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

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

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

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 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

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.

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 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

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?

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

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

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 400,000.00 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.) Alternative II Alternative III Alternative I Cost = 5 × (.8 × 400) = $1600 Cost = 5 × 400 = $2000 Cost = .75 × 400 + 4 × (.8 × 400) + .75 × 400 = $1880

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.