OPERATIONS RESEARCH

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Apr 20, 2023 Operations Research 1

OPERATIONS RESEARCH

GRADUATE SCHOOL OF SYSTEM ENGINEERING FACULTY OF ENGINEERING

UNIVERSITAS GADJAH MADA

SUHANAN, JOKO WALUYO, AGUS PRASETYA

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1. Introduction to Operations Research )2. Linear Programming Models3. Simplex methode4. Duality and Sensitivity Analysis 5. Transportation model6. Network Flow Programming Models : PERT/CPM7. Integer programming models and methods8. Dynamic Programming9. Non Linear Programming, constrained and un-constrained.10.Markov Chain Models11.Queing Model

Riset Operasi (Operations Research) (TKT 6105) 3 SKS

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Referensi/Acuan:

Rao, S. S., 2009, Engineering Optimization: Theory and Practice, 3rd edition, John Wiley & SonsMonplaisir, L., 2007, Deterministic Optimization, College of Engineering, WayneStateUniversity, DetroitP.A. Jensen and JF. Bard, 2003, Operations Research:Model and Methods, John Wiley & Sons, New York.http://www.amazon.com/ Engineering-Optimization-Practice-Singiresu ao/dp/0470183527/ref= sr_1_1?ie=UTF8&s=books&qid=1264141985&sr=8-1Bendsoe, M.P. and O. Sigmund, 1995, Topology Optimization: Theory, Methods and Applications, Springer PublisherDe Groot, M. H.,1970,Optimal Statistical Decision,McGraw-Hill,New YorkHillier, F.S., and Lieberman, G.J., 1995, Introduction to Operations Research, 6th ed., McGraw – Hill Inc., Singapore

Kriteria penilaian:Tugas mandiri/quiz (20%), UTS (40%), UAS (40%)

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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.

the use of mathematical models in providing guidelines to managers for making effective decisions within the state of the current information, or in seeking further information if current knowledge is insufficient to reach a proper decision.”

Operations research (OR) is a discipline explicitly devoted to aiding decision makers.

Operational Research can be considered as being the application of scientific method by inter-disciplinary teams to problems involving the control of organized (man-machine) systems so as to provide solutions which best serve the purposes of the organization as a whole.

Operations research (also known as management science) is a collection of techniques based on mathematics and other scientific approaches that finds solutions to your problems

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Is to provide a framework for constructing models of decision making-problems, finding the best solutions with respect to given measure of merit, and implementing those solutions in an attemp to solve the problems.

Goal of OR

The problem is a situation arising in an organization that requires some solution

The problem may be actual or abstract, it may involve current operations or proposed expansions or contractions due to expected market shifts, it may become apparent through consumer complaints or through employee suggestions, it may be a conscious effort to improve efficiency or a response to an unexpected crisis.

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Nature of O.R : Characteristics

• Inter-disciplinary team approach• Systems approach• Helpful in improving the quality of solution• Apply the scientific method to develop the solution

methodology• Goal oriented optimum solution• Use of mathematical models• Require willing executives• Reduces complexity•Use a high speed computer

The decision maker is the individual or group responsible for making decisions regarding the solution.

The individual or group called upon to aid the decision maker in the problem solving process is the analyst.

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5. Manufacturing Production scheduling

Applications of OR

1. Finance, budgeting and investments Cash flow analysis, long range capital requirements, investment portfolios, etc.

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

3. Physical distribution Location and size of warehouses, distribution centers; logistics and supply systems

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

Field of OR comprises a rich of analytic techniques that have been developed over the last 50 years to solve complex problem arising in all aspect of human activity

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

Applications of OR …… (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 strategies

8. Personnel Selection of personnel, recruiting policies, assignments of jobs

9. Research and development Reliability, control of development projects

10. Military Allocation of military forces and resources

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• After World War II: success attracted industrial managers to solve complex managerial problems

• 1950: O.R. began to develop in industrial field in US• 1953: Operations Research Society of America was formed• 1957: International Federation of Operational Research Society

Development of O.R.

• Developed in military context during world war II, pioneered by the British scientists– Research on military operations

• US military management was motivated– Development of new flight pattern– Planning sea mining– Effective utilization of electronic equipment

• Similar operations in Canada and France• Till 50’s: use of O.R. confined to military purposes

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• Action phase– Implementation of the tested results of the model

Phases of O.R. study

• Judgment phase– Determination of the problem– Establishment of the objectives and values– Determination of suitable measures of effectiveness

• Research phase– Observation and data collection– Formulation of hypothesis and models– Observation and experimentation to test the hypothesis– Prediction of various results, generalization,

consideration of alternative method

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1. Formulating the problem2. Constructing the model3. Deriving the solution – Analytical method – Numerical method – Simulation method4. Testing the model and establish a

procedure5. Implementing the solution

Methodology of O.R.

1. Formulating the problem

The first analytical step of the solution process is to formulate the problem in more precise terms.

At the formulation stage, statements of objectives, constraints on solutions, appropriate assumptions, descriptions of processes, data requirements, alternatives for action and metrics for measuring progress are introduced.

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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

A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated.

2. Constructiing the model

A model is always an abstraction that is, by necessity, simpler than the reality

Models must be both tractable -- capable of being solved, and valid -- representative of the true situation.

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3. Deriving the model (find a solution)

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

It may be necessary to develop new techniques specifically tailored to the problem at hand.

Development of algorithms which are techniques for solving models

A model that is impossible to solve may have been formulated incorrectly or burdened with too much detail.

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Is the solution intuitively acceptable? Comparison with historical data Sensitivity analysis - How do small changes in numbers in

the model affect the final outcome?

4. Testing the model and establish a procedure

Once a solution is accepted a procedure must be designed to retain control of the implementation effort

Control may be achieved with a set of operating rules, a job description, laws or regulations promulgated by a government body, or computer programs that accept current data and prescribe actions.

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5. Implementing the solution

• 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

• Check the initial performance periodically until

the new mode of operation has become routine

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The OR Process

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5-Step Process of OR Study

Formulation of the problem

Construction of the model

Solution of the model

Testing the results

Implementation of the final results

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What is Operations Research?

OperationsThe activities carried out in an organization. ResearchThe process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. ModelAn abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.

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Systems ApproachInclude broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered.

Optimal SolutionA solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. TeamA group of individuals bringing various skills and viewpoints to a problem. Operations Research TechniquesA collection of general mathematical models, analytical procedures, and algorithms.

OPERATIONS RESEARCH

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