost is:

� ∗��

To calculate the storage cost it is assumed that the cost of holding one unit in stock for a

specified period is known. This cost is represented by h. As the amount in stock varies we

need to calculate the average stock level, and from Figure 4.1 you can see that this must

be:

�2

Hence the storage cost is:

ℎ ∗�2

Example 1

Imagine that you work for a Computer Center of an Educational institution and you have

been asked to decide on the best inventory control policy for the computer sets. You are

told that the demand is fairly constant at 5000 units p.a. and it costs N14.40 to place an

order. You are also told that the storage cost of holding one unit of the set per annum is

N10. To investigate how inventory costs vary with order size, you decide to work out the

order and storage costs for different order quantities.

38

Solution:

This means that the two costs are equal at the optimum. This is generally true, so:

� ∗ �

= ℎ ∗ �

Multiplying both sides by 2Q and rearranging gives you:

Q2 = 2� ∗ ��

That is: (2��/ℎ)

This formula is known as the economic order quantity (EOQ), and in words it means:

(2 ∗ �� ∗ ��/ℎ�� )

All you should do to use this formula is simply to substitute the values for C, D, and h.

C = Cost per Order

D = Demand

h = holding cost per unit

Use the EOQ formula to calculate the value of Q that minimizes the sum of the ordering and holding

costs. What is this cost?

For an order size of 20:

Order cost = � ∗ �

= 14.4 ∗ $%%%�%

= N3600 p.a

Storage = h ∗ �

= 10 ∗ �%�

= N100 p.a

Total cost = N3600 + N100

= N3700 p.a

39

Solution:

Time between orders and the re-order level in the Computer center showed that the

number of orders per year at the EOQ of 120 is

= $%%%&�%

= 41.67

If the institution works for 300 days a year, this means that the time between orders should be

'%%(&.)*

= 7.2 days on average

From Figure 4.1 you will see that a new order arrives just as the stock level reaches zero.

For this to happen, an order must have been placed sometime previously. In practice an

order is placed when the stock reaches a predetermined level. To calculate this level all

that is required is the lead (or delivery) time. If the lead time is, say, 4 days, then during

this time a certain amount of stock will have been sold. With a demand of 5000 a year,

the daily sales will be;

5000 = 16.7 on average

300

Q = 2 ∗ 14.4 ∗ 5000/10)

Q = √14400

Q = 2 ∗ 14.4 ∗ 5000/10)

Q = 120

and the cost is N1200 p. a.

40

In 4 days, 66.8 or about 67 games will be sold, and therefore an order will need to be

placed when the stock is down to this level. This re-order level is shown in Figure 4.2.

Fig 4.2. Reorder level in EOQ


In this lecture, you have learned that;

1. Inventory is the physical stock of items held in any business for future

productionor sales. In a production shop the inventory may be in the form of raw

materials.

2. An inventory policy is a standard set of rules/boundaries and guidelines that

provide the framework for an organisation to make better informed and timely

decisions on which stock to purchase or manufacture, how much stock to purchase

or manufacture and where to store and distribute to customers.

3. Several stocking policies can be implemented to improve stock management

performance, these being: Reorder point; Min/Max; lot for lot; days of supply and

item location.

4. The physical stock an organisation may store as an asset is in the following forms:

raw materials; work in process; finished goods; maintenance, repair and Operating

(MRO).

5. Some reasons for keeping stock are; improve customer service; economies of scale

for purchasing; transportation costs; variation in consumer demand and economic

conditions, strikes etc.

(Lead time)

Reorder Level

Stock Level

Q

67

4 4

(Average time)

Days

7.2

41

6. The Economic Order Quantity (EOQ) model minimizes the stock holding cost

plus the ordering cost. If discounts are given for large orders, this can be cheaper

than ordering the EOQ. Most inventory systems have a buffer stock to avoid

running out of stock.

7. Economic Order Quantity (EOQ) modelassumptions are as follows; demand is

known and constant; lead time is constant; only one item is involved; stock is

monitored on a continuous basis and an order is made when the stock; level

reaches a re-order point; when an order arrives; the stock level is replenished

instantaneously and stock-outs do not occur.






Identify the TRUE/FALSE statements in the list provided below.

a. Inventory is the physical stock of items held in any business for current

productionor sales.

b. An inventory policy is a standard set of rules/boundaries and guidelines that

provide the framework for an organisation to make better informed and timely

decisions on which stock to purchase or manufacture, how much stock to

purchase or manufacture and where to store and distribute to customers.

c. A stockis a type of security that signifies ownership in a corporation and

represents a claim on part of the corporation's assets and earnings.


Based on your understanding of this lecture, how would you describe inventory policies

and the methods best suited for an organization?


What major differences do you think exist between Days of Supply, Demand-Based Days

of Supply (DOS) and Days of Supply, Forecast-Based DOS.

42


You learnt in this lecture that organisations must strive towards reducing stock on regular

basis, what are some of the strategies that can be deployed in doing this?

References

Andrew C. and John L., 2010 "Economic Theory and the World of Practice: A

Celebration of the (S,s) Model", Journal of Economic Perspectives, Winter, V 24,

N 1

Malakooti, B. 2013. Operations and Production Systems with Multiple Objectives. John

Wiley & Sons. ISBN 978-1-118-58537-5

43

Study Session Five: Equipment Replacement Policies

(Individual and Mass/Group Techniques for

Non-Durable Items, Npv and Least Cost

Methods for Durable Items)

Expected duration: 2 weeks or 2 contact hours

Introduction

Welcome back to EME 302 class. This is another phase in the course where we shall be

discussing on equipment replacement policies. It is good for you to note that if any

equipment or machine is used for a long period, due to wear and tear, the item tends to

worsen. A remedial action to bring the item or equipment to the original level is desired.

Then the need for replacement becomes necessary. This need may be caused by a loss of

efficiency in a situation leading to economic decline. By passing away of time, the parts

of an item are being worn out and the cost of maintenance and operation is bound to

increase year after year. The resale value of the item goes on diminishing with the

passage of time. The depreciation of the original equipment is a factor, which is

responsible not to favour replacement because the capital is being spread over a long time

leading to a lower average cost. Thus, there exists an economic trade-off between

increasing and decreasing cost functions. So, what do we do in this situation? we strike a

balance between the two opposing costs with the aim of obtaining a minimum cost. The

problem of replacement is to determine the appropriate time at which a remedial action

should be taken which minimizes some measure of effectiveness. Another factor namely

technical and/or economic obsolescence may force us for replacement. This and more

would form the framework of this lecture. As usual I urge you to pay utmost attention.




5.2. Explain the term “equipment replacement policies”.(SAQ 5.1.)

44

5.3. Identify items regarded as deteriorating and non- deteriorating.(SAQ 5.2)

5.4. Discuss the Net Present Value and its usage is decision-making. (SAQ 5.3.)

Key words; replacement theory, replacement, replacement policy, replacement

models, and hurdle rate.

5.1. Replacement Theory, Maintenance, and Models in Operation Research

5.1.1. Replacement Theory inOperation Research

Machine replacement problem can be linked to operation research and management

science (Nahmias, 1997). It could be regarded as Renewal theory which is a useful tool in

modeling many systems. The quantity-based replacement policy and time-based

replacement policy for a single machine problem are reported. These two kinds of

policies have been applied to inventory management problems. In a quantity-based

replacement policy, a machine is replaced when an accumulated product of size q is

produced. In this model, one must determine the optimal production size q. While in a

time-based replacement policy, a machine is replaced in every period of T. For this

model, one must determine the optimal replacement period T in each production cycle.

Replacement theory is generally concerned with theproblem of replacement of

machines, bulbs and men due to deteriorating efficiency, failure or break down.

Replacement is usually carried out under the following situations:

• When existing items have outlived their effective lives and it may not be

economical to continue with them anymore.

• When the items might have been destroyed either by accidents or otherwise.

Take note that the above replacement situations may be categorized into the following

four categories. These categories are;

• Replacement of items that deteriorated with time.

• Replacement of items which did not deteriorate but failed completely after certain

use.

• Replacement of an equipment that became out of date due to new development.

• Gradual diminishing of the existing working staff in an organization due to

retirement, death etc.

45

The Replacement Theory in Operations Research is used in the decision-making process

of replacing a used equipment with a substitute; mostly a new equipment of better usage.

The replacement might be necessary due to the deteriorating property or failure or

breakdown of equipment.

The ‘Replacement Theory’ is used in the cases like; existing items have out-lived, or it

may not be economical anymore to continue with them, or the items might have been

destroyed either by accident or otherwise. The above discussed situations can be solved

mathematically and categorised on some basis which may be called as Replacement

Models. Items that deteriorate with time e.g. machine tools, vehicles, equipment

buildings etc.

A replacement policy is a specification of “keep” or “replace” actions, one for each

period. Two simple examples are the policy of replacing the equipment every period and

the policy of keeping the first machine until the end of the period N. An optimal policy is

a policy that achieves the smallest total net cost of ownership over the entire planning

horizon and it has the property that whatever the initial state and initial decision are, the

remaining decisions must constitute an optimal policy with regard the state resulting from

the first decision. In practice, the replacement problem can be easily addressed using

dynamic programming and Markov decision processes.

In-text Question

• Dele works in the audit department of a school. He notices that the chairs in the

staff room have begun to squeak and one of the teachers had a minor accident in

the school as the legs of the chair she sat on gave way during a general staff

meeting. He immediately called for the inventory list to notice that the chairs used

in the staff room were purchased 7years ago. His immediate request school

management to change these set of furniture was instantly granted. What category

of replacement will this fall into?

o For the answer, see the note on replacement categories above.

46

Box 5.1. Replacement Theory

Replacement is usually carried out under the following situations:

1. When existing items have outlived their effective lives and it may not be economical to continue with

them anymore.

2. When the items might have been destroyed either by accidents or otherwise.

5.1.2. Replacement and Maintenance

Replacement problems involve items that degenerate with use or with the passage of time

and those that fail after a certain amount of use or time. Items that deteriorate are likely to

be large and costly (e.g., machine tools, trucks, ships, and home appliances). Non-

deteriorating items tend to be small and relatively inexpensive (e.g., light bulbs, vacuum

tubes, ink cartridges). The longer a deteriorating item is operated the more maintenance it

requires to maintain efficiency. Furthermore, the longer such an item is kept the less is its

resale value and the more likely it is to be made obsolete by new equipment. If the item is

replaced frequently, however, investment costs increase. Thus, the problem is to

determine when to replace such items and how much maintenance (particularly

preventive) to perform so that the sum of the operating, maintenance, and investment

costs is minimized.

In the case of non-deteriorating items the problem involves determining whether to

replace them as a group or to replace individuals as they fail. Though group replacement

is wasteful, labour cost of replacements is greater when done singly; for example, the

light bulbs in a large subway system may be replaced in groups to save labour.

Replacement problems that involve minimizing the costs of items, failures, and the

replacement labour are solvable either by numerical analysis or simulation.The “items”

involved in replacement problems may be people. If so, maintenance can be interpreted

as training or improvements in salary, status, or fringe benefits. Failure can be interpreted

as departure, and investment as recruiting, hiring, and initial training costs. There are

many additional complexities in such cases; for example, the effect of one person’s

resigning or being promoted on the behaviour of others. Such controllable aspects of the

environment as location of work and working hours can have a considerable effect on

productivity and failure rates. In problems of this type, the inputs of the behavioral

sciences are particularly useful.

47

In- text Question

• How do you think replacement problems that involve minimizing the cost of items, failures, and

the replacement labour can be solved?

• That is best done by numerical analysis or simulation.

5.1.3. Reasons for Equipment Replacement

The factors necessitating the replacement of machines and equipment can broadly be

classified into the following two categories:

1. Technical factors.

2. Cost factors

Box 5.2. Replacement and maintenance

Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships,

and home appliances). Non-deteriorating items tend to be small and relatively

inexpensive (e.g., light bulbs, vacuum tubes, ink cartridges). The longer a deteriorating

item is operated the more maintenance it requires to maintain efficiency.

The Technical factorsresponsible for equipment replacement as discussed earlier are;

1. Wear and tear of equipment

2. Obsolescence caused by new invention.

3. Unsuitability of existing equipment due to:

a. Size of the work

b. Speed of operation

c. Degree of accuracy

d. Rate of output

e. Need for power

4. Automation combining two or more processes.

5. To eliminate the slack time of some machines through line balancing.

6. Reduced safety as compared to new equipment.

7. Additional operations by the new machine.

48

8. Reduction or elimination of manual operation and the resultant hazards by the new

machine.

9. Easy, quick and convenient setting-up and operation of new machine.

10. Reliability of performance

On the other hand, we also have Cost Factors such as;

1. High repair cost of existing machine

2. Reduction in the spoiled work by the new machine.

3. More output at faster rate from new machine.

4. Combination of two or more existing operations into one by a new machine.

5. Reduction in the labor cost caused by the reduced number and lower type of

operators.

6. Consumption of less power of fuel by the new machine.

7. Lesser space required by the new machine.

8. Improvement in the quality with the use of new machine.

9. Flexibility in the use of the new machine for other types of operations.

10. Probable economic life of the new machine.

11. Reduction in the cost of jigs, tools, fixtures, etc.using new machine.

12. Size of the investment required in new machine.

It should be noted that there are certain intangible factors which are incidental to

equipment replacement. They are;

1. Displacement of employees caused by replacements and

2. Introduction of hazards by new equipment.

Being intangible factors they are not measured in monetary value and hence are not

included in the replacement analysis. They involve sociological and humanitarian

considerations with far reaching influences. A careful consideration based on the above

factors must be made before implementing equipment replacement. It is prudent to defer

replacement if the information is on cards that advanced model of the same machine is

developed and is available in the very near future. This enables the replacement by state

of the art version of the machine and the replacement is more justified for the capital

invested.

49

5.1.4. Models in Replacement and Maintenance

As we proceed in this lecture, let us consider the models used in replacement and

maintenance. These are;

Model 1: “Replacement of items whose maintenance Cost increases with time and the

value of the money remains constant during the period”

Model 2: “Replacement of items whose maintenance cost increases with time and value

of money also changes with time”.

Model 3: “Group Replacement policy”

From model 1: Notation and symbols

C - Purchase cost of the machinery or equipment

S - Salvage value or resale value or scrap value of the machinery or equipment

Tc - total cost increased on the item or equipment during the period y

Then,

Tc = C + m(Y) – S

Where M(Y) is the cumulative maintenance cost in that period.

G(Y) Average cost incurred on the equipment or item during the period.

G(Y) = Tc / y

Example 5.1

The cost of the machine is N6100 and its scrap value is Rs 100 at the end of every year. The Maintenance

Cost found from experience are as follows:

Year 1 2 3 4 5 6 7 8

M.C 100 250 400 600 900 1200 1600 2000

When should the machine be replaced?

Table 5.1: Example 5.1

50

Solution to Example 5.1:

Given: C = 6100 and S = 100

Year (Y) Maintenance Cumulative

Maintenance cost

m(y)

Total Cost

C-S + m(y)

Average Cost

g(y)

1 100 100 6100 6100

2 250 350 6350 3175

3 400 750 6750 2250

4 600 1350 7350 1837.5

5 900 2250 8250 1650

6 1200 3450 9450 1575

7 1600 5050 11050 1578.5

8 2000 7050 13050 1631.25

Table 5.2: Solution to Example 5.1

It is clear from table 5.2 analysis that the machine needs to be replaced at the end of 6th

year or at the beginning of 7th year because the maintenance cost of 7th year is more than

the average cost of the machine i.e. 1578.5 > 1575.5.

5.2. Net Present Value (Npv) and Least Cost Methods

5.2.1. Net Present Value

The NPV is the value obtained by discounting all cash outflows and inflows of an

investment opportunity by a chosen rate of return. The NVP valuation method requires

estimating the size and timing of all the incremental cash flows from the project. These

future cash flows are then discounted to determine their present value. If we treat

outflows of the projects as negative and inflows as positive, the NPV of the project is the

sum of the PVs of all flows that arise because of doing the project. The NPV decision

rule is to accept all positive NPV projects in an unconstrained environment, or if projects

are mutually exclusive, accept the one with the highest NPV. If NPV is negative, the

project is not financially viable. If the NPV is zero, the project just breaks even.

The NPV is greatly affected by the discount rate, so, selecting the proper rate (sometimes

called the hurdle rate) is critical to making the right decision. The hurdle rate is the

minimum acceptable return on an investment. It should reflect the riskiness of the

investment, typically measured by the volatility of cash flows, and must consider the

51

financing mix. Managers may use models such as the CAPM or the APT to estimate a

discount rate appropriate for each particular project, and use the weighted average cost of

capital (WACC) to reflect the financing mix selected. A common practice in choosing a

discount rate for a project is to apply a WACC that applies to the entire firm, but a higher

discount rate may be more appropriate when a project's risk is higher than the risk of the

firm.

5.2.2. Advantages of Net Present Value (NPV)

At this point, let us consider some of the advantages of Net Present Value. These are;

1. It considers the time value of money.

2. It is an absolute measure of return.

3. It uses cash flows and not profits.

4. It considers the whole life of the project.

5. It leads to selection of project that increase shareholders’ wealth.

5.2.3. Disadvantages of NPV

Here are some of the disadvantages of NPV. We have;

1. It is difficult to explain to managers

2. It requires knowledge of the cost of capital

3. It is relatively difficult to calculate (compare to ARR and Payback period)

In-text Question

• The NVP valuation method requires estimating the size and timing of all the

decremental cash flows from the project. Do you support this statement?

• No, NPV only monitors incremental cash flows from the project.

Example 5.2

Shaw Limited is considering a capital investment costing 180,000. The estimated cash

flows are given as follows:

Year Cash flow

1 90,000

2 110,000

3 60,000

4 40,000

Table 5.3: Example 5.2

52

The company’s cost of capital is 15%. What is the NPV of the project, and should it be

undertaken?

Solution to example 5.2

Year Cash flow Discounting factor @

15%

Present Value

0 (180,000) 1.000 (180,000)

1 90,000 0.870 78,300

2 110,000 0.756 83,160

3 60,000 0.658 39,480

4 40,000 0.572 22,880

Net Present Value 43,820

Table 5.4: Solution to Example 5.2

Since the NPV is positive, the project should be undertaken.

5.2.4.Least Cost Method

In least cost method, you should start by giving allocations from the minimum cost in the

matrix. It means that cell for which cost is minimum is given allocation first. Then

allocation is given in next minimum cost and so on. It means lower cost cells are given

priority over higher cost cells.Other steps are;

STEP 1: Determine the least cost among all the rows of the transportation table.

STEP 2: Identify the row and allocate the maximum feasible quantity in the cell

corresponding to the least cost in the row. Then eliminate that row (column)

when an allocation is made.

STEP 3: Repeat steps 1 and 2 for the reduced transportation table until all the

available quantities aredistributed to the required places. If the minimum cost

is not unique, the tie can be broken arbitrarily.

To illustrate, consider this example;

53

Example 5.3

Origin P Q R Supply

A 5 7 8 70

B 4 4 6 30 0

C 6 7 7 50

Demand 65 42 43

55

Table 5.5: Destination

We examine the rows A, B and C, 4 is the least

cost element in the cell (B,P) and (B, Q) and the

tie can be broken arbitrarily. Select (B, P).The

origin B can supply 30 items to P and thus origin

B is exhausted. P still requires 35 more units.

Hence, deleting the row B, we have the reduced

matrix as in the table 5.6.

Origin P Q R Supply

A 35

5

7

8

70

35

C 6 7 7 50

Demand 35 42 43

0


In the reduced matrix (table 5.6) we observe that

5 is the least element in the cell (A, P) and

examine the supply at A and demand at P. The

destination P requires 35 items and this

requirement is satisfied from A so that the

column P is deleted next. So, we have the reduce

matrix as in table 5.7.

Origin Q R Supply

A 35

7

8

35

0

C 7 7 50

Demand 35 43

7


In the reduced matrix (table 5.7) we choose 7 as

least element corresponding to the cell (A. Q).

Wesupply 35 units from A to Q so have the

reduced matrix in table 5.8.

Origin Q R Supply

A 7

7

43

8

50

0

Demand 7 43

0 0


Now, only one row is left behind. Hence, we

allow 7 items from C to Q and 43 items C to R.

We now have the allotment as per the least cost

method as shown in the table 5.9

Origin P Q R Supply

A 35 35 70

B 30 30

C 7 43 50

Demand 65 42 43


The cost of the allocation by the least cost

method is 35 × 5 + 35 × 7 + 30 × 4 + 7 × 7 + 43

× 7 = N890

54



1. Replacement theory is generally concerned with theproblem of replacement of


2. Replacement is usually carried when existing items have outlived their effective

lives and it may not be economical to continue with them anymore or after been

destroyed by accidents or otherwise.

3. The Replacement Theory in Operations Research is used in the decision-making

process of replacing a used equipment with a substitute; mostly a new equipment

of better usage.

4. A replacement policy is a specification of “keep” or “replace” actions, one for

each period. Two simple examples are the policy of replacing the equipment every

period and the policy of keeping the first machine until the end of the period N.

5. Replacement problems involve items that degenerate with use or with the passage

of time and those that fail after a certain amount of use or time.

6. The factors necessitating the replacement of machines and equipment can broadly

be classified into the following two categories: technical and factors.

7. The models in replacement and maintenance are; replacement of items whose

maintenance cost increases with time and the value of the money remains constant

during the period; replacement of items whose maintenance cost increases with

time and value of money also changes with time; and Group Replacement policy.

8. The Net Present Value (NPV) is the value obtained by discounting all cash

outflows and inflows of an investment opportunity by a chosen rate of return. The

NPV decision rule is to accept all positive NPV projects in an unconstrained

environment, or if projects are mutually exclusive, accept the one with the highest

NPV.

9. In least cost method, you should start by giving allocations from the minimum cost

in the matrix. It means that cell for which cost is minimum is given allocation first.





55

SAQ 5.1. (tests learning outcomes 5.1. and 5.2.)

Using the statements provided below, identify the TRUE/FALSE items.

a. Replacement theory is generally concerned with theproblem of replacement of


b. Replacement happens when existing items have s newer version or models.

c. A replacement policy is a specification of “keep” or “replace” actions, one for

each period.

d. Replacement Models is used solved qualitatively and categorised on some basis

which may be called as.

e. The hurdle rate is the minimum acceptable return on an investment.


Replacement problems involve items that degenerate with use or with the passage of time

and those that fail after a certain amount of use or time. Kindly distinguish between these

items.

SAQ 5.3. (tests learning outcome 5.4)

As an expert in management, how would you describe net present value and its relevance

to managerial decisions?

References

Hira D.S., 2004 Operation Research, S.Chand & Company Ltd., New Delhi.

Nahmias, S. 1997. Production and Operation Analysis, McGraw Hill International,

Chicago.

Taha, H. A, 2013 Operation Research - An Introduction, Prentice Hall of India, 7th

edition, Ravindran, Phillips and Solberg, Operations Research: Principles and

Practice, John Wiely & Sons, 2nd Edition.

56

Study Session Six: Queuing Theory


Introduction

I hope you have been finding this course educative? This another phase in EME 302

where the focus will be on Queuing Theory. It is a common phenomenon in everyday life

to see many people waiting in front of abooking counter in a railway station or in a

theatre or in a ration shop to have some service carried out. This formation of queue

occurs whenever the present demand for a service exceeds the present capacity to provide

the necessary government, industry, schools, hospitals, etc.Thus, this lecture has been

geared towards equipping you with the necessary skills needed to manage such.

Learning Outcomes for StudySession 6



6.2. Explain Queuing Theory.(SAQ 6.2)

6.3. Identify terms used in queuing model. (SAQ 6.1)

6.4. Describe how an effective Queuing system can be designed. (SAQ 6.3)

6.5. Clearly differentiate between the various Queuing notations. (SAQ 6.1)

Key word; queuing theory.

6.1. Meaning and Definition of Terms in Queuing Theory

6.1.1. Meaning of Queuing Theory

To kick-start this lecture, let us take a moment to discuss on man’s daily activities. From

the time of birth (usually involving an approximately 9-month period from the moment of

conception) until death (an entire life-time - whether brief, extensive or in between) and

at many moments along the way human beings often find themselves waiting for things,

events, conditions, etc. A major topic of Applied Mathematics that deals with this

phenomenon of waiting is called Queuing Theory. Using the word "Queue", which is

57

more common in British than American English and means "a line up" or "to form a

line", a closely reasoned body of mathematical theory has been developed to describe this

common human activity; theory applicable to normal economic activity. Realistic

applications can be made to the phenomena of customers awaiting the delivery of

goods/services, as well as to goods-in-process coming to be finished goods.

The first queuing theory problem was considered by Erlang in 1908 who looked at how

large a telephone exchange needed to be to keep to a reasonable value the number of

telephone calls not connected because the exchange was busy (lost calls). Within ten

years he had developed a (complex) formula to solve the problem. Queuing theory is

used to develop more efficient queuing systems that reduce customer wait times and

increase the number of customers that can be served. For example, a 2003 paper by

Stanford School of Business professor Lawrence Wein used queuing theory to analyze

the potential effects of a bioterrorism attack on U.S. soil and propose a system to reduce

wait times for medications that would decrease the number of deaths caused by such an

attack.

Queuing theory is the mathematical study that deals with problems which involve

queuing (or waiting lines), or queues. In queuing theory, a model is constructed so that

queue lengths and waiting times can be predicted. Queuing theory is generally considered

a branch of operations research because the results are often used when making

organisation decisions about the resources needed to provide a service.

6.1.2. Definition of Terms inQueuing Model

Customer: The arriving unit that requires some service to be provided is called the

customer. The customer may represent people, machines, etc.

Server: A server is one who provides the arriving customer the necessary service. It may

be personsin the counter or machines, etc.

Waiting Line or Queue: The queue represents the number of customers waiting to be

served.Normally the queue does not include the customer being served.

Service Channel: This refers to the type of service provided. If we have one serving unit

only, we have a single channel model or single server model. If service involves more

58

than one server, we have a multi-channel server model. We use the symbol k to denote

the number of service channels.

Real-life applications of queuing theory include:

a. providing faster customer service,

b. improving traffic flow,

c. shipping orders efficiently from a warehouse,

d. designing telecommunications systems such as call centers.

e. banks/supermarkets - waiting for service

f. computers - waiting for a response

g. failure situations - waiting for a failure to occur e.g. in a piece of machinery

h. public transport - waiting for a train or a bus

As we know queues are common in every-day experience as seen in Fig 6.1. Queues

form because resources are limited. In fact, it makes economic sense to have queues. For

example,imagine how many supermarket tills you would need to avoid queuing? how

many buses or trains would be needed if queues were to be avoided/eliminated?

Fig 6.1. An image showing Nigerians who queued while waiting to cast their votes in the last election

Image source: http://www.nigerianeye.com/2015/03/nigeria-decides-2015-live-update.html

59

In designing queuing systems, we need to aim for a balance between service to customers

(short queues implying many servers) and economic considerations (not too many

servers). In essence, all queuing systems can be broken down into individual sub-systems

consisting of entities queuing for some activity. Typically, we can talk of this individual

sub-system as dealing with customers queuing for service. To analyse this sub-system we

need information relating to:

Arrival process:

This answer questions such as;

� how customers arrive e.g. singly or in groups (batch or bulk arrivals)

� how the arrivals are distributed in time (e.g. what is the probability distribution of

time between successive arrivals (the inter-arrival time distribution)

� whether there is a finite population of customers or (effectively) an infinite

number

The simplest arrival process is one where we have completely regular arrivals (i.e. the

same constant time interval between successive arrivals). A Poisson stream of arrivals

corresponds to arrivals at random. In a Poisson stream successive customers arrive after

intervals which independently are exponentially distributed. The Poisson stream is

important as it is a convenient mathematical model of many real-life queuing systems and

is described by a single parameter - the average arrival rate. Other important arrival

processes are scheduled arrivals; batch arrivals; and time dependent arrival rates (i.e. the

arrival rate varies according to the time of day).

In-text Question

• You meet Bisi and James at an ATM booth collection. James laments that inspite

of the fact that there 5 functional ATMs. The queues remain overwhelming.

Explain to him the sense around this phenomenon and how this can be managed

through designing queuing systems.

• When explaining to James note that queues form because resources are limited. In

fact, it makes economic sense to have queues. For example, imagine how many

supermarket tills you would need to avoid queuing? how many buses or trains

would be needed if queues were to be avoided/eliminated?

60

• In designing queuing systems, we need to aim for a balance between service to

customers (short queues implying many servers) and economic considerations (not

too many servers).

Another information that is needed in designing queuing model is known as;

Service mechanism: This caters for information such as;

� a description of the resources needed for service to begin

� how long the service will take (the service time distribution)

� the number of servers available

� whether the servers are in series (each server has a separate queue) or in parallel

(one queue for all servers)

� whether preemption is allowed (a server can stop processing a customer to deal

with another "emergency" customer)

If the service times for customers are independent and do not depend upon the arrival

process is common. Another common assumption about service times is that they are

exponentially distributed.

As we proceed on the information needed to analyse a sub system, another needed

information is the;

Queue characteristics: this answer questions such as;

� how, from the set of customers waiting for service, do we choose the one to be

served next (e.g. FIFO (first-in first-out) - also known as FCFS (first-come first

served); LIFO (last-in first-out); randomly) (this is often called the queue

discipline)

� do we have:

o balking (customers deciding not to join the queue if it is too long)

o reneging (customers leave the queue if they have waited too long for service)

o jockeying (customers switch between queues if they think they will get served

faster by so doing)

o a queue of finite capacity or (effectively) of infinite capacity

Changing the queue discipline (the rule by which we select the next customer to be

served) can often reduce congestion. Often the queue discipline "choose the customer

with the lowest service time" results in the smallest value for the time (on average) a

61

customer spends queuing.

Note here that integral to queuing situations is the idea of uncertainty in, for example,

inter-arrival times and service times. This means that probability and statistics are needed

to analyse queuing situations. In terms of the analysis of queuing situations the types of

questions in which we are interested are typically concerned with measures of system

performance and might include the following;

Pause to consider these questions;

� How long does a customer expect to wait in the queue before they are served, and

how long will they have to wait before the service is complete?

� What is the probability of a customer having to wait longer than a given time

interval before they are served?

� What is the average length of the queue?

� What is the probability that the queue will exceed a certain length?

� What is the expected utilisation of the server and the expected time during which

he will be fully occupied (remember servers cost us money so we need to keep

them busy)? In fact, if we can assign costs to factors such as customer waiting

time and server idle time then we can investigate how to design a system at

minimum total cost.

Box 6.1. Queue Characteristics

Under queue characteristics, we have the following;

1. Balking (customers deciding not to join the queue if it is too long)

2. Reneging (customers leave the queue if they have waited too long for service)

3. Jockeying (customers switch between queues if they think they will get served faster

by so doing)

4. A queue of finite capacity or (effectively) of infinite capacity.

These are questions that need to be answered so that management can evaluate

alternatives tocontrol/improve the situation. Some of the problems that are often

investigated in practice are:

� Is it worthwhile to invest effort in reducing the service time?

� How many servers should be employed?

� Should priorities for certain types of customers be introduced?

62

� Is the waiting area for customers adequate?

To get answers to the above questions there are two basic approaches:

• analytic methods or queuing theory (formula based); and

• simulation (computer based).

The reason for being two approaches (instead of just one) is that analytic methods are

only available for relatively simple queuing systems. Complex queuing systems are

almost always analysed using simulation (more technically known as discrete-event

simulation).

At this point, you need to note that the simple queuing systems that can be tackled via

queuing theory essentially have the following features;

• consist of just a single queue; linked systems where customers pass from one

queue to another cannot be tackled via queuing theory

• have distributions for the arrival and service processes that are well defined (e.g.

standard statistical distributions such as Poisson or Normal); systems where these

distributions are derived from observed data, or are time dependent, are difficult to

analyse via queuing theory.

Activity 6.1.

Recall some of your experiences on the queue and identify some of the people you have

queued with in relation to queue characteristics you learnt in this lecture.


You should have met this set of people;

a. Balking (customers deciding not to join the queue if it is too long)

b. Reneging (customers leave the queue if they have waited too long for service)

c. Jockeying (customers switch between queues if they think they will get served

faster by so doing).

63

Additional queuing theory information are:

Queuing notation and a simple example

It is common to use the symbols:

λ = Arrival Rate: lamda to be the mean (or average) number of arrivals per time, i.e. the

mean arrival rate

µ = Service Rate: µ to be the mean (or average) number of customers served per time,

i.e. the mean service rate

Therefore, ρ = λ / µ

Others are:

There is a standard notation system to classify queuing systems as A/B/C/D/E, where:

� A represents the probability distribution for the arrival process

� B represents the probability distribution for the service process

� C represents the number of channels (servers)

� D represents the maximum number of customers allowed in the queuing system

(either being served or waiting for service).

� E represents the maximum number of customers in total

Common options for A and B are:

• M for a Poisson arrival distribution (exponential interarrival distribution) or a

exponential service time distribution

• D for a deterministic or constant value

• G for a general distribution (but with a known mean and variance)

If D and E are not specified, then it is assumed that they are infinite.

While:

M/D/1 case (random Arrival, Deterministic service, and one service channel)

Expected average queue length E(m)= (2ρ- ρ2)/ 2 (1- ρ)

Expected average total time E(v) = 2- ρ / 2 µ (1- ρ)

Expected average waiting time E(w) = ρ / 2 µ (1- ρ)

64



1. A queue is a waiting line, and queuing involves dealing with items or people in

sequence. Thus, a queuing problem consists either of determining what facilities to

provide or scheduling the use of them.

2. The first queuing theory problem was considered by Erlang in 1908 who looked at

how large a telephone exchange needed to be to keep to a reasonable value the

number of telephone calls not connected because the exchange was busy (lost

calls).

3. Queuing theory is the mathematical study that deals with problems which involve

queuing (or waiting lines), or queues.

4. In designing queuing systems, we need to aim for a balance between service to

customers (short queues implying many servers) and economic considerations (not

too many servers).

5. To analyse queuing problem, there is a need to analyse the; arrival process; service

mechanism; and queue characteristics.

6. Questions that need to be answered so that management can evaluate alternatives

to control/improve the situation. Some of the problems that are often investigated

in practice are; is it worthwhile to invest effort in reducing the service time? how

many servers should be employed? should priorities for certain types of customers

be introduced? is the waiting area for customers adequate?





SAQ 6.1. (tests learning outcomes 6.1, 6.3, and 6.5.)

In the statements provided below, select the appropriate option that fits each item

1. _________ is the mathematical study that deals with problems which involve

queuing (or waiting lines), or queues.

a). Queuing systems b. Queuing theory c) Queuing model d)Queuing time.

65

2. Which of these is not a term in Queuing theory?

a). Server b). Waiting Queuing c). Service channel. d) Custody.

3. Real-life applications of queuing theory include;

a). providing slow customer service b). improving traffic light. c) shipping orders

efficiently from a warehouse. d) banks/supermarkets - waiting for order.

4. Which of the following is not a term in queuing model?

a) Network server b) customer c) waiting line d) Queuing channel.

5. Which of the following queuing notation has the corresponding meaning?

a). λ = Service Rateb). µ = Arrival Rate c) G for a general distribution. d)

A represents the probability distribution for the service process.


Based on what you have learnt in this lecture, simply explain what Queueing theory

entails.


While standing on the queue to pay your departmental levy in school, you observed that

you have spent 45mins on the queue causing you to miss one of your lectures for that

day. Write a report to your Head of Department clearly stating how an effective queuing

system can be designed for your department to save time spent on the queue by students.

References

Artalejo, J., and Gómez-Corral, A. 2008; Retrial queuing systems. Springer, Berlin.

Dattatreya, G. 2008; Performance analysis of queuing and computer networks. CRC

Press, Boca Raton.

Ivo, A. and Jacques R. 2002; Queuing Theory; Department of Mathematics and

Computing Science, Eindhoven University of Technology P.O. Box 513, 5600

MB Eindhoven, The Netherlands.

66

Study Session Seven: Total Quality Management in Education


Introduction

This is another lecture in (EME 310) Operations Management in Educational Practice. In

this lecture, we shall be considering Total Quality Management (TQM) in Education. It is

essential to know that TQM is a timely tool which must be clearly understood, adopted

and implemented as soon as possible. This lecture discusses various concepts, issues,

processes, models and implementation strategies for TQM in educational settings. Right

from creation, the idea of management arose out of the need for survival. The needs of

people then were simple. Today our needs are complex and sometimes out of place. It has

become necessary to improve development through the vehicles of education, science and

technology, hence the need for Total Quality Management.




7.2. Trace timeline of events in the origin of TQM. (SAQ 7.2)

7.3. Discuss the relevance of TQM in an organization. (SAQ 7.3)

7.4. Identify the 8 primary elements of TQM. (SAQ 7.4)

7.5. Outline at least 6 generic models for implementing TQM. (SAQ 7.5)

Key words: total quality management, profitability, competitiveness, implementation,

technical, operational, and process.

67

7.1. Origin, Meaning, and Principles of Total Quality Management

7.1.1. The Origin of Total Quality Management

Total Quality Management (TQM)in the form of statistical quality control was invented

by Walter A. Shewhart. It was initially implemented at Western Electric Company in the

form developed by Joseph Juran who had worked there with the method. TQM was

demonstrated on a grand scale by Japanese industry through the intervention of W.

Edwards Deming with the help of missionary labors in the U.S. and across the world. He

is the "father" of quality control, quality circles, and quality movement generally. Walter

Shewhart, then working at Bell Telephone Laboratories first devised a statistical control

chart in 1923; it is still named after him. He published his method in 1931 as Economic

Control of Quality of Manufactured Product. The method was first introduced at Western

Electric Company's Hawthorn plant in 1926. Joseph Juran was one of the people trained

in the technique. In 1928, he wrote a pamphlet entitled Statistical Methods Applied to

Manufacturing Problems. This pamphlet was later incorporated into the AT&T Statistical

Quality Control Handbook, still in print. In 1951, Juran published his very influential

Quality Control Handbook.

W. Edwards Deming trained as a mathematician and statistician, went to Japan at the

behest of the U.S. State Department to help Japan in the preparation of the 1951 Japanese

Census. The Japanese were already aware of Shewhart's methods of statistical quality

control. Japanese application of the method had significant and undeniable results

manifesting as dramatic increases in Japanese product quality and Japanese success in

exports. This led to the spread of the quality movement across the world.

In the late 1970s and 1980s, U.S. producers scrambled to adopt quality and productivity

techniques that might restore their competitiveness. Deming's approach to quality control

came to be recognized in the United States, and Deming himself became a sought-after

lecturer and author. Total Quality Management, the phrase applied to quality initiatives

proffered by Deming and other management gurus became a staple of American

enterprise by the late 1980s. But while the quality movement has continued to evolve

beyond its beginnings, many of Deming's emphases, particularly those associated with

management principles and employee relations were not adopted in Deming's sense but

68

continued as changing fads, including the movement to "empower" employees and to

make "teams" central to all activities.

TQM in education surfaced in 1988 at Mt. Edgecombe High school in Sitka, Alaska,

when David Langford, the school’s technology teacher/coordinator, applied Total Quality

concepts in his classes. TQM has become increasingly popular in education, as evidenced

by the plethora of books and journal articles since 1990 (Tucker 1992). TQM has also

spread into mainstream of educational organisations. The Association for Supervision

and Curriculum Development devoted its entire November, 1992 issue of its journal;

Educational Leadership to the quality movement in education.

7.1.2. Meaning of Total Quality Management (TQM)

Total Quality Management (TQM) refers to management methods used to enhance

quality and productivity in profit making organizations. In other words, Total Quality

Management (TQM) describes a management approach to long–term success through

customer satisfaction. In a TQM effort, all members of an organization participate in

improving processes, products, services, and the culture in which they work.TQM is a

comprehensive management approach that works horizontally across an organization,

involving all departments and employees and extending backward and forward to include

both suppliers and clients/customers. TQM is only one of many acronyms used to label

management systems that focus on quality. Other acronyms include CQI (continuous

quality improvement), SQC (statistical quality control), QFD (quality function

deployment), QIDW (quality in daily work), TQC (total quality control), etc. Like many

of these other systems, TQM provides a framework for implementing effective quality

and productivity initiatives that can increase the profitability and competitiveness of

organizations.

In-text Question

• Mr Dauda’s school has been in operation for over 5years. He has there have been

several complaints from parents of poor teaching standards and general attitude of

staff towards their job. He is at loss as to the next step. In view of what you have

just learnt explain to him what TQM is and how this problem can be curbed and

eventually solved if he chooses to use TQM.

69

o Recall that TQM refers to management methods used to enhance quality and

productivity in profit making organizations. In other words, Total Quality

Management (TQM) describes a management approach to long–term success

through customer satisfaction.

Let’s continue our discussion,

In view of the framework discussed earlier, TQM is a management philosophy that seeks

to integrate all organizational functions (marketing, finance, design, engineering, and

production, customer service, etc.) to focus on meeting customer needs and

organizational objectives. TQM views an organization as a collection of processes. It

maintains that organizations must strive to continuously improve these processes by

incorporating the knowledge and experiences of workers. The simple objective of TQM

is "Do the right things, right the first time, every time". TQM is infinitely variable and

adaptable. Although originally applied to manufacturing operations, and for some years

only used in that area, TQM is now becoming recognized as a generic management tool,

just as applicable in service and public sector organizations. There are some evolutionary

strands with different sectors creating their own versions from the common ancestor.

TQM is the foundation for activities, which include:

1. Commitment by senior management and all employees

2. Meeting customer requirements

3. Reducing development cycle times

4. Just in Time/Demand Flow Manufacturing

5. Improvement teams

6. Reducing product and service costs

7. Systems to facilitate improvement

8. Line Management ownership

9. Employee involvement and empowerment

10. Recognition and celebration

11. Challenging quantified goals and benchmarking

12. Focus on processes / improvement plans

13. Specific incorporation in strategic planning

70

In respect to TQM foundational activities stated above, you will observe that this shows

that TQM must be practiced in all activities, by all personnel, in Manufacturing,

Marketing, Engineering, Research and Development (R&D), Sales, Purchasing, HR, etc.

Fig 7.1. Foundations of Total Quality Management

If you take a good look at Fig. 7.1., you will realise that the core of TQM is the customer-

supplier interfaces both externally and internally and at each interface lie a few processes.

This core must be surrounded by commitment to quality, communication of the quality

message, and recognition of the need to change the culture of the organization to create

total quality. These are the foundations of TQM and they are supported by the key

management functions of people, processes and systems in the organization as shown in

Fig 7.1.

Culture

Commitment

Communication

Systems

Processes

Customer

Supplier

People

71

Box 7.1. Features of TQM

TQM is a management philosophy that seeks to integrate all organizational functions

(marketing, finance, design, engineering, and production, customer service, etc.) to focus

on meeting customer needs and organizational objectives. TQM views an organization as

a collection of processes. It maintains that organizations must strive to continuously

improve these processes by incorporating the knowledge and experiences of workers.

7.1.3. Total Quality Management (TQM)Principles

At this point, let us consider the principles of TQM. Different consultants and schools of

thought emphasize different aspects of TQM as it has developed over time. These aspects

may be technical, operational, or social/managerial.The basic elements of TQM, as

expounded by the American Society for Quality Control, are

1. policy, planning, and administration;

2. product design and design change control;

3. control of purchased material;

4. production quality control;

5. user contact and field performance;

6. corrective action; and

7. employee selection, training, and motivation.

The real root of the quality movement or the "invention" on which it rests is statistical

quality control. SQC is retained in TQM in the fourth element, above, "production quality

control." It may also be reflected in the third element, "control of purchased material,"

because SQC may be imposed on vendors by contract.In a nutshell, this core method

requires that quality standards are first set by establishing measurements for an item and

thus defining what constitutes quality. The measurements may be dimensions, chemical

composition, reflectivity, etc. in effect any measurable feature of the object. Test runs are

made to establish divergences from a base measurement (up or down) which are still

acceptable. This "band" of acceptable outcomes is then recorded on one or several

Shewhart charts. Quality control then begins during the production process itself.

Samples are continuously taken and immediately measured, the measurements recorded

on the chart(s). If measurements begin to fall outside the band or show an undesirable

72

trend (up or down), the process is stopped and production discontinued until the causes of

divergence are found and corrected. Thus, SQC, as distinct from TQM, is based on

continuous sampling and measurement against a standard and immediate corrective

action if measurements deviate from an acceptable range.

In-text Question

• Can you identify the real root of the quality movement or the "invention" on which

it rests?

o Yes, that is statistical quality control (SQC) which is retained in TQM in the

fourth element.

7.2. The Elements, Generic Model, and Building Blocks of Total Quality

Management (TQM)

7.2.1. The Primary Elements of TQM

We have come to another section of this lecture where we shall discuss the primary

elements of TQM. Total quality management can be summarized as a management

system for a customer-focused organization that involves all employees in continual

improvement. It uses strategy, data, and effective communications to integrate the quality

discipline into the culture and activities of the organization. These elements are discussed

as follows;

1. Customer-focused: The customer ultimately determines the level of quality. No

matter what an organization does to foster quality improvement—training

employees, integrating quality into the design process, upgrading computers or

software, or buying new measuring tools—the customer determines whether the

efforts were worthwhile.

2. Total employee involvement: All employees participate in working toward

common goals. Total employee commitment can only be obtained after fear has

been driven from the workplace, when empowerment has occurred, and

management has provided the proper environment. High-performance work

systems integrate continuous improvement efforts with normal business

operations. Self-managed work teams are one form of empowerment.

3. Process-centered: A fundamental part of TQM is a focus on process thinking. A

process is a series of steps that take inputs from suppliers (internal or external) and

73

transforms them into outputs that are delivered to customers (again, either internal

or external). The steps required to carry out the process as defined, and

performance measures are continuously monitored to detect unexpected variation.

4. Integrated system: Although an organization may consist of many different

functional specialties often organized into vertically structured departments, it is

the horizontal processes interconnecting these functions that are the focus of

TQM. These processes are;

• Micro-processes add up to larger processes, and all processes aggregate into

the business processes required for defining and implementing strategy.

Everyone must understand the vision, mission, and guiding principles as well

as the quality policies, objectives, and critical processes of the organization.

Business performance must be monitored and communicated continuously.

• An integrated business system may be modeled after the Baldrige National

Quality Program criteria and/or incorporate the ISO 9000 standards. Every

organization has a unique work culture, and it is virtually impossible to achieve

excellence in its products and services unless a good quality culture has been

fostered. Thus, an integrated system connects business improvement elements

to continually improve and exceed the expectations of customers, employees,

and other stakeholders.

5. Strategic and systematic approach: A critical part of the management of quality is

the strategic and systematic approach to achieving an organization’s vision,

mission, and goals. This process, called strategic planning or strategic

management, includes the formulation of a strategic plan that integrates quality as

a core component.

6. Continual improvement: A major thrust of TQM is continual process

improvement. Continual improvement drives an organization to be both analytical

and creative in finding ways to become more competitive and more effective at

meeting stakeholder expectations.

7. Fact-based decision making: To know how well an organization is performing,

data on performance measures are necessary. TQM requires that an organization

continually collect and analyze data to improve decision making accuracy, achieve

consensus, and allow prediction based on history.

74

8. Communication: During times of organizational change, as well as part of day-to-

day operation, effective communication plays a large part in maintaining morale

and in motivating employees at all levels. Communication involve strategies,

method, and timeliness.

These elements are considered so essential to TQM that many organizations define them

as a set of core values and principles on which the organization is to operate.

Box. 7.2. The Primary Elements of TQM

The elements of TQM are;

1. Customer-focused

2. Total employee involvement:

3. Process-centered:

4. Integrated system

5. Strategic and systematic approach

6. Continual improvement

7. Fact-based decision making

8. Communication

7.2.2. Generic Model for Implementing TQM

As we proceed in our lecture on TQM in Education, another point we need to consider is

the generic model for implementing TQM. Some of these are;

1. Top management learns about and decides to commit to TQM. TQM is identified

as one of the organization’s strategies.

2. The organization assesses current culture, customer satisfaction, and quality

management systems.

3. Top management identifies core values and principles to be used, and

communicates them.

4. A TQM master plan is developed based on steps 1, 2, and 3.

5. The organization identifies and prioritizes customer demands and aligns products

and services to meet those demands.

75

6. Management maps the critical processes through which the organization meets its

customers’ needs.

7. Management oversees the formation of teams for process improvement efforts.

8. The momentum of the TQM effort is managed by the steering committee.

9. Managers contribute individually to the effort through planning, training,

coaching, or other methods.

10. Daily process management and standardization take place.

11. Progress is evaluated and the plan is revised as needed.

12. Constant employee awareness and feedback on status are provided and a

reward/recognition process is established.

In-text Question

• Do remember Mr Dauda the school owner, who you advised to use TQM to get his

school back into running optimally? (see in text question in section 7.1.2) He

decided to take your advise and use TQM. However, he is doesn’t know how he

can go about using TQM. So he has come to you for help. This time, your task is

to explain to him the Generic Model for Implementing TQM in his school. You

can start with the first five points.

o Refer to section 7.2.2 of this study session as you guide Mr Dauda

7.2.3. The Buildingblocks of TQM

The building blocks of TQM are: processes, people, management systems and

performance measurement.

You need to understand that everything we do is a Process, which is the transformation

of a set of inputs, which can include action, methods and operations, into the desired

outputs, which satisfy the customers’ needs and expectations. In each area or function

within an organization there will be many processes taking place, and each can be

analyzed by an examination of the inputs and outputs to determine the action necessary to

improve quality. In every organization, there are some very large processes which are

groups of smaller processes called key or core business processes. These must be carried

out well if an organization is to achieve its mission and objectives. This section on

processes discusses processes and how to improve them, and implementation covers

how to prioritize and select the right process for improvement.

76

Fig 7.2. The building blocks of TQM

Considering Fig 7.2, you will observe that the only point at which true responsibility for

performance and quality can lie is with the people who do the job or carry out the

process, each of which has one or several suppliers and customers. An efficient and

effective way to tackle process or quality improvement is through teamwork. However,

people will not engage in improvement activities without commitment and recognition

from the organization’s leaders, a climate for improvement and a strategy that is

implemented thoughtfully and effectively. The section on people expands on these issues,

covering roles within teams, team selection and development and models for successful

teamwork.

As we continue our discussion on the building blocks of TQM, you should note that an

appropriate documented Quality Management System will help an organization not only

achieve the objectives set out in its policy and strategy, but also sustain and build upon

them. It is imperative that the leaders take responsibility for the adoption and

documentation of an appropriate management system in their organization if they are

serious about the quality journey. The Systems section discusses the benefits of having

Suppliers Customers

Outputs Inputs

Materials

Procedures

Methods

Information

People

Skills

Products

Services

Information

Paperwork

Voice Of Process: Feedback

Voice Of Customer: Feedback

Process

77

such a system, how to set one up and successfully implement it. Once the strategic

direction for the organization’s quality journey has been set, it needs Performance

Measures to monitor and control the journey, and to ensure the desired level of

performance is being achieved and sustained. They can, and should be established at all

levels in the organization, ideally being cascaded down and most effectively undertaken

as team activities and this is discussed in the section on Performance.

Activity 7.1. Time Allowed: 1 hour

Take a moment to study the building blocks of TQM, upon doing this, get a broadsheet or

cardboard paper and make a sketch of the building blocks of TQM with the arrows

indicating different activities.


I expect you to provide a replica of what you studied before embarking on the activity.



1. Total Quality Management (TQM) in the form of statistical quality control was

invented by Walter A. Shewhart.

2. TQM in education surfaced in 1988 at Mt. Edgecombe High school in Sitka,

Alaska, when David Langford, the school’s technology teacher/coordinator,

applied Total Quality concepts in his classes.

3. Total Quality Management (TQM) refers to management methods used to enhance

quality and productivity in profit making organizations.

4. Total Quality Management (TQM) describes a management approach to long–

term success through customer satisfaction.

5. Like many of these other systems, TQM provides a framework for implementing

effective quality and productivity initiatives that can increase the profitability and

competitiveness of organizations.

78

6. The elements of TQM are; customer-focused; total employee involvement;

process-centered; integrated system; strategic and systematic approach; continual

improvement; fact-based decision making; and communication.

7. The building blocks of TQM are: processes, people, management systems and

performance measurement.

8. TQM practice involves activities related to all personnel in organization (HR), in

manufacturing, marketing, engineering, research and development (R&D), sales,

purchasing etc. Total Quality Management can be summarized as a management

system for a customer-focused organization that involves all employees in

continual improvement. It uses strategy, data, and effective communications to

integrate the quality discipline into the culture and activities of the organization.






In the statements provided below, fill the blanks with the appropriate keywords

a. _________ is the transformation of a set of inputs, which can include action,

methods and operations, into the desired outputs, which satisfy the customers’

needs and expectations

b. __________ covers how to prioritize and select the right process for improvement.

c. The management methods used to enhance quality and productivity in profit

making organizations is known as _________.

d. TQM framework can improve _________ and ________ in an in a profit-making

organization.

e. _______, ________ are aspects of TQM principles.


Using the knowledge gained in this lecture, identify at least 3 major pioneers in the

development of TQM.

79


You have been chosen to make a class presentation as part of your continuous assessment

tests on the topic “The Relevance of TQM in any Organization”. Briefly give a highlight

of points to be raised in the presentation.


Total quality management can be summarized as a management system for a customer-

focused organization that involves all employees in continual improvement. Using this

background statement as an aid, identify other key elements in TQM.


In designing TQM for an educational system, outline at least 6 models that can be

adopted in getting this done.

References

Ali, N. A. & Zairi, M. 2005 Service Quality in Higher Education. Bradford University

School of Management, Bradford.

Mukhopadahyay, M. 2006 Total Quality Management in Education. Sage, New Delhi.

Thakkar, J., Deshmukh, S. G. & Shastree, A. 2006 Total quality management (TQM) in

self-financed technical institutions: a quality function deployment (QFD) and

force field analysis approach. Quality Assurance in Education 14, 1, 54-74

80

Study Session Eight: Resource Allocation/Assignment: Hungarian

Method


Introduction

You are welcome back from our lecture on TQM, I want to believe that you are now a

TQM expert. This is lecture 18 titled “Hungarian method in resource allocation”. Other

methods will also be considered in the coming lectures. A special type of problem called

the assignment problem is also an allocation problem. Here we have n jobs to perform

with n persons and the problem is how to distribute the jobs to the different persons

involved. Depending on the intrinsic capacity, merit or potential of the individual to be

able to accomplish the task in different times. Then the objective function in assigning

the different jobs to different persons is to find the optimal assignment that will minimize

the total time taken to finish all the jobs by the individuals. For example, we have four

different building activities say, construction of a hotel, a theatre, a hospital and a

multistoried building and there are four contractors competing for these jobs. Each

contractor must be assigned only one job. The allocation should aim to minimize the total

time taken to complete the construction of all four activities after assigning only one job

to one individual.



8.1. Describe the Hungarian Method in resource allocation.(SAQ 8.1)

8.2. Identify the steps in minimization and maximization of assignment

problem. (SAQ 8.2)

8.3. Calculate minimization and maximization cost in assignment problem.

(SAQ 8.3)

81

8.1. Meaning and Hungarian Method of Resource Allocation

8.1.1. Meaning of Resource Allocation

There are problems where certain facilities must be assigned to specified jobs to

maximize the overall performance of the assignment. The Hungarian Method can also

solve such assignment problems, as it is easy to obtain an equivalent minimization

problem by converting every number in the matrix to an opportunity loss. The conversion

is accomplished by subtracting all the elements of the given matrix from the highest

element. It turns out that minimizing opportunity loss produces the same assignment

solution as the original maximization problem.

8.1.2. Hungarian Method for Solving Assignment Problem

Hungarian method can be used in minimizing and the maximizing assignment problem.

Let us consider the two approaches;

1. Minimization of assignment problem

Example 8.1

A departmental head has four subordinates, and four tasks to be performed. The

subordinates differ in efficiency, and the tasks differ in their intrinsic difficulty. His

estimate, of the time each man would take to perform each task, is given the matrix below.

Men

Person 1 2 3 4

A 18 26 17 11

B 13 28 14 26

C 38 19 18 15

D 19 26 24 10

Solution to Example 8.1:

Step 1

Identify the minimum element in each row and subtract it from every element of

that row, we get the reduced matrix.

82

Men

Person 1 2 3 4

A 7 15 6 0

B 0 15 1 13

C 23 4 3 0

D 9 16 14 0

Step 2

Identify the minimum element in each column and subtract it from every element of that column.

Men

Person 1 2 3 4

A 7 11 5 0

B 0 11 0 13

C 23 0 2 0

D 9 12 13 0

Step 3

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the

following way:

Now proceed as in the previous example.

Optimal assignment is: A→G, B → E, C →F and D→ H

The minimum total time for this assignment scheduled is 17 +13+19+10 or 59 man-

hours.

Box 8.1. Hungarian Method in Resource Allocation

In a situation whereby certain facilities must be assigned to specified jobs to maximize

the overall performance of the assignment, the Hungarian Method can solve such

assignment problems, as it is easy to obtain an equivalent minimization problem by

converting every number in the matrix to an opportunity loss. The conversion is

accomplished by subtracting all the elements of the given matrix from the highest

element. It turns out that minimizing opportunity loss produces the same assignment

solution as the original maximization problem.

Let us also consider the other approach. We have;

2. Maximization of assignment problem

The Hungarian Method: The following algorithm applies the above theorem to a given n

× n cost matrix to find an optimal assignment. The steps needed are;

83

Step 1: Subtract the smallest entry in each row from all the entries of its row.

Step 2: Subtract the smallest entry in each column from all the entries of its column.

Step 3: Draw lines through appropriate rows and columns so that all the zero entries of

the cost matrix are covered and the minimum number of such lines is used.

Step 4: Test for Optimality:

a. If the minimum number of covering lines is n, an optimal assignment of

zeros is possible and we are finished.

b. If the minimum number of covering lines is less than n, an optimal

assignment of zeros is not yet possible. In that case, proceed to Step 5.

Step 5: Determine the smallest entry not covered by any line. Subtract this entry from

each uncovered row, and then add it to each covered column. Return to Step 3.

Example 8.2

You work as a sales manager for a toy manufacturer, and you currently have three sales

people on the road meeting buyers. Your salespeople are in Kano, KW; Lagos, IKJ; and

Enugu, COAL. You want them to fly to three other cities: Ibadan, IB; Abuja, ABJ; and

Kaduna, KDN. The table below shows the cost of airplane tickets in dollars between

these cities.

From / To Ibadan Abuja Kaduna

Kano 250 400 350

Lagos 400 600 350

Enugu 200 400 350

Where should you send each of your salespeople to minimize airfare?

Solution to example 8.2

Step 1: Subtract 250 from Row 1, 350 from Row 2, and 200 from Row 3.

Step 2: Subtract 0 from Column 1, 150 from Column 2, and 0 from Column 3.

250 400 350

400 600 350

200 400 250

0 150 100

50 250 0

0 200 50

84

Step 3: Cover all the zeros of the matrix with the minimum number of horizontal or

vertical

lines.

Step 4: Since the minimal number of lines is 3, an optimal assignment of zeros is

possible and we are finished.

Since the total cost for this assignment is 0, it must be an optimal assignment.

Here is the same assignment made to the original cost matrix.

0 150 100

50 250 0

0 200 50

0 150 100

50 250 0

0 200 50

0 0 100

50 100 0

0 50 50

250 400 350

400 600 350

200 400 250

0 150 100

50 250 0

0 200 50

85

Box 8.1. Steps in Minimization and Maximization of Assignment Problem using

Hungarian Method.

For Minimization;

STEP 1: Identify the minimum element in each row and subtract it from every element of

that row, we get the reduced matrix.

STEP 2: Identify the minimum element in each column and subtract it from every

element of that column

STEP 3: Make the assignment for the reduced matrix obtain from steps 1 and 2

For Maximization;

STEP 1: Subtract the smallest entry in each row from all the entries of its row.

STEP 2: Subtract the smallest entry in each column from all the entries of its column.

STEP 3: Draw lines through appropriate rows and columns so that all the zero entries of


STEP 4: Test for Optimality: If the minimum number of covering lines is n, an optimal

assignment of zeros is possible and we are finished. If the minimum number of covering

lines is less than n, an optimal assignment of zeros is not yet possible. In that case,

proceed to Step 5.

STEP 5: Determine the smallest entry not covered by any line. Subtract this entry from


Let us consider this second example on maximization of assignment problem

Example 8.3:

Pearson

Counter A B C D E

1 30 37 40 28 40

2 40 24 27 21 36

3 40 32 33 30 35

4 25 38 40 36 36

5 29 62 41 34 39

How should the counters be assigned to persons tomaximize the profit?

Solution to Example 8.3

Here, the highest value is 62. So, we subtract each value from 62. The conversion is shown in the

following table.

86

Pearson

Counter A B C D E

1 10 3 8

2 16 13 15 4

3 8 7 6 5

4 15 2 4

5 33 21 24 23

Draw the minimum number of vertical and horizontal lines necessary to cover all the

zeros in the reduced matrix.

Pearson

Counter A B C D E

1 10 3 8

2 16 13 15 4

3 8 7 6 5

4 15 2 4

5 33 21 24 23

Draw the minimum number of vertical and horizontal lines necessary to cover all the

zeros in the reduced matrix.

Select the smallest element from all the uncovered elements, i.e., 4. Subtract this element

from all the uncovered elements and add it to the elements, which lie at the intersection

of two lines. Thus, we obtain another reduced matrix for fresh assignment. Repeating step

3, we obtain a solution which is shown in the following table.

87

Final Table: Maximization Problem

Pearson

Counter A B C D E

1 14 3 8

2 12 9 11

3 4 3 2 1

4 19 2 4

5 37 21 24 23

The total cost of assignment = 1C + 2E + 3A + 4D + 5B

Substituting values from original table:

40 + 36 + 40 + 36 + 62 = 214.

Take note of this point to be discussed afterwards.

Prohibited Assignment

Sometimes it may happen that a resource (say a man or machine) cannot be assigned to

perform aa activity. In such cases, the cost of performing that activity by a resource is

very high (written as M or ∞) to prohibit the entry of this pair of resource-activity into the

final solution.



1. There are problems where certain facilities must be assigned to specified jobs to

maximize the overall performance of the assignment. The Hungarian Method can

also solve such assignment problems, as it is easy to obtain an equivalent

minimization problem by converting every number in the matrix to an opportunity

loss.

2. Suppose we have n resources to which we want to assign to n tasks on a one-to-

one basis and if we know the cost of assigning a given resource to a given task and

wish to find an optimal assignment–one which minimizes total cost. This

Mathematical Model ca be used: Let ci,j be the cost of assigning the ith resource to

the jth task. We define the cost matrix to be the n × n matrix

88

C =

3. An assignment is a set of n entry positions in the cost matrix, no two of which lie

in the same row or column. The sum of the n entries of an assignment is its cost.

An assignment with the smallest possible cost is called an optimal assignment.

4. The Hungarian Method: The Hungarian method (see above) is an algorithm which

finds an optimal assignment for a given cost matrix.






How would you describe the Hungarian Method in resource allocation?


Based on what you have learnt in this lecture, identify the steps needed in minimization

and maximization of problem assignment in Hungarian Method.

C1,1 C1,2

C1,3

C2,1 C2,2C1,n

⁞ ⁞ ⁞

C C

89


1. A job has four men available for work on four separate jobs. Only one man can

work on any one job. The cost of assigning each man to each job is given in the

following table. The objective is to assign men to jobs such that the total cost of

assignment is minimum.

Job

Person 1 2 3 4

A 20 25 22 28

B 15 18 23 17

C 19 17 21 24

D 25 23 24 24

Calculate the minimum cost of assignment.

2. Five different machines can do any of the five required jobs, with different profits

resulting from each assignment as given below:

Machines

Jobs A B C D E

1 30 37 40 28 40

2 40 24 27 21 36

3 40 32 33 30 35

4 25 38 40 36 36

5 29 62 41 34 39

Using the Hungarian Method, solve the above problem. Find out the maximum

profit possible through optimum assignment?

References

Hira, D.S. 2004; Operation Research, S.Chand & Company Ltd., New Delhi.

Taha, H A, 2003; Operation Research - An Introduction, Prentice Hall of India, 7th

edition.

Ravindran, Phillips and Solberg, Operations Research: Principles and Practice, John

Wiely & Sons, 2nd Edition

90

Study Session Nine: Resource Allocation/Assignment:

Transportation Problem I (Simplex and

Transportation Method)


Introduction

This is another method in resource allocation. In a transportation problem, we have

certain origins which may represent factories where we produce items and supply a

required quantity of the products to a certain number of destinations. This must be done

in such a way as to maximize the profit or minimize the cost. Thus, we have the places of

production as origins and the places of supply as destinations. Sometimes the origins and

destinations are also termed as sources and sinks. The transportation problem is

concerned with finding the minimum cost of transporting a single commodity from a

given number of sources (e.g. factories) to a given number of destinations (e.g.

warehouses). The data of the model include; the level of supply at each source and the

amount of demand at each destination and the unittransportation cost of the commodity

from each source to each destination.A transportation problem can be solved by two

methods, using (a) Simplex Method and (b) Transportation Method. We shall illustrate

this with the aid of an example in the course of the lecture.




9.2. Describe Transportation problem and its types. (SAQ 9.2)

9.3. State the variants of simplex method. (SAQ 9.3)

9.4. Highlight the steps in transportation method.(SAQ 9.4)

Key words;demand and supply

91

9.1. Meaning of Transportation Problem

The transportation problem and cycle canceling methods are classical in optimization.

The usual attributions are to the 1940's and later. However, Tolsto (1930) was a pioneer

in operations research and hence wrote a book on transportation planning which was

published by the National Commissariat of Transportation of the Soviet Union, an article

called Methods of ending the minimal total kilometrage in cargo-transportation planning

in space, in which he studied the transportation problem and described a number of

solution approaches, including the, now well-known, idea that an optimum solution does

not have any negative-cost cycle in its residual graph.

The transportation problem is concerned with finding an optimal distribution plan for a

single commodity. A given supply of the commodity is available at a number of sources,

there is a specified demand for the commodity at each of the destinations, and the

transportation cost between each source-destination pair is known. In the simplest case,

the unit transportation cost is constant.

Transportation Problem (TP) is based on supply and demand of commodities transported

from several sources to the different destinations. The sources from which we need to

transport refer the supply while the destination where commodities arrive referred the

demand. It has been seen that on many occasion, the decision problem can also be

formatted as TP. In general, we try to minimize total transportation cost for the

commodities transporting from source to destination. There are two types of

Transportation Problem namely:

1. Balanced Transportation Problem and

2. Unbalanced Transportation Problem.

In-text Question

• What do you think is the major concern of transportation problem?

o The transportation problem is concerned with finding an optimal distribution

plan for a single commodity.

Now let us consider the two problems earlier mentioned one after the other.

92

1. Balanced Transportation Problem: A Transportation Problem is said to be balanced

transportation problem if total number of supply is same as total number of demand.

Solution of the transportation problem

A balanced transportation problem has Total supply = Total demand which can be

expressed as

Σmi ai= Σn bj …..(eq….1)

t =1 j=1

A consequence of this is that the problem is defined by n + m - 1 supply and demand

variables since, if ai, i = 2; 3; : : : ;m and bj , j = 1; 2; : : : ; n are specified, then a1 can

be found from (eq…...1). This means that one of the constraint equations is not required.

Thus, a balanced transportation model has n + m - 1 independent constraint equations.

Since the number of basic variables in a basic solution is the same as the number of

constraints, solutions of this problem should have n + m - 1 basic variables which are

non-zero and all the remaining variables will be non-basic and thus have the value zero.

On the other hand, we also have;

2. Unbalanced Transportation Problem: A Transportation Problem is said to be

unbalanced transportation problem if total number of supply is not same as total

number of demand.

Box 9.1. The Basis of Transportation Model

Transportation Problem (TP) is based on supply and demand of commodities transported

from several sources to the different destinations. The sources from which we need to

transport refer the supply while the destination where commodities arrive referred the

demand. There are two types of Transportation Problem namely:

(1) Balanced Transportation Problem and

(2) Unbalanced Transportation Problem.

93

Example 1: Balanced transportation model.

Consider the following problem with 2 factories and 3 warehouses:

Warehouse 1 Warehouse 2 Warehouse 3 Supply

Factory 1 c11 c12 c13 20


Demand 7 10 13

Total supply = 20 + 10 = 30

Total demand = 7 + 10 + 13 = 30

= Total supply

Since Total supply = Total demand, the problem is balanced.

Example 2: Unbalanced transportation model

There are two cases to consider, namely excess demand and excess supply.

The First Case

Suppose the demand at warehouse 1 above is 9 units. Then the total supply and total

demand are unequal, and the problem is unbalanced. In this case, it is not possible to

satisfy all the demand at each destination simultaneously.We reformulate the model as

follows: since demand exceeds supply by 2 units, we introduce a dummy source (i.e. a

fictitious factory) which has a capacity of 2. The amount shipped from this dummy

source to a destination represents the shortage quantity at that destination.

It is necessary to specify the costs associated with the dummy source. There are two

situations to consider. These are;

a. Since the source does not exist, no shipping from the source will occur, so the unit

transportation costs can be set to zero.

b. Alternatively, if a penalty cost, P, is incurred for every unit of unsatisfied

demand, then the unit transportation costs should be set equal to the unit penalty

costs.

94

Warehouse 1 Warehouse 2 Warehouse 3 Supply



Dummy P P P 2

Demand 7 10 13

In effect, we are allocating the shortage to different destinations.

Second Case

If supply exceeds demand, then a dummy destination is added which absorbs the surplus

units. Any units shipped from a source to a dummy destination represent a surplus at that

source. Again, there are two cases to consider for how the unit transportation costs should

be determined. These are;

(a) Since no shipping takes place, the unit transportation costs can be set to zero.

(b) If there is a cost for storing, S, the surplus production then the unit transportation

costs should be set equal to the unit storage costs.

Warehouse 1 Warehouse 2 Warehouse 3 Dummy Supply

Factory 1 c11 c12 c13 S 20

Factory 2 c21 c22 c23 S 10

Demand 7 10 13 4

Here we are allocating the excess supply to the different destinations.

From now on, we will discuss balanced transportation problems only, as any unbalanced

problem can always be balanced according to the above constructions.

Example 9.1:

A transportation tableau is given below. Each cell represents a shipping route (which is

an arc on the network and a decision variable in the LP formulation), and the unit

shipping costs are given in an upper right hand box in the cell.

D1 D2 D3 Supply

S1 15 30 20 50

S2 30 40 35 30

Demand 25 45 10

95

To solve the transportation problem by its special purpose algorithm, the sum of the

supplies at the origins must equal the sum of the demands at the destinations (Balanced

transportation problem).

• If the total supply is greater than the total demand, a dummy destination is added

with demand equal to the excess supply, and shipping costs from all origins are

zero.

• Similarly, if total supply is less than total demand, a dummy origin is added. The

supply at the dummy origin is equal to the difference of the total supply and the

total demand.

The costs associated with the dummy origin are equal to zero.

When solving a transportation problem by its special purpose algorithm, unacceptable

shipping routes are given a cost of +M (a large number).

9.2. Variants of the Simplex Method

In this section, we present certain complications encountered in the application of the

simplex method and how they are resolved. These are called the variants of simplex

method. We can illustrate the typical cases through numerical examples. The following

variants are being considered.

i. Minimization

ii. Inequality in the wrong direction

iii. Degeneracy

iv. Unbounded solution

v. Multiple solutions

vi. Non-existing feasible solution

vii. Unrestricted variables

9.2.1. Simplex Method

The simplex method generates a sequence of feasible iterates by repeatedly moving from

one vertex of the feasible set to an adjacent vertex with a lower value of the objective

function. When it is not possible to find an adjoining vertex with a lower value, the

current vertex must be optimal, and termination occurs.

96

Example 9.2:

A firm owns facilities at six places. It has manufacturing plants at places A, B and C with

daily production of 50, 40 and 60 units respectively. At point D, E and F it has three

warehouses with daily demands of 20, 95 and 35 units respectively. Per unit shipping

costs are given in the following table. If the firm wants to minimize its total

transportation cost, how should it route its products?

Warehouse

D E F

Plant

A 6 4 1

B 3 8 7

C 4 4 2

Using the Simplex Method,

The given problem can be expressed as an LPP as follows:

Let xij represent the number of units shipped from plant i to warehouse j. Let Z

representing the total cost, it can state the problem as follows.

The objective function is to,

Minimise Z = 6x11+4x12+1x13+3x21+8x22+7x23+4x31+4x32+2x33

Subject to constrains:

x11+x12+x13 =50 x11+x21+x31 =20

x21+x22+x23 =40 x12+x22+x32 =95

x31+x32+x33 =60 x13+x23+x33=35

xij≥0 for i=1,2,3 and j=1,2,3

Using Simplex method, the solution is going to be very lengthy and a cumbersome

process because of the involvement of a large number of decision and artificial variables.

Hence, for an alternate solution, procedure called the transportation method which is an

efficient one that yields results faster and with less computational effort.

97

9.2.2. Transportation Method

The transportation method consists of the following three steps.

1. Obtaining an initial solution, and making an initial assignment in such a way that a

basic feasible solution is obtained.

2. Ascertaining whether it is optimal or not, by determining opportunity costs

associated with the empty cells, and if the solution is not optimal.

3. Revising the solution until an optimal solution is obtained.

9.2.3. Methods for Obtaining Basic Feasible Solution for Transportation Problem

The first step in using the transportation method is to obtain a feasible solution, namely,

the one that satisfies the rim requirements (i.e. the requirements of demand and supply).

The initial feasible solution can be obtained by several methods. The commonly used are:

i. North – west Corner Method

ii. Least Cost Method (LCM)

iii. Vogel’s Approximation Method (VAM)

These will be discussed in subsequent chapters.



1. The transportation problem is concerned with finding the minimum cost of

transporting a single commodity from a given number of sources (e.g. factories) to

a given number of destinations (e.g. warehouses). The data of the model include;

the level of supply at each source and the amount of demand at each destination

and the unittransportation cost of the commodity from each source to each

destination.

2. A transportation problem can be solved by two methods. These are;

a. Simplex Method and

b. Transportation Method.

• North – west Corner Method

• Least Cost Method (LCM)

� Vogel’s Approximation Method (VAM)

98






Fill the blanks in the statement provided below with the appropriate keywords

In the basis of transportation problem, the sources from which we need to transport refer

the _______ while the destination where commodities arrive referred the _________.


Based on what you have learnt in this lecture, shed more light on transportation problem

by laying emphasis on the types.


Identify some of the variants of simplex method in transportation problem.


In adopting a transportation method for resource allocation, what are some of those steps

you need to keep yourself abreast of?

References

Hira, D.S. 2004; Operation Research, S.Chand & Company Ltd., New Delhi.

Taha, H A, 2003; Operation Research - An Introduction, Prentice Hall of India, 7th

edition.

Ravindran, Phillips and Solberg, Operations Research : Principles and Practice, John

Wiely & Sons, 2nd Edition

99

Study Session Ten: Resource Allocation/Assignment: Transportation

Problem II (North-West Rule Model)


Introduction

You are welcome back to EME 302 class. This lecture is a continuation of the topic we

started in the last 2 lectures. I urge you follow along as usual. The North-West rule is

another transportation method used solving problems most especially in determining the

feasible solution of transportation problems



10.1. State the steps involved in the use of NWCR.(SAQ 10.1)

10.2. Determine the initial feasible solution by North West Corner Method.

(SAQ 10.2)

10.1. Overview and Meaning of the North-West Rule Model (NWRM)

10.1.1. Overview of the North-West Rule Model

The method is the simplest but most inefficient as it has the highest total transportation

cost in comparison to all other methods. The main reason that can be attributed to this is

that the method does not consider the cost of transportation for all the possible alternative

routes.

10.1.2. North-West Corner Method (NWCM)

The North-West Corner Rule or North-West Rule Model is a method for computing a

basic feasible solution of a transportation problem where the basic variables are selected

from the North – West corner (i.e., top left corner).

As we proceed in this lecture, let us examine the steps involved in this method. These are;

100

1. Select the north west (upper left-hand) corner cell of the transportation table and

allocate as many units as possible equal to the minimum between available supply

and demand requirements, i.e., min (s1, d1).

2. Adjust the supply and demand numbers in the respective rows and columns

allocation.

3. If the supply for the first row is exhausted, then move down to the first cell in the

second row.

4. If the demand for the first cell is satisfied, then move horizontally to the next cell

in the second column.

5. If for any cell supply equals demand, then the next allocation can be made in cell

either in the next row or column.

6. Continue the procedure until the total available quantity is fully allocated to the

cells as required.

Box 10.1. North West Corner Method (NWCM)

The North-West Corner Rule or North-West Rule Model is a method for computing a basic feasible

solution of a transportation problem where the basic variables are selected from the North – West corner

(i.e., top left corner).

Example 10.1:

Basic Feasible Solution Using North-West Corner Method

Table 10.1

Warehouse

D E F

Plant

A 6 4 1

B 3 8 7

C 4 4 2

The table 10.2 above this leads to table 10.2 below

101

Table 10.2

From To D E F Supply

A

6

4

1 50

B 3

8

7 40

C 4

4

2

60

Demand 20 95 35 150

Total Cost: (6*20) + (4*30) + (8*40) + (4*25) + (2*35) = N730

This routing of the units meets all the rim requirements and entails 5 (=m+n-1 =3+3-1)

shipments as there are 5 occupied cells; It involves a total cost of N730.

Consider the problem represented by the following transportation tableau. The number in

the bottom right of cell (i; j) is cij, the cost of transporting 1 unit from source i to

destination j. Values of xij, the quantity actually transported from source i to estimation j,

will be entered in the top left of each cell. Note that there are 3 factories and 4

warehouses and so m = 3, n = 4.

W1 W2 W3 W4 Supply

F1 10 0 20 11 20

F2 12 7 9 20 25

F3 0 14 16 18 15

Demand 10 15 15 20

For the above example:

• x11 = 10. Cross out column 1. The amount left in row 1 is 10.

• x12 = 10. Cross out row 1. 5 units are left in column 2.

• x22 = 5. Cross out column 2. 20 units are left in row 2.

• x23 = 15. Cross out column 3. 5 units are left in row 2.

20 30

40

25 35

102

Only column 4 is now left and so both the remaining variables x24 and x34 will be basic.

The only feasible allocation of the 5 units in row 2 and the 15 units in row 3is to allocate

x24 = 5 and x34 = 15, which also ensures that the demand in column 4 is satisfied.

This provides the initial basic feasible solution x11 = 10, x12 = 10, x22 = 5, x23 = 15, x24 = 5,

x34 = 15. The remaining variables are non-basic and therefore equal to zero.

They must always add up to the total supply and demand in each row and column.

Note that some books position the data differently in the cells of the table.

Example10.2:

Solve the Transportation Table to find Initial Basic Feasible Solution using North-West Corner Method.

Total Cost =19*5+30*2+30*6+40*3+70*4+20*14

= N1015

Supply

19 30 50 10

5 2

70 30 40 60

6 3

40 8 70 20

4 14

Demand 34

S1

S2

S3

7

9

18

5 8 7 14

D1 D2 D3 D4

103

Initial table developed using Northwest Corner Method

Total Cost = 12(400)+13(100)+4(700)+9(100) +12(200) +4(500) = 142,000



1. The North-West Corner Rule or North-West Rule Model is a method for

computing a basic feasible solution of a transportation problem where the basic

variables are selected from the North – West corner (i.e., top left corner).

2. The North-West Corner Methodgenerates an initial allocation according to the

following procedure:

• Allocate the maximum amount allowable by the supply and demand

constraints to the variable x11 (i.e. the cell in the top left corner of the

transportation tableau).

• If a column (or row) is satisfied, cross it out. The remaining decision

variables in that column (or row) are non-basic and are set equal to zero. If

a row and column are satisfied simultaneously, cross only one out (it does

not matter which).

• Adjust supply and demand for the non-crossed out rows and columns.

• Allocate the maximum feasible amount to the first available non-crossed

out element in the next column (or row).

• When exactly one row or column is left, all the remaining variables are

basic and are assigned the only feasible allocation.

104






Identify the steps needed to guide you in the usage of the North-West Corner Rule or

North-West Rule Model.


1. The NWCR algorithm applied to this problem resulted to the following table for questions 1 to 3:

Destination

Plant X Y W Z Supply

A 21 18 27 22 50

B 19 18 24 20 60

C 24 25 28 25 50

Demand 50 70 30 10 160

Using the North-West corner method;

a. find the total cost?

b. What is allocated to cell X11?

c. What is the allocated to cell X34?

2. Determine the initial feasible solution by North West Corner Method

Factory Warehouse Factory

Capacities A B C D E

X 5 8 6 4 3 800

Y 4 7 8 6 5 600

Z 8 4 7 5 6 1100

Warehouse

Requirements

350 425 500 650 575 2500

Using the North-West corner method, find the total cost?

105

References

Ahmad, Hlayel Abdallah. 2012 "The Best Candidates Method for Solving Optimization

Problems." Journal of Computer Science, 711-715.

Sudhakar, V.J, Arunnsankar N, Karpagam T. 2012. A new approach for find an Optimal

Solution for Trasportation Problems, European Journal of Scientific Research 68

254-257.

Turkey, Mertin. 2008 "NEW ALTERNATE METHODS OF TRANSPORTATION."

transportation problem, 1008-1012.

106

Study Session Eleven: Resource Allocation/Assignment: Least-Cost

Method


Introduction

Hello, I hope you have been getting equipped with the skills and steps needed when using

the Transportation Problem in resource allocation. In the last lecture, we examined the

North-West Corner Model (NWCM) used in solving problems most especially in

determining the feasible solution of transportation problems. As we continue our

discussion on this topic, the method we are examining now is the Least-cost method

which is another transportation method used in solving problems most especially in

determining the feasible solution of transportation problems.



11.1. State the steps involved in the use of Least-cost Method.(SAQ 11.1.)

11.3. Determine the feasible solution of transportation problems in Least-cost

method in solving resource allocation problems.(SAQ 11.2.)

11.1. Least Cost Method in Resource Allocation

Least-Cost Method is also known as Minimum Cell-Cost Method or as the Matrix

Minima Methods.This method usually provides a better initial basic feasible solution than

the North-West Corner method since it considers the cost variables in the problem.

Let us consider the steps in the method. We have;

1. Assign as much as possible to the cell with the smallest unit cost in the entire

table. If there is a tie, then choose arbitrarily.

2. Cross out the row or column which has satisfied supply or demand. If a row and

column are both satisfied, then cross out only one of them.

3. Adjust the supply and demand for those rows and columns which are not crossed

107

out.

4. When exactly one row or column is left, all the remaining variables are basic and

are assigned the only feasible allocation.

Example 11.1

W1 W2 W3 W4 Supply

F1 10 0 20 11 20

F2 12 7 9 20 25

F3 0 14 16 18 15

Demand 10 15 15 20

For the above example:

• Cells (1; 2) and (3; 1) both have zero cost so we arbitrarily choose the first and

assign




• Only column 4 is now left and so all the variables in this column will be basic. The

• Only feasible allocation is x14 = 5, x24 = 10 and x34 = 5.

This provides the initial basic feasible solution x12 = 15, x31 = 10, x23 = 15, x14 = 5, x24 =

10, x34 = 5. All the other variables are non-basic and are therefore equal to zero.

Again, we have 6 basic variables as required.

In-text Question

• What are the other names used instead of the Least-cost Method?

o It is also known as Minimum Cell-Cost Method or as the Matrix Minima

Methods.

At this point, let us also examine the minimum cell-cost method

11.1.1. Minimum Cell-Cost Method

Although the North-west Corner Rule is the easiest, it is not the most attractive because our objective is

not included in the process.

108

Steps of Minimum Cell-Cost Method

The steps involved in this method are;

1. Select the cell with the minimum cell cost in the tableau and allocate as much to

this cell as possible, but within the supply and demand constraints.

2. Select the cell with the next minimum cell-cost and allocate as much to this cell as

possible within the demand and supply constraints.

3. Continue the procedure until all the supply and demand requirements are satisfied.

In a case of tied minimum cell-costs between two or more cells, the tie can be

broken by selecting the cell that can accommodate the greater quantity.

Initial tableau developed using Minimum Cell-Cost Method

Total Cost = 12(300)+4(200)+4(700)+10(100)+9(200)+4(500)= 120,000

Box 11.1. Steps in Least- cost method of Resource Allocation

The steps here are;

1. Assign as much as possible to the cell with the smallest unit cost in the entire table. If

there is a tie, then choose arbitrarily.



3. Adjust the supply and demand for those rows and columns which are not crossed out.

4. When exactly one row or column is left, all the remaining variables are basic and are

assigned the only feasible allocation.

109

11.1.2. MODI Method (for obtaining reduced costs)

Associate a number, ui, with each row and vj with each column.

The steps under this method are;

• Step 1: Set u1 = 0.

• Step 2: Calculate the remaining ui’s and vj’s by solving the relationship cij = ui +

vj for occupied cells.

• Step 3: For unoccupied cells (i,j), the reduced cost = cij – ui – vj.

Step 1: For each unoccupied cell, calculate the reduced cost by the MODI method. Select

the unoccupied cell with the most negative reduced cost. (For maximization problems

select the unoccupied cell with the largest reduced cost.) If none, STOP.

Step 2: For this unoccupied cell, generate a stepping stone path by forming a closed loop

with this cell and occupied cells by drawing connecting alternating horizontal and vertical

lines between them. Determine the minimum allocation where a subtraction is to be made

along this path.

Step 3: Add this allocation to all cells where additions are to be made, and subtract this

allocation to all cells where subtractions are to be made along the stepping stone path.

(Note: An occupied cell on the stepping stone path now becomes 0 (unoccupied). If more

than one cell becomes 0, make only one unoccupied; make the others occupied with 0′s.)

110

Refer to Step 1

Example 11.2:

Acme Block Co. (ABC)

Acme Block Company has orders for 80 tons of concrete blocks at three suburban

locations as follows: Northwood — 25 tons, Westwood — 45 tons, and Eastwood — 10

tons. Acme has two plants, each of which can produce 50 tons per week. Delivery cost

per ton from each plant to each suburban location is shown below.

How should end of week shipments be made to fill the above orders?

Since total supply = 100 and total demand = 80, a dummy destination is created with

demand of 20 and 0 unit costs.

Iteration 1: Tie for least cost (0), arbitrarily select x14. Allocate 20. Reduce s1 by 20 to

30 and delete the Dummy column.

Iteration 2: Of the remaining cells the least cost is 24 for x11. Allocate 25. Reduce s1 by

25 to 5 and eliminate the Northwood column.

Iteration 3: Of the remaining cells the least cost is 30 for x12. Allocate 5. Reduce the

Westwood column to 40 and eliminate the Plant 1 row.

Iteration 4: Since there is only one row with two cells left, make the final allocations of

40 and 10 to x22 and x23, respectively.

111

Matrix minimum method is a method for computing a basic feasible solution of a

transportation problem where the basic variables are chosen according to the unit cost of

transportation.

The steps are;

1. Identify the box having minimum unit transportation cost (cij).

2. If there are two or more minimum costs, select the row and the column

corresponding to the lower numbered row.

3. If they appear in the same row, select the lower numbered column.

4. Choose the value of the corresponding xij as much as possible subject to the

capacity and requirement constraints.

5. If demand is satisfied, delete that column.

6. If supply is exhausted, delete that row.

7. Repeat steps 1-6 until all restrictions are satisfied.

Table 11.1 Basic Feasible Solution Using Least Cost Method of Example

Warehouse

D E F

Plant

A 6 4 1

B 3 8 7

C 4 4 2

The table 11.1 above this leads to table11. 2 below

Table 11.2

From To D E F Supply

A

6

4

1 50

B 3

8

7 40

C 4

4

2

60

Demand 20 95 35 150

Total Cost: 3*20 + 4*15 + 8*20 +4*60 + 1*35 = N555

This routing of the units meets all the rim requirements and entails 5 (=m+n-1 =3+3-1)


20

15

20

60

35

112

Follow these steps:

Step1: Select the cell having lowest unit cost in the entire table and allocate the

minimum of supply or demand values in that cell.

Step2: Then eliminate the row or column in which supply or demand is exhausted. If

both the supply and demand values are same, either of the row or column can be

eliminated.In case, the smallest unit cost is not unique, then select the cell where

maximum allocation can be made.

Step3: Repeat the process with next lowest unit cost and continue until the entire

available supply at various sources and demand at various destinations is

satisfied.

Next

Next

Next

Supply

19 30 50 10

70 30 40 60

40 8 70 20

8

Demand 34

S3 18

5 8 7 14

S1 7

S2 9

D1 D2 D3 D4

Supply

19 50 10

7

70 40 60

40 70 20

Demand 34

D1 D3 D4

7 14

7

9

S1

S2

S3 10

5

Supply

70 40 60

40 70 20

7

Demand 34

S3 10

5 7 7

S2 9

D1 D3 D4

Supply

70 40

7

40 70

Demand 347

S2

D1 D3

9

3S3

5

113

Next

The total transportation cost obtained by this method =

8*8+10*7+20*7+40*7+70*2+40*3

= N814

Here, we can see that the Least Cost Method involves a lower cost than the North-West

Corner Method.



1. Least-Cost Method is also known as Minimum Cell-Cost Method.This method

usually provides a better initial basic feasible solution than the North-West Corner

method since it considers the cost variables in the problem.

2. The steps under this method are;

• Assign as much as possible to the cell with the smallest unit cost in the entire

tableau. If there is a tie, then choose arbitrarily.

• Cross out the row or column which has satisfied supply or demand. If a row

and column are both satisfied, then cross out only one of them.

• Adjust the supply and demand for those rows and columns which are not

crossed out.

• When exactly one row or column is left, all the remaining variables are basic

and are assigned the only feasible allocation.





Supply

70

2

40

3

Demand 345

S2 2

S3 3

D1

114


As an expert in resource allocation, in using the Least-cost method in determining the

feasible solution of transportation problems, what are those steps that must be followed

rigidly?


For the transportation problem given by the following table, find an initial basic feasible

solution by the least-cost method and then find an optimal solution.

Supply

2 1 3 7

4 5 6 8

Demand 5 6 4

115

Study SessionTwelve: Resource Allocation/Assignment:

(Vogel’s Approximation Method)


Introduction

In the last 3 lectures, we have been examining the Transportation Problem Method in

resource allocation. As stated earlier, we have different methods used in solving problems

most especially in determining the feasible solution of transportation problems. Another

approach we can also use in realising this objective is the Vogel approximation method.

In this lecture, we shall be considering Vogel approximation method and the steps needed

when working with this method.



12.1. Outline the steps involved in the use of Vogel approximation Method.

(SAQ 12.1.)

12.2. Determine the feasible solution of transportation problems using Vogel’s

method.(SAQ 12.2.)

12.1. Vogel’s Approximation Method in Resource Allocation

Vogel approximation method is also known as the Unit Cost Penalty Method. The Vogel

approximation method is an iterative procedure for computing a basic feasible solution of

the transportation problem. Another way of finding an initial solution to problem is

through the Vogel’s Approximation method which is as simple as the North-west corner

method. It is associated with cost, which is an important concept in Educational Planning.

In addition to the northwest corner and intuitive lowest-cost methods of setting an initial

solution to transportation problems, we introduce one other important technique Vogel’s

116

Approximation method(VAM). VAM is not quite as simple as the northwest corner

approach, but it facilitates a very good initial solution as a matter of fact, one that is often

the optimal solution.

Vogel’s Approximation method tackles the problem of finding a good initial solution by

considering the costs associated with each route alternative. This is something that the

northwest corner rule did not do. To apply the VAM, we first compute for each row and

column the penalty faced if we should ship over the second-bestroute instead of the least-

cost route.Vogel’s Approximation is another method used in making decision.

The method is structured with various steps for its usage. These steps are;

1. Identify the boxes having minimum and next to minimum transportation cost in

each row and write the difference (penalty) along the side of the table against the

corresponding row.

2. Identify the boxes having minimum and next to minimum transportation cost

ineach column and write the difference (penalty) against the corresponding

column.

3. Identify the maximum penalty. If it is along the side of the table, make maximum

allotment to the box having minimum cost of transportation in that row. If it is

below the table, make maximum allotment to the box having minimum cost of

transportation in that column.

4. If the penalties corresponding to two or more rows or columns are equal, select the

top most row and the extreme left column.

In-text Question

• Do you think Vogel Approximation Method (VAM) is quite simpler that the

North-West Corner Approach?

o No, VAM is not quite as simple as the northwest corner approach, but it

facilitates a very good initial solution as a matter of fact, one that is often the

optimal solution.

117

Table 12. Basic Feasible Solution Using Vogel’s Approximation Method of Example

Warehouse

D E F

Plant

A 6 4 1

B 3 8 7

C 4 4 2

The table 12.1 leads to table 12.2 below

Table 12.2

D E F Supply Iteration

From To I II

A

6

4

1

50 3 3

B

3

8

7

40 4 1

C

4

4

2 60 2 2

Demand 20 95 35 150

I 1 0 1

II - 0 1

Total Cost: 3*20 + 4*15 + 8*20 +4*60 + 1*35 = N555

This routing of the units meets all the rim requirements and entails 5 (=m+n-1 = 3+3-1)


Box 12.1. Vogel’s Approximation Method

Vogel’s Approximation method tackles the problem of finding a good initial solution by considering the

costs associated with each route alternative. This is something that the northwest corner rule did not do.

To apply the VAM, we first compute for each row and column the penalty faced if we should ship over

the second-best route instead of the least-cost route.

Other ways to get this done are;

Step1: Calculate penalty for each row and column by taking the difference between the

two smallest unit costs. This penalty or extra cost must be paid if one fails to

20 20

60

35 15

118

allocate the minimum unit transportation cost.

Step2: Select the row or column with the highest penalty and select the minimum unit

cost of that row or column. Then, allocate the minimum of supply or demand

values in that cell. If there is a tie, then select the cell where maximum allocation

could be made.

Step3: Adjust the supply and demand and eliminate the satisfied row or column. If a

row and column are satisfied simultaneously, only of them is eliminated and the

other one is assigned a zero value. Any row or column having zero supply or

demand, cannot be used in calculating future penalties.

Step4: Repeat the process until all the supply sources and demand destinations are

satisfied.

Supply Row Diff.

19 30 50 10

70 30 40 60

40 8 70 20

8

Demand 34

Col.Diff.

D4

14

S3

5 8 7

D1 D2 D3

S1

S2

21 22 10 10

9

10

12

7

9

18

Supply Row Diff.

19 50 10

5

70 40 60

40 70 20

Demand 34

Col.Diff.

9

20

20

21 10

S2 9

S3 10

5 7 14

D1 D3 D4

S1 7

10

119

The total transportation cost obtained by this method =

8*8+19*5+20*10+10*2+40*7+60*2

= N779

Here, we can see that Vogel’s Approximation Method involves the lowest cost than

North-West Corner Method and Least Cost Method and hence is the most preferred

method of finding initial basic feasible solution.

Summary ofSession 12


1. Vogel approximation method is also known as the Unit Cost Penalty Method. The

Vogel approximation method is an iterative procedure for computing a basic

feasible solution of the transportation problem.

2. The steps in this method are;

• Step1: Calculate penalty for each row and column by taking the difference

between the two smallest unit costs. This penalty or extra cost must be paid if

one fails to allocate the minimum unit transportation cost.

Supply Row Diff.

50 10

40 60

70 20

10

Demand 34

Col.Diff.

147

S1 2

S2 9

S3 10

D3 D4

40

20

50

10 10

Supply Row Diff.

50 10

2

40 60

Demand 34

Col.Diff.

D3 D4

S1 2

S2 9

7 4

20

10 50

40

Supply Row Diff.

40 60

7 2

Demand 34

Col.Diff.

S2 9

D3 D4

7 2

20

120

• Step2: Select the row or column with the highest penalty and select the

minimum unit cost of that row or column. Then, allocate the minimum of

supply or demand values in that cell. If there is a tie, then select the cell where

maximum allocation could be made.

• Step3: Adjust the supply and demand and eliminate the satisfied row or

column. If a row and column are satisfied simultaneously, only of them is

eliminated and the other one is assigned a zero value. Any row or column

having zero supply or demand, cannot be used in calculating future penalties.

• Step4: Repeat the process until all the supply sources and demand destinations

are satisfied.






Based on the knowledge you have gained in this lecture, what are some of the steps

needed when using the Vogel’s Approximation Method (VAM) in resource allocation?


1. A company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and

W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly

warehouse requirements are 180, 120 and 150 units, respectively. Unit shipping costs

(in Naira) are as follows:

W1 W2 W3 W4

F1 16 20 12 200

F2 14 8 18 160

F3 26 24 16 90

Demand 180 120 150 450

Using the Vogel approximation Method, Determine the optimal distribution for this

company to minimize total shipping cost.

a. 5920

121

b. 6460

c. 6600

d. None of the above

2. The following table shows all the necessary information on the availability of supply

to each warehouse, the requirement of each market and unit transportation cost (in N)

from each warehouse to each market.

Market Supply

P Q R S

Warehouse A 6 3 5 4 22

B 5 9 2 7 15

C 5 7 8 6 8

Demand 7 12 17 9 45

Determine cost value for this transportation problem by using the Vogel approximation Method.

a. 176 b. 150 c. 149 d. None of the above

References

Dwivedi, R. K., Mehta, N. N. and Dubey, O. P., 2009; Interactive Decision Making in

Prioritized Unbalanced Transportation Problems. The Icfai University Journal of

Operations Management, Vol. 8, No. 1, pp. 67-76. Available at SSRN:

http://ssrn.com/abstract=1344168

Goval, S. K. 1984, Improving VAM for unbalance transportation problems, Journal of

Operational Research Society 35, 1113-1114

Pearman, A. D., (1974) Two Errors in Quandt’s Model of Transportation and Optimal

Network Construction Journal of the Regional Science Association, 14, 281-286.

122

Study Session Thirteen: Model in Education

Expected duration: 2 weeksor 4 contact hours

Introduction

I welcome you back from the series of lectures you just concluded on resource allocation.

I want to implore you to attempt the SAQs provided as practice questions to master the

skills required. For this lecture, we shall be focusing on the Models in Education. Most

operations research models are symbolic models because symbols represent properties of

the system. The earliest models were physical representations such as model ships,

airplanes, tow tanks, and wind tunnels. Physical models are usually easy to construct, but

only for relatively simple objects or systems, and are usually difficult to change. The

model is meant for organizations. For organizations that wants to focus on quality in a

systematic way. The models can be applied in any type or organization: large and small,

profit and non-profit, local and international.




13.2. Describe the constituents of a model. (SAQ 13.2)

13.3. Identify the basic activities when deriving solutions from model. (SAQ

13.3)

13.4. Highlight the processes involved in building a model. (SAQ 13.4)

13.5. Make a list of the steps available in Lewin, Mckinsey, and Kotter’s Change

Management Model. (SAQ 13.5)

Key words; model, management model, symbolic models, analogue, physical model,

graphic model, deductive, and inductive.

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13.1. Meaning of a Model

A model is a simplified representation of the real world and as such includes only those

variables relevant to the problem at hand. A model of freely falling bodies, for example

does not refer to the colour, texture, or shape of the body involved. Furthermore, a model

may not include all relevant variables because a small percentage of these may account

for most of the phenomenon to be explained. Many of the simplifications used produce

some error in predictions derived from the model, but these can often be kept small

compared to the magnitude of the improvement in operations that can be extracted from

them.

Please note that aManagement Model is simply the set of choices made by executives

about how the work of management gets done about how they define objectives, motivate

effort, coordinate activities, and allocate resources. The physical model takes the form of

graph, easier to construct and manipulate but more abstract. Since graphic representation

of more than three variables is difficult, symbolic models came into use. There is no limit

to the number of variables that can be included in a symbolic model, and such models are

easier to construct and manipulate than physical models.

A management model is the choices made by organisation’s top executives regarding

how they define objectives, motivate effort, coordinate activities and allocate resources;

in other words, how they define the work of management. Inspired by changes in the

expectations of their employees, new technological capabilities and the offerings of

emerging competitors, some companies are discovering that a distinctive management

model can itself be a key driver of its competitiveness.

For Symbolic models, they are completely abstract. When the symbols in a model are

defined, the model is given content or meaning. This has important consequences.

Symbolic models of systems of very different content often reveal similar structure.

Hence, most systems and problems arising in them can be fruitfully classified in terms of

relatively few structures. Furthermore, since methods of extracting solutions from models

depend only on their structure, some methods can be used to solve a wide variety of

problems from a contextual point of view. Finally, a system that has the same structure as

124

another, may be different in content can be used as a model of the other. Such a model is

called an analogue. By use of such models much of what is known about the first system

can be applied to the second.Despite the obvious advantages of symbolic models there

are many cases in which physical models are still useful, as in testing physical structures

and mechanisms; the same is true for graphic models. Physical and graphic models are

frequently used in the preliminary phases of constructing symbolic models of systems.

In-text Question

• How would you describe a management model based on what you have learnt in

this lecture?

o Management Model is simply the set of choices made by executives about how

the work of management gets done, how they define objectives, motivate

effort, coordinate activities, and allocate resources.

Let us proceed on our discussion on the meaning of a model;

Operations research models represent the causal relationship between the controlled

and uncontrolled variables and system performance; they must therefore be explanatory,

not merely descriptive. Only explanatory models can provide the requisite means to

manipulate the system to produce desired changes in performance.Operations research

analysis is directed toward establishing cause-and-effect relations. Though experiments

with actual operations of all or part of a system are often useful, these are not the only

way to analyze cause and effect. There are four patterns of model construction, only two

of which involve experimentation: inspection, use of analogues, operational analysis, and

operational experiments. They are considered here in order of increasing complexity. In

some cases, the system and its problem are relatively simple and can be grasped either by

inspection or from discussion with persons familiar with it. In general, only low-level and

repetitive operating problems, those in which human behaviour plays a minor role can be

so treated.

Another point you need to register here is that, when the researcher finds it difficult to

represent the structure of a system symbolically, it is sometimes possible to establish a

similarity, if not an identity, with another system whose structure is better known and

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easier to manipulate. It may then be possible to use either the analogous system itself or a

symbolic model of it as a model of the problem system. For example, an equation derived

from the kinetic theory of gases has been used as a model of the movement of trains

between two classification yards. Hydraulic analogues of economies and electronic

analogues of automotive traffic have been constructed with which experimentation could

be carried out to determine the effects of manipulation of controllable variables. Thus,

analogues may be constructed as well as found in existing systems.In some cases,

analysis of actual operations of a system may reveal its causal structure. Data on

operations are analyzed to yield an explanatory hypothesis which is tested by analysis of

operating data. Such testing may lead to revision of the hypothesis. The cycle is

continued until a satisfactory explanatory model is developed.

For example, an analysis of the cars stopping at urban automotive service stations located

at intersections of two streets revealed that almost all came from four of the 16 possible

routes through the intersection (four ways of entering times four ways of leaving).

Examination of the percentage of cars in each route that stopped for service suggested

that this percentage was related to the amount of time lost by stopping. Data were then

collected on time lost by cars in each route. This revealed a close inverse relationship

between the percentage stopping and time lost. But the relationship was not linear; that is,

the increases in one were not proportional to increases in the other. It was then found that

perceived lost time exceeded actual lost time, and the relationship between the percentage

of cars stopping and perceived lost time was close and linear. The hypothesis was

systematically tested and verified and a model constructed that related the number of cars

stopping at service stations to the amount of traffic in each route through its intersection

and to characteristics of the station that affect the time required to get service.

In situations where it is not possible to isolate the effects of individual variables by

analysis of operating data, it may be necessary to resort to operational experiments to

determine which variables are relevant and how they affect system performance.

Such is the case, for example, in attempts to quantify the effects of advertising (amount,

timing, and media used) upon sales of a consumer product. Advertising by the producer is

only one of many controlled and uncontrolled variables affecting sales. Hence, in many

126

cases its effect can only be isolated and measured by controlled experiments in the field.

The same is true in determining how the size, shape, weight, and price of a food product

affect its sales. In this case laboratory experiments on samples of consumers can be used

in preliminary stages, but field experiments are eventually necessary. Experiments do not

yield explanatory theories, however. They can only be used to test explanatory

hypotheses formulated before designing the experiment and to suggest additional

hypotheses to be tested.

Box 13.1. Meaning of a Model

There are four patterns of model construction, only two of which involve

experimentation: inspection, use of analogues, operational analysis, and operational

experiments. They are considered here in order of increasing complexity. In some cases,

the system and its problem are relatively simple and can be grasped either by inspection

or from discussion with persons familiar with it. In general, only low-level and repetitive

operating problems, those in which human behaviour plays a minor role can be so treated.

Another point you need to note when describing a model is that it is sometimes necessary

to modify an otherwise acceptable model because it is not possible or practical to find the

numerical values of the variables that appear in it. For example, a model to be used in

guiding the selection of research projects may contain such variables as “the probability

of success of the project,” “expected cost of the project,” and its “expected yield.” But

none of these may be calculable with any reliability. Models not only assist in solving

problems but also are useful in formulating them; that is, models can be used as guides to

explore the structure of a problem and to reveal choices that might otherwise be missed.

In many cases the course of action revealed by such application of a model is so

obviously superior to previously considered possibilities that justification of its choice is

hardly required.

In some cases, the model of a problem may be either too complicated or too large to

solve. It is frequently possible to divide the model into individually solvable parts and to

take the output of one model as an input to another. Since the models are likely to be

interdependent, several repetitions of this process may be necessary.

127

13.2.DerivingSolutionsfromModels

Another aspect of this lecture to be considered now is the derivation of solutions from

models. Procedures for deriving solutions from models are either deductive or inductive.

With deduction one moves directly from the model to a solution in either symbolic or

numerical form. Such procedures are supplied by mathematics; for example, the calculus.

An explicit analytical procedure for finding the solution is called an algorithm. Even if a

model cannot be solved, and many are too complex for solution, it can be used to

compare alternative solutions. It is sometimes possible to conduct a sequence of

comparisons, each suggested by the previous one and each likely to contain a better

alternative than was contained in any previous comparison. Such a solution-seeking

procedure is called heuristic.

Inductive procedures involve trying and comparing different values of the controlled

variables. Such procedures are said to be iterative (repetitive) if they proceed through

successively improved solutions until either an optimal solution is reached or further

calculation cannot be justified. A rational basis for terminating such a process known

as “stopping rules” involves the determination of the point at which the expected

improvement of the solution on the next trial is less than the cost of the trial. Such well-

known algorithms as linear, nonlinear, and dynamic programming are iterative

procedures based on mathematical theory. Simulation and experimental optimization are

iterative procedures based primarily on statistics.

Box. 13.2. Meaning of a Model

Models not only assist in solving problems but also are useful in formulating them; that

is, models can be used as guides to explore the structure of a problem and to reveal

choices that might otherwise be missed. In many cases the course of action revealed by

such application of a model is so obviously superior to previously considered possibilities

that justification of its choice is hardly required.

13.2.1. Testing the Model and the Solution

Let me start by asking you this question. Why do you think a model can be deficient i.e.

not serving the purpose it is meant for? A model may be deficient because it includes

128

irrelevant variables, excludes relevant variables, contains inaccurately evaluated

variables, is incorrectly structured, or contains incorrectly formulated constraints. Tests

for deficiencies of a model are statistical in nature; their use requires knowledge of

sampling and estimation theory, experimental designs, and the theory of hypothesis

testing.

Sampling-estimation theory is concerned with selecting a sample of items from a large

group and using their observed properties to characterize the group. To save time and

money, the sample taken is as small as possible. Several theories of sampling design and

estimation are available, each yielding estimates with different properties.

The structure of a model consists of a function relating the measure of performance to the

controlled and uncontrolled variables; for example, a business may attempt to show the

functional relationship between profit levels (the measure of performance) and controlled

variables (prices, amount spent on advertising) and uncontrolled variables (economic

conditions, competition). To test the model, values of the measure of performance

computed from the model are compared with actual values under different sets of

conditions. If there is a significant difference between these values, or if the variability of

these differences is large, the model requires repair. Such tests do not use data that have

been used in constructing the model, because to do so would determine how well the

model fits performance data from which it has been derived, not how well it predicts

performance.

Pause to answer this question

In-text Question

• What are some of the factors that can render a model deficient?

o A model may be deficient when it includes irrelevant variables, excludes

relevant variables, contains inaccurately evaluated variables, is incorrectly

structured, or contains incorrectly formulated constraints.

The solution derived from a model is tested to find whether it yields better performance

than some alternative, usually the one in current use. The test may be prospective, against

129

future performance, or retrospective, comparing solutions that would have been obtained

had the model been used in the past with what did happen. If neither prospective nor

retrospective testing is feasible, it may be possible to evaluate the solution by “sensitivity

analysis,” a measurement of the extent to which estimates used in the solution would

have to be in error before the proposed solution performs less satisfactorily than the

alternative decision procedure. The cost of implementing a solution should be subtracted

from the gain expected from applying it, thus obtaining an estimate of net improvement.

In a situation where errors or inefficiencies in applying the solution are possible, these

should also be considered in estimating the net improvement.

Fig 13.1. The four dimensions of Management

Image source: http://www.managementexchange.com/blog/what-your-management-model

If you take a good look at Fig 13.1., you will note that for each of the four dimensions, it

is possible to identify different principles by which that activity is undertaken. On the left

side, we see what might be called "traditional" principles that everyone can recognize. On

the right side, we see "alternative" principles that are less well-known but are arguably

more relevant to today’s fast-moving business environment. The 4 dimensions of

management are;

i. Choices about how activities are coordinated in the firm. Do managers focus on

using formal and well-structured management processes to deliver outputs? Or do

they encourage a process of informal and spontaneous coordination through

mutual adjustment?

ii. Choices about how decisions are made in the firm. Do managers take personal

responsibility for decision making, and rely primarily on their own deep

130

knowledge and experience? Or do they prefer to tap into the disparate knowledge

of their subordinates and assign collective responsibility?

iii. Choices about the nature of the objectives the firm pursues. Do managers have a

clear set of short-term goals for the firm? Or do they pursue an oblique, or

indirect, path through the definition of a higher-level and longer-term set of

objectives?

iv. Choices about how individuals are motivated to pursue these objectives. Do

managers attempt to hire and retain good people by making extrinsic rewards,

such as salary, benefits, and bonuses attractive? Or do they focus on intrinsic

rewards such as the opportunity to contribute to society, a feeling of achievement,

or peer recognition?

In-text Question

• In testing the solution derived from a model, identify the dimensions in which

such tests could take?

o The test may be prospective, against future performance, or retrospective,

comparing solutions that would have been obtained had the model been used in

the past with what is obtained.

Box 13.3. The 4 dimensions of management are;

1. Choices about how activities are coordinated in the firm

2. Choices about how decisions are made in the firm

3. Choices about the nature of the objectives the firm pursues

4. Choices about how individuals are motivated to pursue these objectives

13.3. Model Building Process

We are still on our lecture discussing Model in Education. At this point, we are looking at

the Model Building Process.According to Bailey (1981) for the SEL at NASA Goddard

Space Flight Centre. The processes stated here are;

1. Compute the background equation

i. Picking and defining measures of size and effort

ii. Selecting the form of the base-line equation

iii. Calculating an initial base-line for use in the model

131

2. Analyze the factors available to explain the difference between actual effort and

effort as predicted by the background equation

i. Choosing a set of factors (could be a large number >100)

ii. Grouping and compressing this data

iii. Isolating the important factors and groups

iv. Incorporating the factors by performing a multiple regression to predict the

deviations of the points from the computed base-line

3. Use this model to predict the effort for the new project

i. Estimate size of new project

ii. Use base-line to get standard effort

iii. Estimate necessary factor values

iv. Compute difference this project should exhibit

v. Apply that difference to standard effort

At this point, let us consider some of the management models that we have.

13.4. Lewin’s Change Management Model

This change management model was created in the 1950s by psychologist Kurt Lewin.

Lewin noted that most people tend to prefer and operate within certain zones of safety.

He recognized three stages of change. As presented in Fig 13.2., these stages are;

1. Unfreeze – Most people make an active effort to resist change. To overcome this

tendency, a period of thawing or unfreezing must be initiated through motivation.

2. Transition – Once change is initiated, the company moves into a transition period,

which may last for some time. Adequate leadership and reassurance is necessary

for the process to be successful.

3. Refreeze – After change has been accepted and successfully implemented, the

company becomes stable again, and staff refreezes as they operate under the new

guidelines.

While this change management model remains widely used today, it is takes time to

implement. Of course, since it is easy to use, most companies tend to prefer this model to

enact major changes.

132

Fig 13.2. Lewin’s Change Management Model

Image source: http://2012books.lardbucket.org/books/management-principles-v1.0/s11-04-planning-and-executing-

change-.html

Box 13.4. Model Building Processes

The processes are;

1. Compute the background equation.

2. Analyze the factors available to explain the difference between actual effort and effort

as predicted by the background equation.

3. Use this model to predict the effort for the new project.

13.5. McKinsey 7-S Model

The McKinsey 7-S model offers a holistic approach to organization. This model, created

by Robert Waterman, Tom Peters, Richard Pascale, and Anthony Athos during a meeting

in 1978, has 7 factors that operate as collective agent of change as seen in Fig 13.3. These

factors are; shared values; strategy; structure; systems; style; staff and skills.

133

Fig. 13.3. Mc Kinsey 7-S Model

Image source: http://www.slideshare.net/manumelwin/mc-kinsey-7s-model-strategic-implementation-manu-melwin-

joy

13.5.1. The Benefits of McKinsey 7-S Model

You need to note that this model offers the following benefits;

1. It offers an effective method to diagnose and understand an organization.

2. It provides guidance in organizational change.

3. It combines rational and emotional components.

4. All parts are integral and must be addressed in a unified manner.

13.5.2. The Disadvantages of McKinsey 7-S Model are:

1. When one part changes, all parts change, because all factors are interrelated.

2. Differences are ignored.

3. The model is complex.

4. Companies using this model have been known to have a higher incidence of failure.

134

13.6. Kotter’s 8 Step Change Model

Another model we are about to consider here is Kotter’s 8 step Change Model. This

model was created by Harvard University Professor John Kotter, causes change to

become a campaign. Employees buy into the change after leaders convince them of the

urgent need for change to occur. As presented in Fig 13.4., there are 8 steps are involved

in this model.

Fig 13.4. Kotter’s 8 step change model

Image source: https://www.linkedin.com/pulse/using-kotters-8-step-organisational-

change-model-success-riche

As presented in Fig 13.4., the steps available in this model are;

1. Increase the urgency for change.

2. Build a team dedicated to change.

3. Create the vision for change.

4. Communicate the need for change.

5. Empower staff with the ability to change.

6. Create short term goals.

7. Stay persistent.

8. Make the change permanent.

135

Activity 13.1.

Take a good look at the different models discussed during this lecture and make a

schematic representation of each of these models on a cardboard paper showing how the

different steps interact.


Your sketch should clearly indicate the different steps involved in each model.

13.6.1. Advantages of Kotter’s 8 Step Change Model

Significant advantages to the model are:

1. The process is an easy step-by-step model.

2. The focus is on preparing and accepting change, not the actual change.

3. Transition is easier with this model.

13.6.2. Disadvantages of Kotter’s 8 Step Change Model

There are some disadvantages offered by this model. These are;

1. Steps can’t be skipped.

2. The process takes a great deal of time.

It doesn’t matter if the proposed changed is a change in the process of project planning or

general operations. Adjusting to change is difficult for an organization and its employees.

Using almost any model is helpful, because it offers leaders a guideline to follow, along

with the ability to determine expected results. This is helpful because change is difficult

to implement and manage.



1. A model is a simplified representation of the real world and as such includes only

those variables relevant to the problem at hand.

2. There are four patterns of model construction, only two of which involve

experimentation: inspection, use of analogues, operational analysis, and

operational experiments.

136

3. Models not only assist in solving problems but also are useful in formulating

them; that is, models can be used as guides to explore the structure of a problem

and to reveal choices that might otherwise be missed.

4. Procedures for deriving solutions from models are either deductive or inductive.

5. A model may be deficient because it includes irrelevant variables, excludes

relevant variables, contains inaccurately evaluated variables, is incorrectly

structured, or contains incorrectly formulated constraints.

6. The solution derived from a model is tested to find whether it yields better

performance than some alternative, usually the one in current use. The test may be

prospective, against future performance, or retrospective, comparing solutions that

would have been obtained had the model been used in the past with what is

obtainable.

7. A Management Model is simply the set of choices made by executives about how

the work of management gets done about how they define objectives, motivate

effort, coordinate activities, and allocate resources.

8. The four dimensions of management:

• Choices about how activities are coordinated in the firm.

• Choices about how decisions are made in the firm.

• Choices about the nature of the objectives the firm pursues.

• Choices about how individuals are motivated to pursue these objectives.

9. The Model Building Processes are:

• Compute the background equation

• Analyze the factors available to explain the difference between actual effort

and effort as predicted by the background equation

• Use this model to predict the effort for the new project

10. Some of the management models we have are; Lewin's Change Management

Model; Mckinsey 7sModel; Kotter's 8 step change model etc.





137


In the statements provided here, fill the blanks with the most appropriate keywords

a. A _______is a simplified representation of the real world and includes only those

variables relevant to the problem at hand.

b. The choices made by organisation’s top executives regarding how they define

objectives, motivate effort, coordinate activities and allocate resources can be best

described as _________.

c. _________ model is used to describe a system that has the same structure as another

but may be different in content and can be used as a model of the other.

d. _________and ________ models are frequently used in the preliminary phases of

constructing symbolic models of systems.

e. With _______ one moves directly from the model to a solution in either symbolic or

numerical form.

f. __________ procedures involve trying and comparing different values of the

controlled variables.


Using the knowledge gained in this lecture, how would you describe a model in a

managerial context?


One of the chief functions of a model is to derive solution to a problem. In doing this,

what are the procedures involved?


As a manager, model building is a task that is needed to improve productivity in the

organization. To achieve this, how can a model be built?


Based on what you have learnt in this lecture, identify some of the models treated and

state the steps involved.

138

References

Sutton, C.D. (2005). Classification and Regression Trees, Bagging, and Boosting, in

Handbook of Statistics, Vol. 24, pp. 303-329, Elsevier.

Quinlan, J. R. 2006. Bagging, Boosting, and C4.5. In AAAI 96: Proceedings of the 13th

National. Conference on Artificial Intelligence (Vol. 2, pp. 725–730).

139

Study SessionFourteen: Decision Making Process: PPBS

Expected duration: 2 weeks or 4 contact hours

Introduction

Welcome back to the 14th lecture on EME 302. At this stage, it should not be strange to

you that managers at all organizational levels make decisions although they differ in

terms of type and scope. At the top level of the organization, decisions establishing

overall objectives and strategies are among the most important to be made. Middle level

managers are generally more involved with decisions involving overall operating policies

and plans. First line supervisors in turn, are concerned with short range decisions that

relate to specific activities to be carried out within the framework of policies and plans,

established at middle management levels. In this lecture, you will get to learn more from

the decision-making process in Planning, Programming, Budgeting system.




14.2. Explain what Decision-Making entails. (SAQ 14.2)

14.3. Distinguish clearly between types of decisions. (SAQ 14.3)

14.4. State the procedure of PPBS to organisation’s decision making process.

(SAQ 14.4)

14.5. Outline at least 5 techniques used in decision-making. (SAQ 14.5)

Key words; decision-making, decision-making process, programmed decisions, non-

programmed decisions, and groups.

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14.1. Meaning of Decision Making and Types of Decisions

14.1.1. Meaning of Decision Making

Decision making is so basic that no management function can be performed without it.

For management purposes, decisions are obviously required in planning, organization,

actuating, and controlling.Decision making is the cornerstone of planning because it is

the catalyst that drives the planning process. An organization’s goals follow from

decisions made by various managers. Furthermore, in deciding to adopt the best plan for

achieving goals, decision making basically reflects the selection of the best choice among

possible alternatives and putting it into practice. Effective decision making requires that

the decision maker understands the situation driving the decision. However, it can be

argued that management is simply decision making and that the essence of managerial

behaviour is found by studying decision making. In addition, decision making often

reflects the manager’s effort to make sense of the complicated environment, to attain

some control over the uncontrollable and to achieve some sense of order. Finally, when

an organized approach to decision making is employed, such as having a clear

understanding of the present state of affairs, historical basis for improving decisions, and

the possible errors that can be made, it enables managers to make better decisions and to

reach personal and organizational goals.

Decision making is a continuous process that pervades all organizational activities.

Managers in every type of organization; business; hospital; government and education

make decisions every day. To this extent, understanding what makes an organization

successful depends upon our knowledge of how people make effective decisions. A

decision is defined as a conscious choice among alternative courses of action followed by

activities to implement the choice. Thus, we must recognize that managerial decision

making entails both a process and subsequent action. A decision-making process is a

series or chain of related steps that lead up to an action or an outcome and assessment.

Ivancevich, et al, (1994) explain that decision making can be understood as a series of

steps that run from clearly identifying a problem to implementing and assessing actions.

Using such a systematic approach to decision making ensures that relevant information

has been gathered, alternative choices have been considered, and possible consequences

of actions understood.

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Box 14.1. Decision Making

Note that;

• Effective decision making requires that the decision maker understands the situation

driving the decision. It can be argued that management is simply decision making and

that the essence of managerial behaviour is found by studying decision making.

• A decision-making process is a series or chain of related steps that lead up to an action

or an outcome and assessment.

14.1.2. Types of Decisions

There are basically 2 types of decisions, these are; Programmed and Non-Programmed

Decisions.

1. Programmed Decisions – if a situation occurs often and in the same form, a

routine procedure usually will be worked out for dealing with it. Decisions are

programmed to the extent that they are repetitive and routine. Examples are: the

procedure for opening a bank account; reorder of inexpensive materials; procedure

for admitting patients in hospitals.

2. Non-programmed Decisions – decisions are non-programmed when the problem

is unstructured.

14.2. Planning, Programming, Budgeting System (PPBS)

We have come to another phase in this lecture where we shall examine the PPBS

technique. Output budgeting wide ranging management technique introduced into the

USA in the mid-1960s, not always with ready cooperation with the administrators and

based on the industrial management techniques of program budgeting. Subsequently, the

technique has been introduced into other countries, including the UK where it is often

called output budgeting. PPBS is in effect on integrating of several techniques in a

planning and budgeting process for identifying, costing and assigning a complexity of

resources for establishing priorities and strategies in a major program and for forecasting

costs, expenditure and achievements within the immediate financial year or over a longer

period.Some of the procedures of PPBS are discussed afterwards.

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14.2.1. Decision-Making under states of Certainty, Uncertainty and Risk

It is essential for you to know that decision-making can fall under 3 states as it will be

discussed below. We have;

1. Decision making certainty:When decision maker knows with certainty the

probabilities of the outcomes of each alternative and what conditions are

associated with each alternative, the decision is said to be under certainty. An

example of this type of decision is a decision to purchase items from a supplier

that regularly supplies the items.

2. Decisions making under uncertainty: When the decisions maker has absolutely

no knowledge of the probabilities of the outcomes of each alternative, the risks

associated with each, or the consequences each alternative is likely to have.

3. Decisions making under risk: When the decisions maker has some probabilistic

estimate of the outcomes of each alternative.

In-text Question

• Based on what you have learnt, how would you describe around procedures such

as the procedure for opening a bank account; reorder of inexpensive materials;

procedure for admitting patients in hospitals.

o These are called programmed decisions.

14.2.2. Proactive and Reactive Decisions

Another point you need to know under PPBS is that decisions can be viewed from 2

perspectives such as;

1. Proactive Decisions: A decision made in anticipation of a change in the external

environment or other condition is called a proactive decision. Managers who

utilize a systematic, proactive approach anticipate problems and seek to prevent

them from occurring or minimizing their impact on operations.

2. Reactive Decisions: A reactive decisions is one made in response to external

changes that have already taken place. When a manager initiates action to correct

product defects because of persistent customer complaints, he or she adopting a

reactive approach to making decisions. Rather than apply preventive maintenance

(proactive), a machine shop manager may spend money only to repair broken

down machines (reactive).

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14.2.3. The Rational Decision Making Process

As the heading implies, for a decision to be tagged rational, it must pass through the

following processes as seen in Fig 14.1.

Fig 14.1. Rational Decision Making Process

Image source: https://www.24point0.com/example-decision-making-template/

Step 1: Diagnose and Define Problem or Opportunities: The origin of a problem is not

always obvious. If managers are to remedy a situation, they must first find out what the

real problem is. One way to do this is to ask what past action or lack of action might have

caused this situation to arise? In this way, managers can focus upon the events or

circumstances that most likely led to the problem. An opportunity is a gap, an unsatisfied

need or a need that is being inadequately satisfied by existing competitors and which can

be profitably exploited. As part of the process of defining the problem, managers should

also begin to determine which problems they should or would like to solve. Managers

therefore need to distinguish between their “musts” and their “should” so that they will

have a basis for proposing and evaluating solutions. That is, managers prioritize problems

to determine the ones that must be attended to and those that should be attended to.

Step 2: Establish specific Goals and Objectives: It is crucial to note that decisions

making is always done in the context of goals and objectives; and that all behaviour is

basically goal oriented. If goals and objectives are adequately established, they will

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dictate what results must be achieved and the measure that indicate whether they have

been achieved. Such measure is also referred to as the decision criteria.

Step 3: Generate Alternatives: No major decisions can be made until several possible

solutions have been generated. Otherwise, managers may be tempted to adopt the first

and most obvious solution they find. The first solution may not always be the correct one.

The manager needs to list all possible alternatives to solving the problem.

Step 4: Gather and Analyse the Relevant Facts: Once the possible alternatives have

been generated, the next logical step is to gather data suggested by each alternative. Data

may be collected from internal sources – records available in the company or external

sources. Analysis of data consists of combining or arranging the data in a firm as to

provide meaning or insight into the problem at hand. What resources will be available to

help us solve the problem? Managers will rarely get all the answers they need to such

questions. At some point, however, they should have enough information to be able to

formulate possible solutions.

Step 5: Evaluate the Alternatives: Once managers have developed a set of alternatives,

they must evaluate them to see how effective each alternative will be in solving the

problem. Effectiveness is determined based on the decision criteria identified in Step 2.

Based on the information available, the questions to be asked are: (i) how realistic the

alternative is in terms of the goals and resources of the organization, and (ii) how well

will the alternative help solve the problem. The alternatives must also be evaluated in

terms of how well they would solve the “must” and “should” of the problem. Thereafter

the alternatives are arranged in a hierarchy, which is from most desirable to least

desirable.

Step 6: Select an Alternative: At this stage, the manager chooses the best alternative

based on the decision criteria earlier established. The alternative selected is the one that is

most desirable of all the alternatives evaluated.

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Step 7: Analyse the Possible Consequences of the Decision: Once managers have

selected their best alternative, they must try to anticipate what problems will occur when

implementing the decision. For example, there is often great resistance in organizations to

change.There may be practical problems involved in implementing the decision, such as

the need to obtain additional funding. Other departments in the organization that might be

affected by the decision must be consulted. Competitors may be affected by the decision,

and their reactions should be considered. Usually, however, analyzing the possible

consequences of their action will simply allow managers to take the necessary steps to

deal with them.

Step 8: Implement the Decision: Ultimately, no decision is better than the action taken to

make it a reality. If the decision is a good one, but subordinates are not willing or able to

carry it out, then it is unlikely the decision will be very effective. A frequent error of

managers is to assume that once they decide, action on it will automatically follow. Since

in most situations, implementing decisions involves people, the test of decision

soundness is the behaviour of the people who put it into action or are affected by it,

Subordinates cannot be manipulated in the same manner as other resources. Effectively

communicating with the appropriate individuals and groups and groups will ensure

success.

Step 9: Follow Up: Effective management involves periodic measurement of results.

Actual results are compared with planned results (the objective). If deviation exists,

changes must be made. Here again, we see the importance of measurable objectives. If

actual results do not meet planned results, changes must be made in the solution chosen,

in its implementation, or in the original objective if it is deemed unattainable. If the

original objective must be revised, then the entire decision making process will be

reactivated.

14.2.4. Individual Decision Making

A key function of managers is decision making. Many decisions in the organization are

made by managers as individuals. This is often the case when the decisions are routine or

programmed decisions. When the risk involved in the decision is low, managers also tend

to make such decisions as individuals. When managers select a course of action to solve a

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given problem or to take advantage of an opportunity all by himself/herself, it is known

as individual decision making. The manager may obtain information from colleagues but

the choice is made by him/ her. Examples of individual decision making are: allocation of

work to subordinates, decision to reorder raw materials from a known or regular supplier,

handling customer complaints, decision on how much discount to give a customer, etc.

The Advantages of Individual Decision making include:

a. Decision is fast.

b. Responsibility for the decision can be assigned to the person that made the

decision.

c. Implementation of the decision will be fast.

d. Job satisfaction of the manager will be high.

e. The manager’s experience is brought to bear on the decision.

Some of the disadvantages of individual decision making include:

a. The outcomes of individual decision may not be satisfactory because the decision

is likely to be influenced by individual perceptions, values and priorities.

b. The decision maker can only rely on a limited amount of information to make the

decision.

c. There might be a tendency for the manager to “pass the buck”.

d. Individual decision making is often not appropriate when the problem is complex,

novel or when the level of uncertainty is high.

14.2.5. A Group Decision-Making

A group can be defined as two or more freely interacting individuals who share a

common identity and purpose. Firstly, a group must be made up of two or more people if

it is to be considered a social unit. Secondly the individuals must share something in

common. Fourth, interacting individuals must also have a common purpose. That is, there

must be at least a rough consensus on why the group exists (Kreitner, 2000). In today’s

world, a great deal of decision making is achieved through groups. These interacting

groups and teams are the most common form of decision making groups with such names

committees, teams, boards, task forces, etc. This tendency toward group decision making

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is due in part to organizations‟ increased complexity and the large amount of information

needed to make sound decisions.

Many favour group decision making, believing it gives those who will be affected by a

decision a chance to participate in it and helps to develop the members of the group.

Furthermore, the advocates of group decision making state that in this age of

technological change, government influence, and social responsibility, the issues to be

decided have grown beyond the expertise of a single manager. The input of many people

is called for since each is unique in knowledge and experience. The sharing of decision

making responsibilities establishes inter-dependence among the parties. Thus, group

cooperation is enhanced and the old authoritarian concept of decision making is reduced.

Group decision making would become particularly appropriate for non-programmed

decisions because these decisions are complex and few individuals have all the

knowledge and skills necessary to make the best decisions. Thus, group decision making

becomes invaluable when they can maximize the unique contribution of everyone.

Advantages of Group Decision-Making

In general, it is expected that a group would tend to make more effective decisions than

would any single individual. Some of the advantages of group decision making are

summarized below:

a. Since the group members have different specialties, they tend to provide more

information and tend to be more comprehensive in nature.

b. The group can generate a greater number of alternatives.

c. Implementation of the decisions is more effective, since the people who are going

to implement the decision also participated in the decision process. This increases

the commitment of the people to see to the implementation for success.

d. The input from many people eliminates the biases that are generally introduced in

individual decision making. It also reduces the unreliability of individual’s

decisions.

e. The participative decision making process builds up a training ground for

subordinates who develop the skills of objective analysis, evaluation and decision

making.

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f. Group decision making is more democratic in nature while the individual decision

making is more autocratic in nature. The democratic processes are more easily

acceptable and are consistent with the democratic ideals of our society.

Disadvantages of Group Decision-Making

There are certain drawbacks to group decisions also. Some disadvantages are:

a. It is time-consuming. It takes a great deal of time to assemble the group. In

addition, a group takes more time in reaching a decision since there are many

opinions to be taken into consideration.

b. Some members may simply agree with the others for the sake of agreement since

there are social pressures to conform and not to be the odd person.

c. There may be some personality conflicts that may create inter-personal obstacles

which may diminish the efficiency of the process as well as the quality of the

decision.

d. The decision made by the group may not always be in accord with the goals and

objectives of the organization. This is especially true when the goals of the group

conflict with those of the organization.

e. The group members may exhibit “focus effect.” This means that the group may

focus on one or a few suggested alternatives and spend all the time evaluating

these and may never come up with other ideas, thus limiting the choices.

Box 14.2. The procedures in PPBS are;

1. Decision-Making under states of Certainty, Uncertainty and Risk

2. Proactive and Reactive Decisions

3. The Rational Decision Making Process

4. Individual Decision Making

5. A Group Decision-Making

14.3. Decision Making Techniques

We have come to another point in this lecture where we shall be considering decision

making techniques. Decision making techniques can be defined as tools that managers

can use to enhance the efficiency and effectiveness of decision making. There are

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different techniques discussed in this section that are used at different stages of the

decision-making process. These techniques consist of an orderly, systematic framework

for defining, analyzing and solving problems in an objective and scientific manner. They

are intended to improve the manager’s decision making ability and provide them with a

means for justifying and evaluating their own managerial performance. Some of these

techniques are discussed below;

14.3.1. Brainstorming

In many situations, groups are expected to produce imaginative solutions to

organizational problems. In such instances, brainstorming has often enhanced the group’s

creative output. Brainstorming is a process where a group of individuals generate ideas

according to a firm set of rules designed to promote the generation of new ideas while at

the same time avoiding members‟ inhibitions that face-to-face groups usually cause. The

basic rules are: (a) No idea is too ridiculous. Group members are encouraged to state any

extreme or outlandish ideas that occur to them. (b) Each idea presented belongs to the

group, not the person stating it. In this way, group members utilize and build on the ideas

of others. (c) No idea can be criticized. The session’s purpose is to generate ideas, not to

evaluate them.

14.3.2. The Delphi Technique

The Delphi technique is a systematic procedure sometimes used for developing a

consensus among a group of experts. Here, the experts are given a series of detailed

questionnaires about a problem and then are asked to provide their own written opinions.

The use of questionnaires avoids direct contact and debate among experts, which might

induce hasty formulation and commitment to certain ideas. After reading the anonymous

answers of other participants, each expert revises his or her own answers. Eventually,

after a series of “rounds” of this type, convergence of opinion usually occurs. (Stoner,

1978:208). When the opinions stabilize, the average opinion is taken to represent the

decision of the “group” of experts. (Griffin, 1999:281) The underlying belief is that the

consensus estimate results in a better decision after several rounds of anonymous group

judgement. While it is possible to continue the procedure for several rounds, research has

shown that, typically, no significant changes occur after the second round of feedback.

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14.3.3. The Nominal Group Technique (NGT)

NGT is a process of bringing people together as a group to solve a problem. NGT

combines both verbal and non-verbal stages. Basically, NGT is a structured group

meeting that proceeds as follows:

a. A group of 7 to 10 individuals sit around a table but do not speak to one another.

Talking to each other is not permitted during the first stage of NGT. Rather, each

person writes ideas on a note pad about the problem to be solved.

b. After five minutes, a structured sharing of ideas takes place. Each person presents

one idea. A person designated as recorder writes the ideas down on a flip chart in

full view of the entire group. This continues until all the participants indicate that

they have no further ideas to share. There is still no discussion.

c. The output of this phase is usually a list of 18 to 25 ideas. The next phase involves

structured discussion in which each idea receives attention before a vote is taken.

d. In the next stage, independent voting, each participant privately selects priorities

by ranking or voting. The group decision is the mathematically pooled outcome of

the individual votes. Both the Delphi technique and NGT have excellent records of

successes. There are two basic differences between them:

i. In the Delphi process, all communication between participants is by way of

written questionnaires and feedback from monitoring staff. In NGT,

communication is direct between participants.

ii. NGT participants meet face-to-face around a table, while Delphi participants are

physically distant, never meet face-to-face, and are typically anonymous to one

another. Practical considerations, of course, often influence which technique is

used. These considerations can include:

� the number of working hours available

� costs, and

� participants‟ physical proximity.

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14.3.4. Marginal Analysis

Marginal analysis is a technique that can be used to evaluate alternatives by comparing

the additional revenues and additional costs as output increases. The technique is useful

where the objective is to maximize profit, or to find the best output of a typical

educational institution. The idea of marginal analysis is based on the simple economic

postulation that profit is maximized where marginal revenue (additional revenue) is equal

to marginal cost (additional cost). Hence in evaluating alternatives, the decision maker

seeks to find the point where the additional revenue is equal to the additional cost or the

point where the value of additional input is equal to the value of additional output.

14.3.5. Cost Benefit or Cost Effectiveness Analysis

Cost Benefit Analysis is an improvement on marginal analysis. It enables the decision

maker to compare the ratio of costs to benefits of alternative courses of action and to

select the alternative that has the best ratio. The best ratio is that which yields the least

costly means of achieving an objective or the expenditure that yields the greatest value.

14.3.6. Decision Trees

One of the best ways to analyze a decision is to use the so-called decision tree. Decision

trees depict, in the form of a “tree,” the decision points, chance events and probabilities

involved in various courses that might be undertaken as described in the example

presented on Fig 14.2.

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Fig 14.1. An image showing an example of a decision-making tree

Image source: https://www.edrawsoft.com/decisiontreeexamples.php

We can also define a decision tree as a graphical method of displaying various parts of

the decision-making process including courses of action, risks involved and likely

outcomes. It enables the decision makers to consider alternative solutions, assign

financial values to them, estimate the probability of a given outcome for each alternative,

make comparisons and choose the best alternative. A common problem occurs in

business when a new product is introduced. The manager must decide, among various

options, whether to: (a) Install expensive permanent equipment and ensure production at

the lowest possible cost or (b) Undertake cheaper technology tooling that will involve a

higher manufacturing cost but lower capital investments that will result in smaller losses

if the product does not sell as estimated.

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Box 14.3. Decision-Making Techniques

Some of the decision-making techniques are;

1. Brainstorming

2. The Delphi Technique

3. The Nominal Group Technique (NGT)

4. Marginal Analysis

5. Cost benefit or cost effectiveness analysis.

Activity 14.1.

You have been faced with a demand to decide on the best way to pass your examinations

either by studying at intervals or waiting for the release of examination timetable before

commencing study. Using the decision tree, get a broadsheet of paper and analyse why

you need to decide on the option you are going for.


On your decision tree, passing your examination should be the primary decision which

will be linked to your evaluation of the approaches and methods you are deploying in

arriving at that decision.

Summary of Unit 14


1. Decision making is the selection of a course of action from among alternatives; it

is the core of planning. Managers make decisions that must be carried out by

others. The type of decisions they make, and the conditions under which they

make them, will vary. They must therefore tailor their decision-making approach

to their problems and circumstances.

2. Programmed decisions are those that are suggested by habit or policy. Non-

programmed decisions are those that are new.

3. Decision-making can fall under 3 states such as certainty, uncertainty, and risks.

4. Most important decisions will be non-programmed: they will require careful and

logical consideration.They involve nine stages: (i) diagnose and define the

problem (ii) Establishing specific goals and objectives (iii) generate alternatives

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(iv) gather and analyse the facts (v) evaluate alternatives (vi) select best alternative

(vii) analyse possible consequences (viii) Implement decision, and (ix) follow up.

Finally, various management techniques in decision making were highlighted.

5. Many decisions in the organization are made by managers as individuals. This is

often the case when the decisions are routine or programmed decisions.

6. Some of the decision-making techniques we have are; brainstorming; Delphi

technique; norminal group technique; marginal analysis; cost benefit or cost

effective analysis and decision trees.







a. ________ is the cornerstone of planning because it is the catalyst that drives the

planning process.

b. If a situation occurs often and in the same form, a routine procedure usually worked

out for dealing with such can be termed __________.

c. Decisions are __________ when the problem is unstructured.

d. A ________ can be defined as two or more freely interacting individuals who share

a common identity and purpose.

e. A _________ is a series or chain of related steps that lead up to an action or an

outcome and assessment.


Decision making is vital in an organization as it can either make or mar an

organizationalgoal. On this note, shed more light on decision making.

155


Considering these 2 scenarios, identify the types of decisions present in both

1. How you manage blackout at your hostel whenever there is a need for you to study.

2. Changing your course of study based on your inability to meet your current course

requirements.


In describing PPBS to organisation’s decision making process, what are the procedures

involved?


During this lecture, it was mentioned that managers can use certain tools to enhance the

efficiency and effectiveness of decision making.Outline some of these tools.

References

Doh, J. C. 1971. The planning-programming-budgeting systems in three federal agencies.

Manchester, NH: Irvington.

Grimes, S. R. Carlisle, P. A. 2008; “PPBS to PPBE: A Process or Principles?” U.S. Army

War College.

Wade P. H., Milton L. T., Gordon C. V., Rachel D. D, 2010; Planning, Programming, and

Budgeting System (PPBS)/Multi-year Programming, Institute for Defense

analysis; Reading Guide, IDA Document D-4057, Log: H 10-000982

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Study Session Fifteen: Management by Objectives (MBO)


Introduction

As we approach the end of this course, this lecture is geared towards exposing you to the

topic; management by objectives. The principle behind Management by Objectives

(MBO) is to make sure that everybody within the organization has a clear understanding

of the aims, or objectives, of that organization, as well as awareness of their own roles

and responsibilities in achieving those aims. Employee empowerment is allowing

workers to make decisions that would otherwise come from management. By

empowering employees who have direct knowledge about the matter at hand, services are

delivered efficiently. Also, a decentralized decision-making process is cost-effective

because it streamlines the firm by getting rid of excess manpower, mainly in the middle

management.




15.2. State MBO in relation to the organisation’s mission, vision and objectives.

(SAQ 15.2)

15.3. Identify the trends in which MBO works in an organization. (SAQ 15.3)

15.4. Enumerate the elements of MBO according to Peter Drucker.(SAQ 15.4)

Key words; goal-setting, planning, top-down process, and bottom-up process.

15.1. Meaning, Strengths and Weaknesses of Management by Objectives

15.1.1. Meaning of Management by Objectives

Management by Objectives is a technique used by management to achieve collaboration

between managers and their subordinates in goal-setting and planning processes. The

approach was first proposed by Peter Drucker in his 1954 book “The Practice of

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Managemen”. Since that time, MBO has spurred a great deal of discussions, evaluation,

research, and inspired many similar programmes. The features of this concept are:

i. It refers to a formal set of procedures that begins with goal setting and continues

through performance review.

ii. Managers and those they supervise act together to set common goals.

iii. Each person’s major areas of responsibility are clearly defined in terms of

measurable expected results or objectives. These are used by subordinates in

planning their work.

iv. At periodic intervals, the expected results or objectives jointly set by managers and

their subordinates are used to monitor and review progress.

v. Based on the agreed objectives or results, the performance of subordinates is

evaluated.

A management system is in which the objectives of an organization are agreed upon so

that management and employees understand a common way forward. Management by

objectives aims to serve as a basis for the following; You can pause to consider these

bases.

• greater efficiency through systematic procedures,

• greater employee motivation and commitment through participation in the

planning process, and

• planning for results instead of planning just for work. In management by

objectives practice, specific objectives are determined jointly by managers and

their subordinates, progress toward agreed-upon objectives is periodically

reviewed, end results are evaluated, and rewards are allocated based on the

progress.

In-text Question

• What basic function do you think management by objectives strives to achieve in

an organization?

o It is used to achieve collaboration between managers and their subordinates in

goal-setting and planning processes.

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In addition, Management by objective (MBO) is a process through which specific goals

are set collaboratively for the organization and every unit and individual within it; the

goals then are used as a basic for planning, managing organizational activities, and

assessing and rewarding contributions. In Management by objectives (MBO) specific

performance goals are jointly determined by employees and their managers. Progress

towards accomplishing these goals is periodically reviewed, and rewards are

allocatedbased on this progress. Peter Drucker stated that Management by Objectives

consists of four elements which are;

i. Goal specificity

ii. Participative decision making

iii. Explicit time-period

iv. Performance feedback

MBO makes objectives operational through the process by which they cascade down

through the organization. Although there is considerable variation across organizations.

MBO processes typically include five steps which are;

1. Organizational goals are developed based on organizational missions.

2. Specific goals are established for departments, subunits, and individuals.

• In the top-down process, upper-level managers, conferring with their

immediate managerial subordinates, formulate specific objectives for their

areas of responsibility. These in turn enter the formulation of objectives for the

next level down, and so forth.

• In the bottom-up process, operational goals are proposed by lower-level

managers based on what they think they can achieve. These in turn are

developed into tactical and finally strategic plans.

3. Action plans are formulated, describing what is to be done, how, when, where,

andby whom to achieve a goal.

4. Individuals are given the responsibility of reaching their objectives and that

goalswill ultimately be met.

5. Performance is appraised at the end of the goal-setting cycle, typically at one-

yearintervals. Praise, recognition, and rewards should be given for effective

performance.

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Box 15.1. The Elements of Management by Objectives according to Peter Druker

are;

1. Goal specificity

2. Participative decision making

3. Explicit time-period

4. Performance feedback

As we proceed in this lecture, let us consider the strengths of Management by Objectives

(MBO).

15.1.2. Strengths of Management by Objectives

These are;

1. Aids coordination of goals and plans.

2. Helps clarify priorities and expectations.

3. Facilitates vertical and horizontal communications.

4. Fosters employee motivation.

15.1.3. Weaknesses of Management by Objectives

The weaknesses of MBO are that it;

1. Tends to falter without strong, continual commitment from top management.

2. Necessitates considerable training of managers.

3. Can be misused as a punitive device.

4. May cause overemphasis of quantitative goals.

The "spirit" of MBO is tremendous. In practice,MBO has been successful only about 20

to 25 percent of the time, primarily because of lack of support from top management and

poor goal-setting and communication skills. For MBO to be successful, the objectives

must meet five criteria. They must be;

1. arranged in order of their importance;

2. expressed quantitatively, wherever possible;

3. realistic;

4. consistent with the organization's policies, and;

5. compatible with one another.

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Suggested by the management guru Peter Drucker (1909-2005) in early 1950s,

management by objectives enjoyed huge popularity for some time but soon fell out of

favor due to its rigidity and administrative burden. Its emphasis on setting clear goals,

however, has been vindicated and remains valid.

15.2. Activities in Management by Objectives (MBO)

Some of the activities in management by objectives are;

1. Time Span of Goals and Plans

• Strategic goals and plans generally involve time periods of 3-5 years.

• Tactical goals and plans typically involve time periods of 1 to 3 years.

• Operational goals and plans can be for as short a period as 1 week or as long as

1 year.

Characteristics of Well-Designed Goals are;

a. Written in terms of outcomes

b. Measurable and quantifiable

b. Clear as to a time frame

c. Challenging but attainable

d. Written down

e. Communicated to all organizational members

So, if I may ask you, what are the Steps in Goals Setting? These steps are stated below;

a. Review the organization's mission. Goals should reflect what the mission statement says.

b. Evaluate available resources.

c. Determine individually, or with input from others, the goals.

d. Write down the goals and communicate them to all who need to know.

e. Review results and whether goals are being met.

161

2. Developing Plans

The process of developing plans is influenced by three contingency factors and by the

planning approach are;

a. Manager's level in the organization: Operational planning usually dominates the

planning activities of lower-level managers. As managers move up through the

levels of the organization, their planning becomes more strategic.

b. Degree of environmental uncertainty: The greater the environmental uncertainty,

the more plans should be directional and emphasis placed on the short term.When

uncertainty is high, plans should be specific, but flexible.Managers must be

prepared to rework and amend plans, or even to abandon their plans.

c. Length of Future Commitments: Commitment concept means that plans should

extend far enough to meet those commitments made when the plans were

developed.Planning for too long or for too short a period is inefficient and

ineffective.

Before rounding up this lecture, let us examine this;

Approaches to Establishing Goals

Goals can be established through a process of traditional goal setting or through MBO.

Traditional goal setting is defined as the process whereby goals are set at the top of

theorganization and then broken down into sub goals for each level in an organization. In

this process;

1. Top managers are assumed to know what's best because they see the "big picture."

2. These goals are also often largely non-operational.

3. Specificity is achieved as each manager applies his or her own set of

interpretations and biases.

4. However, what often results are that objectives lose clarity and unity as they move

from top to bottom.

5. When the hierarchy of objectives is clearly defined, it forms an integrated means-

end chain in which higher-level objectives are linked to lower-level objectives.

These lower-level objectives serve as the means for the accomplishment of the

higher-level objectives. And the goals at the lower levels (means) must be

achieved to reach the goals at the next level ends.)

162

In the same vein, do you know that goals setting has some pitfalls.? These would be

discussed shortly

Potential pitfalls in Goals Setting

These are;

1. Setting difficult goals increases the risk that they will not be reached.

2. High goals may increase the stress levels of organizational members.

3. Failure to meet high goals may undermine the self-confidence of organizational

members.

4. Non-goal areas may be ignored.

5. Setting goals may encourage excessive shot-range thinking.

6. Inappropriate goals may lead to dishonesty and cheating.



1. MBO is an effective technique for integrating goal setting and planning. This

process of MBO essentially involves managers and subordinates meeting to

establish specific objectives and periodically reviewing progress toward those

objectives.

2. A management system is in which the objectives of an organization are agreed

upon so that management and employees understand a common way forward.

3. Peter Drucker stated that Management by Objectives consists of four elements

which are; goal specificity; participative decision making; explicit time-period;

and performance feedback.

4. MBO makes objectives operational through the process by which they cascade

down through the organization.

5. The strengths of MBO are that it aids coordination of goals and plans, helps clarify

priorities and expectations, facilitates vertical and horizontal communications and

fosters employee motivation.

6. The weaknesses of MBO are that it; tends to falter without strong, continual

commitment from top management; necessitates considerable training of

163

managers; can be misused as a punitive device and may cause overemphasis of

quantitative goals.

7. For MBO to be successful, the objectives must meet five criteria. They must be;

arranged in order of their importance; expressed quantitatively wherever possible;

realistic; consistent with the organization's policies, and; compatible with one

another.

8. Some potential pitfalls in goals setting are; setting difficult goals increases the risk

that they will not be reached; high goals may increase the stress levels of

organizational members; failure to meet high goals may undermine the self-

confidence of organizational members; non-goal areas may be ignored etc.







a. Management by Objectives is a technique used by management to achieve

collaboration between managers and their subordinates in _________ and

_________ processes.

b. In the ___________, upper-level managers, conferring with their immediate

managerial subordinates, formulate specific objectives for their areas of

responsibility.

c. In the __________, operational goals are proposed by lower-level managers based

on what they think they can achieve.


In describing Management by Objectives (MBO), how does it relates with organisation’s

mission, vision and objectives?

164


You learnt in this lecture that MBO makes objectives operational through the process by

which they cascade down through the organization. Describe this process.


Peter Drucker stated that Management by Objectives consists of four elements. Identify

these elements.

References

Antoni, C. 2005, Management by objectives – an effective tool for teamwork?

International Journal of Human Resource Management, Vol. 16.

Hollenbeck, J.R. and Klein, H.J. 1987 ‘Goal Commitment and the Goal Setting Process:

Problems, Prospects, and Proposals for Future Research’, Journal of Applied

Psychology.

Locke, E.A. and Latham, G.P. 1990, A Theory of Goal Setting and Performance,

Englewood Cliffs, NJ: Prentice Hall.

165

Study Session Sixteen: Linear Programming


Introduction

I’m welcoming you on board to the last lecture in EME 302 (Operations Management in

Educational Practice). I want to believe that you have gained the needed skills that was

stated in the objectives of this course. To round up the lectures in this course, this lecture

will be discussing Linear Programming. This is a mathematical technique for determining

the optimal allocation of the resources and obtaining an objective when there are

alternative uses of resources. This lecture examines the model in application to education.




16.2. Explain the meaning of Linear Programing. (SAQ 16.1)

16.3. State the general processes for solving linear-programming exercises.

(SAQ 16.2)

16.4. Highlight the assumptions underlining linear model. (SAQ 16.3)

16.5. Outline the guidelines for formulating linear programming model. (SAQ

16.4)

Key words;linear programming, inequalities, iterations, linear, programming, and

iterations.

16.1. Meaning, Formulation, and Structureof Linear Programming

16.1.1. Meaning of Linear Programming

Linear programming is the process of taking various linear inequalities relating to some

situation, and finding the "best" value obtainable under those conditions. A typical

example would be taking the limitations of materials and labor, and then determining the

"best" production levels for maximal profits under those conditions.In "real life", linear

166

programming is part of a very important area of mathematics called "optimization

techniques". This field of study (or at least the applied results of it) are used every day in

the organization and allocation of resources. These "real life" systems can have dozens or

hundreds of variables, or more. In algebra, though, you'll only work with the simple (and

graphable) two-variable linear case.The general process for solving linear-programming

exercises is to;

1. graph the inequalities (called the "constraints") to form a walled-off area on the

x,y-plane (called the "feasibility region").

2. then you figure out the coordinates of the corners of this feasibility region (that is,

you find the intersection points of the various pairs of lines), and

3. test these corner points in the formula (called the "optimization equation") for

which you're trying to find the highest or lowest value.

The most important feature of linear programming is the presence of linearity in the

problem. The various models in linear programming are:

a. Simplex method

b. Transportation model

c. Assignment model

In a linear programming problem, we are given a set of variables, and we want to assign

real values to them to; satisfy a set of linear equations and/or linear inequalities involving

these variables and; maximize or minimize a given linear objective function.

Box 16.1. The general process for solving Linear Programming exercises are;

1. Graph the inequalities (called the "constraints") to form a walled-off area on the x,y-

plane (called the "feasibility region").

2. Figure out the coordinates of the corners of this feasibility region (that is, you find the

intersection points of the various pairs of lines), and

3. Test these corner points in the formula (called the "optimization equation") for which

you're trying to find the highest or lowest value.

167

If you are to find the maximal and minimal value of z = 3x + 4y subject to the following constraints:

The three inequalities in the curly braces are the constraints. The area of the plane that

they mark off will be the feasibility region. The formula "z = 3x + 4y" is the optimization

equation. I need to find the (x, y) corner points of the feasibility region that return the

largest and smallest values of z.My first step is to solve each inequality for the more-

easily graphed equivalent forms:

To find the corner points, which are not always clear from the graph; we shall pair the lines (thus forming

a system of linear equations) and solve:

y = –( 1/2 )x + 7

y = 3x

y = –( 1/2 )x + 7

y = x – 2

y = 3x

y = x – 2

–( 1/2 )x + 7 = 3x

–x + 14 = 6x

14 = 7x

2 = x

y = 3(2) = 6

–( 1/2 )x + 7 = x – 2

–x + 14 = 2x – 4

18 = 3x

6 = x

y = (6) – 2 = 4

3x = x – 2

2x = –2

x = –1

y = 3(–1) = –3

corner point at (2, 6) corner point at (6, 4) corner pt. at (–1, –3)

So, the corner points are (2, 6), (6, 4), and (–1, –3).

168

Somebody smart proved that, for linear systems like this, the maximum and minimum

values of the optimization equation will always be on the corners of the feasibility region.

So, to find the solution to this exercise, I only need to plug these three points into "z = 3x

+ 4y".

(2, 6): z = 3(2) + 4(6) = 6 + 24 = 30

(6, 4): z = 3(6) + 4(4) = 18 + 16 = 34

(–1, –3): z = 3(–1) + 4(–3) = –3 – 12 = –15

Then the maximum of z = 34 occurs at (6, 4), and the minimum of z = –15 occurs at (-1,

–3).

This made linear programming is a mathematical technique designed to aid managers in

allocating scarce resources (such as labor, capital, or energy) among competing activities.

It reflects, in the form of a model, the organization's attempt to achieve some objective

(frequently, maximizing profit contribution, maximizing rate of return, minimizing cots)

in view of limited or constrained resources (available capital or labor, service levels,

available machine time, budgets). The linear programming technique can be said to have

a linear objective function that is to be optimized (either maximized or minimized)

subject to linear equality or inequality constraints and sign restrictions on the variables.

The term linear describes the proportionate relationship of two or more variables. Thus, a

given change in one variable will always cause a resulting proportional change in another

variable.

Some areas in which linear programming have been applied will be helpful in setting the

climate for learning about this important technique. Linear programming will be useful

when;

• A company produces agricultural fertilizers. It is interested in minimizing costs

while meeting certain specified levels of nitrogen, phosphate, and potash by

blending together many raw materials.

• An investor wants to maximize his or her rate of return by investing in stocks and

bonds. The investor can set specific conditions that must be met including

availability of capital.

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• A company wants the best possible advertising exposure among many national

magazines, and radio and television commercials within its available capital

requirements.

• An oil refinery blends several raw gasoline and additives to meet a car

manufacturer's specifications while still maximizing its profits.

• A city wants to maximize the day time use of recreational properties being

proposed for purchase with a limited capital available.

This technique, called linear programming (L.P), is solved in a step-by-step manner

called iterations. Each step of the procedure is an attempt to improve on the solution

until the" best answer" is obtained or until it is shown that no feasible answer exists.

In-text Question

• Do you think the term linear describes the proportionate relationship of two or

more variables? Support your answer with a sentence.

o Yes, because a given change in one variable will always cause a resulting

proportional change in another variable.

16.1.2. Formulation of the Linear Programming Problem

To formulate a real-life problem as a linear program is an art. To aid you in this task, it is

helpful to isolate the essential elements of the problem as a means of asking what the

clients wants and what information can be gained from the data that has been

provided.Linear Programming is a mathematical technique for optimum allocation of

limited or scarce resources, such as labour, material, machine, money, energy and so on,

to several competing activities such as products, services, jobs and so on, based on a

given criteria of optimality.

The term ‘Linear’ is used to describe the proportionate relationship of two or more

variables in a model. The given change in one variable will always cause a resulting

proportional change in another variable.The word, ‘programming’ is used to specify a

sort of planning that involves the economic allocation of limited resources by adopting a

course of action or strategy among various alternatives strategies to achieve the desired

170

objective.Hence, Linear Programming is a mathematical technique for optimum

allocation of limited or scarce resources, such as labour, material, machine, money

energy etc.

16.1.3. Structure of Linear Programming model

The general structure of the Linear Programming model essentially consists of three

components.

� The activities (variables) and their relationships

� The objective function and

� The constraints

The activities are represented by X1, X2, X3 …….Xn.

These are known as Decision variables.

The objective function of an LP (Linear Programming Problem) is a mathematical

representation of the objective in terms a measurable quantity such as profit, cost,

revenue, etc.

Optimize (Maximize or Minimize) Z=C1X1 +C2X2+ ……….Cn Xn

Where Z is the measure of performance variable

X1, X2, X3, X4….Xn are the decision variables

And C1, C2, …Cn are the parameters that give contribution to decision variables.

These are the set of linear inequalities and/or equalities which impose restriction of the

limited resources.

In-text Question

• In Linear Programming, what do you think the word programming stands for?

o The word, ‘programming’ is used to specify a sort of planning that involves the

economic allocation of limited resources by adopting a course of action or

strategy among various alternatives strategies to achieve the desired objective.

171

16.2. Assumptions of Linear Programming Certainty

In all LP models, it is assumed that all the model parameters such as availability of

resources, profit (or cost) contribution of a unit of decision variable and consumption of

resources by a unit of decision variable must be known and constant. Some of the

assumptions are;

1. Divisibility (Continuity)

The solution values of decision variables and resources are assumed to have either whole

numbers (integers) or mixed numbers (integer or fractional). However, if only integer

variables are desired, then Integer programming method may be employed.

2. Additivity

The value of the objective function for the given value of decision variables and the total

sum of resources used, must be equal to the sum of the contributions (Profit or Cost)

earned from each decision variable and sum of the resources used by each decision

variable respectively. The objective function is the direct sum of the individual

contributions of the different variables.

3. Linearity

All relationships in the LP model (i.e. in both objective function and constraints) must be

linear.

16.2.1. General Mathematical Model of an LPP

Optimize (Maximize or Minimize) Z=C1 X1 + C2 X2 +……+CnXn

Subject of constraints,

a1X1+ a 12X2+………………+ a 1nXn (<,=,>) b1

a21X1+ a 2X2+………………+ a 2nXn (<,=,>) b2

a31X1+ a 32X2+………………+ a 3nXn (<,=,>) b3

am1X1+ a m2X2+………………+ a mnXn (<,=,>) bm

and X1, X2 ….Xn >

172

Box 16.2. Assumptions of Linear Programming Certainty

The assumptions of Linear Programming certainty are;

1. Divisibility

2. Additivity

3. Linearity

As we conclude this course, let us briefly examine the guidelines for formulating Linear Programming

Model

16.2.2. Guidelines for Formulating Linear Programming Model

The guidelines are;

1. Identify and define the decision variable of the problem.

2. Define the objective function.

3. State the constraints to which the objective function should be optimized (i.e.

Maximization or Minimization).

4. Add the non-negative constraints from the consideration that the negative values

of the decision variables do not have any valid physical interpretation.

Let us consider this example;

Example 1

A manufacturer produces two types of models M1 and M2.Each model of the type M1

requires 4 hours of grinding and 2 hours of polishing; whereas each model of M2 requires

2 hours of grinding and 5 hours of polishing. The manufacturer has 2 grinders and 3

polishers. Each grinder works for 40 hours a week and each polisher works 60 hours a

week. Profit on M1 model is N3.0 and on model M2 is N4.0.Whatever produced in a

week is sold in the market. How should the manufacturer allocate his production capacity

to the two types of models, so that he makes maximum profit in a week?

a. Identify and define the decision variable of the problem. Let X1 and X2 be the

number of units of M1 and M2 model.

b. Define the objective function since the profits on both the models are given, the

objective function is to maximize the profit.Max Z = 3X1 + 4X2

c. State the constraints to which the objective function should be optimized (i.e.


173

There are two constraints one for grinding and the other for polishing.The grinding

constraint is given by

4X1 + 2X2 < 80

No of hours available on grinding machine per week is 40 hrs. There are two grinders.

Hence the total grinding hour available is 40 X 2 = 80 hours.

The polishing constraint is given by

2X1 + 5X2 < 180

No of hours available on polishing machine per week is 60 hrs. There are three grinders.

Hence, the total grinding hour available is 60 X 3 = 180 hours.

Finally, we have,

Max Z = 3X1 + 4X2

Subject of constraints,

4X1 + 2X2 < 80

2X1 + 5X2 < 180

X1, X2 > 0



1. Linear programming is the process of taking various linear inequalities relating to

some situation, and finding the "best" value obtainable under those conditions.

2. The most important feature of linear programming is the presence of linearity in

the problem. The various models in linear programming are: simplex method;

transportation model; and assignment model.

3. The linear programming technique can be said to have a linear objective function

that is to be optimized (either maximized or minimized) subject to linear equality

or inequality constraints and sign restrictions on the variables.

4. This technique, called linear programming (L.P), is solved in a step-by-step

manner called iterations. Each step of the procedure is an attempt to improve on

the solution until the" best answer" is obtained or until it is shown that no feasible

answer exists.

5. The term ‘Linear’ is used to describe the proportionate relationship of two or more

variables in a model. The given change in one variable will always cause a

resulting proportional change in another variable.

174

6. The word, ‘programming’ is used to specify a sort of planning that involves the

economic allocation of limited resources by adopting a course of action or strategy

among various alternatives strategies to achieve the desired objective.

7. The assumptions of linear programming certainty are; divisibility; additivity; and

linearity.

8. General Mathematical Model of an LPP is

Optimize (Maximize or Minimize) Z=C1 X1 + C2 X2 +……+CnXn

Subject o constraints,

a1X1+ a 12X2+………………+ a 1nXn (<,=,>) b1

a21X1+ a 2X2+………………+ a 2nXn (<,=,>) b2

a31X1+ a 32X2+………………+ a 3nXn (<,=,>) b3

am1X1+ a m2X2+………………+ a mnXn (<,=,>) bm

and X1, X2 ….Xn >





SAQ 16.1. (tests learning outcomes 16.1. and 16.2)


a. __________ is the process of taking various linear inequalities relating to some

situation, and finding the "best" value obtainable under those conditions.

b. In Linear Programming, constraints can also be called ___________.

c. The term _________is used to describe the proportionate relationship of two or

more variables in a model.

d. The word, __________ is used to specify a sort of planning that involves the

economic allocation of limited resources by adopting a course of action or strategy

among various alternatives strategies to achieve the desired objective.

175


As we have discussed in this lecture, what are the general process involved when solving

linear-programming exercises?


In Linear Programming, what are the assumptions guiding model parameters such as

availability of resources, and profit (or cost) contribution of a unit of decision variable?


As an expert in Management, you have been saddled with the task of formulating a linear

programming model. In doing this, what are some of the guidelines you need to strictly

adhere to?

And this brings us to the end of this course. I want to believe you have been able to learn

the essential skills and broadened your knowledge of Operations Management in

Educational Practice. I wish you all the best in your studies….

References

Cohen, J., Cohen P., West, S.G., and Aiken, L.S. 2003. Applied multiple

regression/correlation analysis for the behavioral sciences. (2nd ed.) Hillsdale,

NJ: Lawrence Erlbaum Associates.

Kaw, A. and Kalu, E. 2008, Numerical Methods with Applications (1st ed.), linear and

non-linear regression.

176

APPENDIX

Notes to the Self-Assessment Questions (SAQs) for Session 1

SAQ 1.1.

a. TRUE

b. FALSE

SAQ 1.2.

Management has been practiced in some form or the other since the dawn of civilisation.

Ever since human beings began to live and work together in groups, techniques of

organisation and management were evolved.

SAQ 1.3.

Management thinking and practice have evolved over the last century because of

increased understanding of human and organisational behaviour, the economic climate

and historical context and the changes in generations over time.

SAQ 1.4.

The modern management activities are;

1. The empirical school: Studying experience to draw generalizations and to develop

means of teaching experiences to other practitioners and students.

2. The social school system: This stems from the application of behavioural sciences

to management.

3. The Decision theory school: This concentrates on rational approaches to decision

making-the selection of a course of action from various possible alternatives.


SAQ 2.1.

a. evaluate and estimate

b. cost and time.

c. planning and coordinating.

177

SAQ 2.2.

Program Evaluation and Review Technique (PERT) is a technique adopted by

organizations to analyze and represent the activity in a project and to illustrate the flow of

events in a project. PERT also illustrates the activities and interdependencies in a project.

The main goal of PERT is to reduce the cost and time needed to complete a project.

SAQ 2.3.

The steps to follow are; Identifying tasks and milestones; Placing the tasks in a proper

sequence; Network diagramming; Time estimating and Critical Path estimating.

SAQ 2.4.

The project information input into the computer includes; the earliest start time for each

activity; earliest finish time for each activity; latest start time for each activity; and latest

finish time for each activity without delaying the project completion.


SAQ 3.1.

a. Planning, scheduling, and controlling.

b. Float time

SAQ 3.2.

The critical path method (CPM) is a step-by-step technique for process planning that

defines critical and non-critical tasks with the goal of preventing time-frame problems

and process bottlenecks.

SAQ 3.3.

The key steps in critical path method are;

1. Activity specification

2. Activity sequence establishment

3. Network diagram

4. Estimates for each activity

5. Identification of the critical path; and

6. Critical path diagram to show project progresses.

178

SAQ 3.4.

Some of the benefits to be derived are;

a. Offers a visual representation of the project activities.

b. Presents the time to complete the tasks and the overall project.

c. Tracking of critical activities.

On the other hand, the limitations are;

a. Less focus on non-critical tasks that can cause risk.

b. Based on only deterministic task duration.

c. Critical Path can change during execution.

SAQ 3.5.

CCPM is relevant to CPM in the sense that it helps to surmount the limitations facing

CPM.


SAQ 4.1.

a. FALSE

b. TRUE

c. TRUE

SAQ 4.2.

An inventory policy is a standard set of rules/boundaries and guidelines that provide the

framework for an organisation to make better informed and timely decisions on which

stock to purchase or manufacture, how much stock to purchase or manufacture and where

to store and distribute to customers. The methods best suited for organisations are;

Reorder point; Min/Max; lot for lot; days of supply and item location.

SAQ 4.3.

Days of Supply, Demand-Based Days of Supply (DOS) - Demand is similar to an s,S

inventory policy except that the parameters for minimum and maximum levels are

specified in number of days rather than product quantities. This policy computes the daily

average of product by looking back at the actual demand. How far back to look is given

179

by the DOS window field while Days of Supply, Forecast-Based DOS is similar to an s,S

inventory policy except that the parameters for minimum and maximum levels are

specified in number of days rather than product quantities. This policy computes the daily

average of product by looking forward and using forecasted demand.

SAQ 4.4.

The needed strategies are;

1. Direct deliveries of purchase products in raw material or assembly form can be

delivered to a manufacturing line or processing point and avoid double handling

through a warehouse process.

2. Just in time production by only making what is required resulting in lower WIP

inventory.

3. Direct Deliveries of finished goods by shipping direct from your source of supply

and avoiding your logistics network, if possible.


SAQ 5.1.

a. TRUE

b. FALSE

c. TRUE

d. FALSE

e. TRUE

SAQ 5.2.

Items that deteriorate are likely to be large and costly (e.g., machine tools, trucks, ships,

and home appliances). Non-deteriorating items tend to be small and relatively

inexpensive (e.g., light bulbs, vacuum tubes, ink cartridges). The longer a deteriorating

item is operated the more maintenance it requires to maintain efficiency.

SAQ 5.3.

The NPV is the value obtained by discounting all cash outflows and inflows of an

investment opportunity by a chosen rate of return. The NVP valuation method requires

estimating the size and timing of all the incremental cash flows from the project. These

180

future cash flows are then discounted to determine their present value. Some of the uses

to management are; it considers the time value of money; it is an absolute measure of

return; it uses cash flows and not profits; and it considers the whole life of the project.


SAQ 6.1

1. B

2. D

3. A

4. A

5. C

SAQ 6.2.

Queuing theory is the mathematical study that deals with problems which involve

queuing (or waiting lines), or queues. In queuing theory, a model is constructed so that

queue lengths and waiting times can be predicted.

SAQ 6.3.

Here are some of the major points that will be raised in the report;

1. Analysing the arrival process

2. Checking the service mechanism

3. Examining the queue characteristics. (See Session for details)


SAQ 7.1.

a. Process

b. Implementation

c. TQM

d. Profitability and Competitiveness

e. Technical and Operational

181

SAQ 7.2.

Some of the pioneers in the origin of TQM are;

1. Total Quality Management (TQM)in the form of statistical quality control was

invented by Walter A. Shewhart.

2. TQM was demonstrated on a grand scale by Japanese industry through the

intervention of W. Edwards Deming with the help of missionary labors in the U.S.

and across the world.

3. TQM in education surfaced in 1988 at Mt. Edgecombe High school in Sitka,

Alaska when David Langford the school’s technology teacher/coordinator, applied

Total Quality concepts in his classes.

SAQ 7.3.

Total Quality Management (TQM) refers to management methods used to enhance

quality and productivity in profit making organizations. In other words, Total Quality

Management (TQM) describes a management approach to long–term success through

customer satisfaction. Like many of these other systems, TQM provides a framework for

implementing effective quality and productivity initiatives that can increase the

profitability and competitiveness of organizations.

SAQ 7.4.

The elements of TQM are; Customer-focused; Total employee involvement; Process-

centered; Integrated system; Strategic and systematic approach; Continual improvement;

Fact-based decision making and Communication.

SAQ 7.5.

Some of the generic models in TQM are;

1. Top management learns about and decides to commit to TQM. TQM is identified

as one of the organization’s strategies.

2. The organization assesses current culture, customer satisfaction, and quality

management systems.

3. Top management identifies core values and principles to be used, and

communicates them.

182

4. A TQM master plan is developed based on steps 1, 2, and 3.

5. The organization identifies and prioritizes customer demands and aligns products

and services to meet those demands.

6. Management maps the critical processes through which the organization meets its

customers’ needs.


SAQ 8.1.

There are problems where certain facilities must be assigned to specified jobs to

maximize the overall performance of the assignment. The Hungarian Method can also

solve such assignment problems, as it is easy to obtain an equivalent minimization

problem by converting every number in the matrix to an opportunity loss.

SAQ 8.2.

For Minimization, the steps are;

STEP 1: Identify the minimum element in each row and subtract it from every element

of that row, we get the reduced matrix.

STEP 2: Identify the minimum element in each column and subtract it from every

element of that column

STEP 3: Make the assignment for the reduced matrix obtain from steps 1 and 2

For Maximization;

STEP 1: Subtract the smallest entry in each row from all the entries of its row.

STEP 2: Subtract the smallest entry in each column from all the entries of its column.

STEP 3: Draw lines through appropriate rows and columns so that all the zero entries of


STEP 4: Test for Optimality: If the minimum number of covering lines is n, an optimal

assignment of zeros is possible and we are finished. If the minimum number of

covering lines is less than n, an optimal assignment of zeros is not yet possible.

In that case, proceed to Step 5.

STEP 5: Determine the smallest entry not covered by any line. Subtract this entry from


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SAQ 8.3.

1. 76

2. Maximum profit through this assignment is 214


SAQ 9.1.

Supply, demand

SAQ 9.2.

The transportation problem is concerned with finding an optimal distribution plan for a

single commodity. A given supply of the commodity is available at a number of sources,

there is a specified demand for the commodity at each of the destinations, and the

transportation cost between each source-destination pair is known.There are two types of

Transportation Problem namely:

1. Balanced Transportation Problem and

2. Unbalanced Transportation Problem.

SAQ 9.3.

The following variants are being considered in simplex method;

i. Minimization

ii. Inequality in the wrong direction

iii. Degeneracy

iv. Unbounded solution

v. Multiple solutions

vi. Non-existing feasible solution

vii. Unrestricted variables

SAQ 9.4.

The transportation method consists of the following three steps.

1. Obtaining an initial solution, and making an initial assignment in such a way that a

basic feasible solution is obtained.

2. Ascertaining whether it is optimal or not, by determining opportunity costs

associated with the empty cells, and if the solution is not optimal.

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3. Revising the solution until an optimal solution is obtained.


SAQ 10.1

The steps needed are;

1. Select the north west (upper left-hand) corner cell of the transportation table and

allocate as many units as possible equal to the minimum between available supply

and demand requirements, i.e., min (s1, d1).

2. Adjust the supply and demand numbers in the respective rows and columns

allocation.

3. If the supply for the first row is exhausted, then move down to the first cell in the

second row.

4. If the demand for the first cell is satisfied, then move horizontally to the next cell

in the second column.

5. If for any cell supply equals demand, then the next allocation can be made in cell

either in the next row or column.

6. Continue the procedure until the total available quantity is fully allocated to the

cells as required.

SAQ 10.2.

1a. Total cost= 20(21) + 30(18) + 30(24) + 30(20) + 25(25) +25(25) =

630+540+720+600+625+625 = N3740

1b. N 30

1c. N40

2. 5(400) + 8(400) + 7(300) + 7(300) + 7(530) +5(550) = 2000+ 3200+ 2100+ 2100+

3710 + 2750 = N15,925

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SAQ 11.1.

The steps in Least-cost method are;

1. Assign as much as possible to the cell with the smallest unit cost in the entire

table. If there is a tie, then choose arbitrarily.



3. Adjust the supply and demand for those rows and columns which are not crossed

out.

4. When exactly one row or column is left, all the remaining variables are basic and

are assigned the only feasible allocation.


SAQ 12.1.

The steps in VAM are;

1. Identify the boxes having minimum and next to minimum transportation cost in

each row and write the difference (penalty) along the side of the table against the

corresponding row.

2. Identify the boxes having minimum and next to minimum transportation cost ineach

column and write the difference (penalty) against the corresponding column.

3. Identify the maximum penalty. If it is along the side of the table, make maximum

allotment to the box having minimum cost of transportation in that row. If it is

below the table, make maximum allotment to the box having minimum cost of

transportation in that column.

4. If the penalties corresponding to two or more rows or columns are equal, select the

top most row and the extreme left column.


SAQ 13.1.

a. Model

b. Management model

c. Analogue model

d. Physical and graphic model

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e. Deduction

f. Inductive

SAQ 13.2.

A model is a simplified representation of the real world and as such includes only those

variables relevant to the problem at hand.There are four patterns of model construction,

only two of which involve experimentation: inspection, use of analogues, operational

analysis, and operational experiments. They are considered here in order of increasing

complexity. In some cases, the system and its problem are relatively simple and can be

grasped either by inspection or from discussion with persons familiar with it. In general,

only low-level and repetitive operating problems, those in which human behaviour plays

a minor role can be so treated.

SAQ 13.3.

Procedures for deriving solutions from models are either deductive or inductive. With

deduction one moves directly from the model to a solution in either symbolic or

numerical form. Inductive procedures involve trying and comparing different values of

the controlled variables. (See Session for details)

SAQ 13.4.

The Model Building Processes are:

• Compute the background equation

• Analyze the factors available to explain the difference between actual effort and

effort as predicted by the background equation

• Use this model to predict the effort for the new project

SAQ 13.5.

• The steps in Lewin's management model are; unfreeze, transition, and refreeze.

• The factors in Mckinsey 7s Model are; shared values; strategy; structure; systems;

style; staff and skills.

• The steps available in Kotter's 8 step model are;

1. Increase the urgency for change.

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2. Build a team dedicated to change.

3. Create the vision for change.

4. Communicate the need for change.

5. Empower staff with the ability to change.

6. Create short term goals.

7. Stay persistent.

8. Make the change permanent.


SAQ 14.1.

a. Decision-making

b. Programmed decision

c. Non-programmed decision

d. Group

e. Decision making

SAQ 14.2.

Decision making is the cornerstone of planning because it is the catalyst that drives the

planning process. An organization’s goals follow from decisions made by various

managers. Furthermore, in deciding to adopt the best plan for achieving goals, decision

making basically reflects the selection of the best choice among possible alternatives and

putting it into practice.

SAQ 14.3.

1. Programmed decision

2. Non-programmed decision

188

SAQ 14.4.

The procedures in PPBS are;

1. Decision-Making under states of Certainty, Uncertainty and Risk

2. Proactive and Reactive Decisions

3. The Rational Decision Making Process

4. Individual Decision Making

5. A Group Decision-Making

SAQ 14.5.

Some of the decision-making techniques are;

1. Brainstorming

2. The Delphi Technique

3. The Nominal Group Technique (NGT)

4. Marginal Analysis

5. Cost benefit or cost effectiveness analysis.


SAQ 15.1.

a. Goal setting and planning

b. Top down process

c. Bottom up process

SAQ 15.2.

a. It refers to a formal set of procedures that begins with goal setting and continues

through performance review.

b. Managers and those they supervise act together to set common goals.

c. Each person’s major areas of responsibility are clearly defined in terms of

measurable expected results or objectives. These are used by subordinates in

planning their work.

d. At periodic intervals, the expected results or objectives jointly set by managers

and their subordinates are used to monitor and review progress.

e. Based on the agreed objectives or results, the performance of subordinates is

evaluated.

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SAQ 15.3.

We have the following in the process;

1. Organizational goals are developed based on organizational missions.

2. Specific goals are established for departments, subunits, and individuals.

3. Action plans are formulated, describing what is to be done, how, when, where, and

by whom to achieve a goal.

4. Individuals are given the responsibility of reaching their objectives and that goals

will ultimately be met.

5. Performance is appraised at the end of the goal-setting cycle, typically at one-year

intervals. Praise, recognition, and rewards should be given for effective

performance.

SAQ 15.4.

The elements are;

a. Goal specificity

b. Participative decision making

c. Explicit time-period

d. Performance feedback


SAQ 16.1.

a. Linear programming

b. Inequality

c. Linear

d. Programming

SAQ 16.2.

The general process for solving linear-programming exercises is to;

1. graph the inequalities (called the "constraints") to form a walled-off area on the

x,y-plane (called the "feasibility region").

2. then you figure out the coordinates of the corners of this feasibility region (that is,

you find the intersection points of the various pairs of lines), and

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3. test these corner points in the formula (called the "optimization equation") for

which you're trying to find the highest or lowest value.

SAQ 16.3.

The assumptions of Linear Programming certainty are;

1. Divisibility

2. Additivity

3. Linearity

SAQ 16.4.

The guidelines are;

1. Identify and define the decision variable of the problem.

2. Define the objective function.

3. State the constraints to which the objective function should be optimized (i.e.


4. Add the non-negative constraints from the consideration that the negative values of

the decision variables do not have any valid physical interpretation.

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