decision models in manakgement

7/27/2019 Decision Models in Manakgement

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DECISION MODELS IN

MANAGEMENT

PGDM-I TERM III

by

PROF. R.N.VENKATESWARAN


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Reference Books

An Introduction to Management Science:Quantitative Approaches to Decision Making, by:

Anderson Sweeney, Williams, Thomson South-

Western, 10e

Principles of Operations Research for

Management (2e) - by Budnick; McLeavey, and

Mojena AITB,Delhi edition

Operations Research by Taha, HA (6e), Prenhall Principles of Operations Research with

applications to Managerial Decisions, (2e), by

Wagner, Prenhall, India


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DECISION MODELS

Various names given to body of knowledge which use

Quantitative Methods in Decision Making:Management Science (MS)

Operations Research (OR)

Decision Science

Modern management requires executive-generalists

who are trained and effectively operate in business,

industry, government, hospitals, armed forces, educational

institutions, service industries etc., They could coordinate

the contributions of all of the specialists of an organization.Their task requires the ability to employ structure before

content in coping with the extreme diversity of information

produced by the organization.


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DECISION MODELScontd

Modern Management differs from Taylors scientific

management:

It views efficiency as secondary achievement, which

should follow adequate planning. Both good and poor

decisions can be implemented in an efficient way. A

company can manufacture a high-quality product at a

minimum cost, but the product itself might not be the bestchoice to meet the companys objectives.

Modern management attempts to establish relationship

between organizations objectives and its resources.

It cuts across traditional areas of management andemphasizes inter-disciplinary approach. People with

diverse specialties - e.g. mathematicians, engineers,

behavioural scientists, accountants etc., join together to

solve an organizational problem


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Problem Solving & Decision Making

Problem Solving is the process of identifying a difference

between the actual and the desired state of affairs and then

taking action to resolve the difference.

Decision Making is associated with management process

of planning, organizing, coordinating, controlling etc.,

Managementas defined by Websters Dictionary, is thejudicious use of means to accomplish an end.

Doing and Deciding are both managerial/executive

functions. Routine operations require doing. Exceptions

require deciding.


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Problem Solving & Decision Making Executive is a word derived from a Latin word meaning

to do; the Oxford Dictionary defines it as the action of

carrying out or carrying into effect. This does not suggestthat the main responsibility and function of the executive is

to make decisions.The executive is rewarded and evaluated

in terms of his success at making decisions while

managing his function.

Organization structure is set up to help executives do

decision making

Managerial PROBLEM SOLVING would involve both

doing - with the organization structure and deciding

using various management tools and techniques. The

manager has to form a partnership between those who

perceive they have a problem (users) and those who have

the specialized knowledge or skills in problem-solving

techniques (specialists)


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TAXONOMY OF OR MODELS

Search Methods

Classical Methods

Non-linear Optimization

GOAL

Programming

Transportation& Assignment

Linear Programming

Linear Optimization

Deterministic

MarkovProcesses

Queuing

Models

DecisionAnalysis

Stochastic

Simulation

InventoryModels

Dynamic

Programming

PERT/CPM

HYBRID

ORMODELS

C S O O S


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DECISION MODELS

TOPICS & SESSIONS

Decision Theory & Modeling 2

Linear Programming 7

Multi-Criteria (Goal Programming). 3

Simulation 3

Transportation Models 4 Assignment Problems 3

Game Theory 2

Queuing (Waiting-line) Models 4

(with simulation application) Markov Processes 2


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Evaluation Pedagogy

End-Term Exam ... 50%

Attendance ... 5%

Quizzes ... 20%

Cases/Problems(2 Sessions)... 25%


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Decision-Making Process Role of Quantitative Analysis in the Decision-Making

Process:

Problem

ExperienceSubjective

Analysis

Quantitative

AnalysisOpinion

Decision Inputs

P bl l i P


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Need

Recognition

Problem

Formulation

Model

Construction

Modeling

Real System

Data

Collection

Model

Solution

Model

Validation &

Sensitivity

Analysis

Interpretation

of Results

Implement-

ation &

Control

System of

Interest

Problem-solving Process

Schematic

Diagram ofProblem Solving

Process


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Stages of Problem-Solving Process

Green, Lee and Newsom classify problem-solving process into

three major stages:

Pre-modeling function

Modeling function

Implementation (Post-modeling)function

These stages can be further mapped onto an eight-step process:Pre-modeling:

Recognition of Need

Problem Formulation

Systems Approach Controllable & Uncontrollable variables

Parameters

Constraints

Objective Function


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Objectives,Criteria and Surrogates

Objective: The ultimate desired goal. In DMM we use the

term objective function. Surrogates: To say the company has to perform better is a

qualitative criterion or objective. But it has to be broken

into measurable surrogates - Market Share; Profit after

Tax, ROR etc.,

To say the standard of living of an individual is to be

improved is a qualitative criterion. It is to be broken to

surrogates such as: Income; growth in income; amount of

spending; amount of savings etc.,


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Stages of Problem-Solving Processcontd.

Modeling

Model Construction - Mathematical Models Data Collection - MIS; Databases; Decision-

Support systems

Model Solution(Have alternatives)- OR Models

Model Validation and Sensitivity Analysis(Optimizing/Satisficing)

Post-Modeling

Interpretation of Results and Implication- Selling yourideas

Implementation, and Control - HRD Issues

Doing

Decision making


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MODEL BUILDING A MODEL is a representation of reality intended to

explain the behaviour of some aspect of it.

Taxonomy of Models: Normative & Descriptive

Normative models tend to prescribe what oughtto be:

Physicians possess a normative model of health

Civil Engineers possess a normative model of a building

Philosophers have a code of conduct for ethics

Descriptive Models describe facts and relationships:

Physician conducting tests and analyzing the results to determine

the ailment

A civil engineer analyzing the soil conditions and other parameters

to decide on the type of structure

Constructing a physical scale model to give the projected view

of the final structure/equipment/device.

Analyzing what-if situations in a management problem solving.

In DMM we are concerned with descriptive models.


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MODEL BUILDING SIMULATION MODELS

SIMULATION is one of the key techniques of DMM. It

involves construction of a mathematical model of theproblem; and imitate (simulate) the operation of the

system.(System modeling & simulation is an elective

course in VI term)

E.g: Simulation of an airplane flight in a wind tunnel

Simulation of the traffic in traffic junction

Simulation of customer servicing in a service counters

Simulation of production - in a manufacturing situation.

Simulation modeling process helps to understand andanalyze the various alternatives, over pre-determined time

periods, without physically operating or modifying the

system.(we will learn more about it under simulation)


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PROBLEM SOLVING FRAMEWORK

1. Verbal Statement of the Problem

2. Decisions:

* Verbal Statement

* Mathematical Definition

3. Criteria

* Verbal Statement


4. Constraining Conditions

* Verbal Statement


5. Mathematical Model

6. Model Outcomes

7. Interpretation of the Results


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CLASSICAL DETERMINISTIC

MODELS

Decision Models for Management

E f U i P bl S l i F k


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E.g. of Using Problem Solving FrameworkIn-house Computer -vs.- Service Bureau Decision

A large poly-clinic has 30 full-time and visiting doctors.Currently all billing is done manually by clerks. Due to

the heavy volume of billing, the hospital managementwishes to computerise the billing operation. It has 2options: (1) To buy a computer and carry-out the billing byitself (the make/own option). Or (2) To contract with anagency that would do the operations (the buy/lease option)

Cost Data: The company can lease a small p.c. and therequired software at Rs. 15000 per year. The variable costof doing the billing in this manner is 0.65 paise per bill.

Alternatively, the company can sub-contract the operation

to an outside agency, who would charge Rs. 3000 fixedcharges per year and 0.95 paise per bill processed.

The company would like to know the critical patient volume tomake a decision on make-or buy. (this is also a deterministic

decision making problem)


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Mathematical Representation of Relationships

Assumptions:

Criteria are used to make decisionsThey are quantifiable and can be represented by

mathematical functions

Such mathematical problems are solved by using Algebra,

Simultaneous Equations; Differential Calculus etc.,Functional Notation: A functionis a mathematical

relationship for which the value of a particular variable is

determined from the values of one or more other variables.

Y = f(x) is a general representationY = 5x is a specific case.

Similarly Y = f(x1,x2,x3) is general and

Y = 3x1 + 2x2 + 6x3 is specific.

A l i h F k


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Applying the Framework

1. Verbal Statement of the Problem:

Determine the number of patient-bills, (contrast with no. ofpatients) beyond which the make option is less costly.

2. Decisions:

a. Verbal Statement: Number of patient bills per year

b. Mathematical Definition: Let x = no. of patient bills/yr.

3. Criteria: There are no optimizing criteria. Find out thatnumber of patient bills at which the annual costs of makeor buy are equal.

4. Constraining Conditions:

The critical point beyond which the lease option is lesscostly is known as break-even pointfor the two options

A l i h F k


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Applying the Framework

a. Verbal Statement: The annual cost of agency equalsannual cost of in-house operation

b. Mathematical statement: To find a value for x such thatOwn Cost: 15000 + 0.65 x

Sub-contract: 3000 + 0.95 x

5. Model: Solve for x, where :

3000 + 0.95x = 15000 + 0.65x6. Model Outcomes:

the value of x = 40000

7. Interpretation of the results:

If the break-even number of patient bills = 40000. Hence,if the number is expected to be more than 40000, doingbilling on our own is cheaper. If the bills number is lessthan 40000, it is cheaper to sub-contract the operation.

Are both equal


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Single Product Pricing Problem (Deterministic

Problem; Using problem solving framework)

The Massachusetts Bay Transit Authority (MBTA) wishes

to smooth its demand for subway services. The system

operates to full capacity during the early morning and later

afternoon rush hours. The MBTA wants to stimulate

greater demand during off-peak hours and to encourage

riders who do not need to travel during peak hours to travelat other times.

Currently the normal fares are 75 during normal hours

and 30 during off-peak hours. The demand function is

estimated from data gathered with demand at differentfares. p = off-peak fare; q = off-peak demand (000s of

passengers)

p = 70 65 60 55 50

q = 10.0 12.6 14.9 17.4 20.1


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Single Product Pricing Problem contd

Initial attempt was to fit a least-squares regression line:

q = 45 - ()p or p = -2q + 90

If the objective is to maximize demand for off-peak hours,

this would suggest eliminating such fares, and demand

would be 45,000 passengers.

But if we derive that the revenue is TR = q * p, then

TR = f(p) = 45p - p2/2

This would yield maximum revenue when p = 45.

And the revenue for this is: 1012.5, and substituting this in

the regression formula:q = 45 - ()45 = 22.5 or 22500 passengers.

decision models in manakgement

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