What is Operations Research ?

Penyelidikan Operasional IJurusan Teknik Industri, Ubaya

Introduction to OR What is OR?

• The application of the scientific methods by teams of individuals to solve problems in order to find solutions which best serve the purposes of the entire organization

Characteristics• View the problems within a system perspective• Apply the scientific method to develop the solution

methodology• Use a team for interdisciplinary approach• Use a mathematical model• Use a high speed computer

Scientific Method An organized approach to the problem In a classical approach

Make a hypothesisSystem will perform … if we do …

Conduct an experiment to test the hypothesis But, in many real world situations, an experiment is

infeasible because Costly Time consuming Uncontrollable variables Dangers, etc

Therefore, we Build a model of the real world problem Conduct experiments or process the model

History of OR Initiated in England during World War II

A team of British scientists set out to make decisions regarding the best utilization of war material

After war, it is adapted to improve efficiency and productivity in the civilian sector.

Today, OR is a dominant and indispensable decision-making tool. A cornerstone of OR is mathematical modeling.

But, intangible factors must be accounted for before a final decision can be reach.

Applications of OR in Business and Industry1. Finance, budgeting and investment

Cash flow analysis, long range capital requirement, dividend policies, investment portfolio, etc.

2. Purchasing, procurement, and exploration Determination of quantities and timing of purchases,

replacement policies3. Physical distribution

Location and size of warehouses, distribution centers, logistics, and supply system

4. Facilities planning Number and location of factories, warehouses, hospitals

5. Manufacturing Production scheduling

Applications of OR in Business and Industry (cont.)6. Maintenance, construction, project scheduling

Maintenance policies, preventive maintenance, maintenance crew size, allocation of resources, project scheduling

7. Marketing Product selection, timing, number of salesman,

advertising strategies8. Personnel

Selection of personnel, recruiting policies, assignment of jobs

9. Research and Development Reliability, control, and development projects

10. Others Social and public affairs, population control, etc.

Computers and OR Industrial and commercial organizations are relying

more and more on the use of computers and quantitative models

Computers are useful tools for solving complex OR problems

Some available computer packages for solving OR models

SAS (Statistical Analysis System) SPSS (Statistical Package for Social Services) GPSS (General Purpose Simulation System) ILOG OPL (optimization programming language) LINDO & LINGO (mathematical modeling tools) QS 3.0 TORA

5-Step Process of OR Study1. Formulation of the problem

Someone has an objective to be achieved The decision maker must have a choice of behavior There must be some doubt as to which course of action

is best in terms of decision maker’s objective There must be an environment to which the problem is

relevant2. Construction of the model

A study of the problem environment Define decision variables, objectives, interactions

between variables and making some assumptions or necessary simplifications about the real environment

Construction of symbolic expressions of the formulation, usually in mathematical terms or in computer language

5-Step Process of OR Study (cont.)3. Solution of the model

Development of algorithms which are techniques for solving models

Quality of solution Feasible solution Satisfactory (simply working for a good result) Optimal solution (want the best solution)

4. Testing the results Is the solution intuitively acceptable? Comparison with historical data Sensitivity analysis

How do small changes in numbers in the model affect the final outcome?

5-Step Process of OR Study (cont.)5. Implementation of the final results

Translate the mathematical solution into a set of easily understood operating procedures or decision rules for each of the persons involved in using and applying the solution

Train the people in the proper use of these rules Plan and execute the transition from the present to

the desired mode of operations Institute controls to maintain and update the

solution Check the initial performance periodically until the

new mode of operation has become routine

Process of OR Study

Real World Problem

Model Construction

Solution to the Model

Suggested Real World

Solution

Real World

Abstract World

1

2

5 4

3

Example 1Imagine that you have a 5-week business commitment between Surabaya (SBY) and Jakarta (JKT). You fly out of SBY on Monday and return on Wednesday. A regular round-trip ticket costs Rp 400,000.00 but a 20% discount is granted if the dates of the ticket span a weekend. A one-way ticket in either direction costs 75% of the regular price. How should you buy the tickets for the 5-week period?

Example 1 (cont.) What are the decision

alternatives? Under what restrictions is the

decision made? What is an appropriate objective

criterion for evaluating the alternatives?

Example 1 (cont.)

SBY JKT SBYJKTSBY JKT JKTJKTSBY SBY SBY

Mon Wed Mon WedMonMonMon WedWedWed

Week 1 Week 2 Week 3 Week 4 Week 5

Alternative IAlternative IIAlternative III

Cost = 5 × 400 = $2000Cost = .75 × 400 + 4 × (.8 × 400) + .75 × 400 = $1880Cost = 5 × (.8 × 400) = $1600

Principal Components of an OR Model The principal components of an OR

model: Alternatives (may take the form of

unknown variables) Restrictions An objective function

The end result is a mathematical model relating these components.

Example 2 Amy, Jim, John, and Kelly are standing on

the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 2, 5, and 10 minutes, respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.