1. What is Operations Research ?
Penyelidikan Operasional I
Jurusan Teknik Industri, Ubaya

2. Introduction to OR What is OR? Characteristics
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

3. Scientific Method An organized approach to the problem
In a classical approach
Make a hypothesis
System 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

4. 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.

5. Applications of OR in Business and Industry
Finance, budgeting and investment
Cash flow analysis, long range capital requirement, dividend policies, investment portfolio, etc.
Purchasing, procurement, and exploration
Determination of quantities and timing of purchases, replacement policies
Physical distribution
Location and size of warehouses, distribution centers, logistics, and supply system
Facilities planning
Number and location of factories, warehouses, hospitals
Manufacturing
Production scheduling

6. Applications of OR in Business and Industry (cont.)
Maintenance, construction, project scheduling
Maintenance policies, preventive maintenance, maintenance crew size, allocation of resources, project scheduling
Marketing
Product selection, timing, number of salesman, advertising strategies
Personnel
Selection of personnel, recruiting policies, assignment of jobs
Research and Development
Reliability, control, and development projects
Others
Social and public affairs, population control, etc.

7. 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

8. 5-Step Process of OR Study
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 relevant
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

9. 5-Step Process of OR Study (cont.)
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)
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?

10. 5-Step Process of OR Study (cont.)
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

11. Process of OR Study Real World Suggested Real World Solution
Problem 4 5 1
Solution
to the Model 3 2
Model
Construction
Abstract World

12. Example 1
Imagine 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, 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?

13. 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?

14. Example 1 (cont.) Alternative II Alternative III Alternative I
Cost = 5 × (.8 × 400) = $1600
Cost = 5 × 400 = $2000
Cost = .75 × × (.8 × 400) × 400 = $1880

15. 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.

16. 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.