OPERATIONS RESEARCH suhananugm ac id SUHANAN JOKO WALUYO

OPERATIONS RESEARCH suhanan@ugm. ac. id SUHANAN, JOKO WALUYO, AGUS PRASETYA GRADUATE SCHOOL OF SYSTEM ENGINEERING FACULTY OF ENGINEERING UNIVERSITAS GADJAH MADA 21 -Nov-20 Operations Research 1

Riset Operasi (Operations Research) (TKT 6105) 3 SKS suhanan@ugm. ac. id 1. Introduction to Operations Research ) 2. Linear Programming Models 3. Simplex methode 4. Duality and Sensitivity Analysis 5. Transportation model 6. Network Flow Programming Models : PERT/CPM 7. Integer programming models and methods 8. Dynamic Programming 9. Non Linear Programming, constrained and un-constrained. 10. Markov Chain Models 11. Queing Model 21 -Nov-20 Operations Research 2

Referensi/Acuan: suhanan@ugm. ac. id ü Rao, S. S. , 2009, Engineering Optimization: Theory and Practice, 3 rd edition, John Wiley & Sons ü Monplaisir, L. , 2007, Deterministic Optimization, College of Engineering, Wayne. State. University, Detroit ü P. A. Jensen and JF. Bard, 2003, Operations Research: Model and Methods, John Wiley & Sons, New York. ü http: //www. amazon. com/ Engineering-Optimization-Practice. Singiresu ao/dp/0470183527/ref= sr_1_1? ie=UTF 8&s=books&qid=1264141985&sr=8 -1 ü Bendsoe, M. P. and O. Sigmund, 1995, Topology Optimization: Theory, Methods and Applications, Springer Publisher ü De Groot, M. H. , 1970, Optimal Statistical Decision, Mc. Graw-Hill, New York ü Hillier, F. S. , and Lieberman, G. J. , 1995, Introduction to Operations Research, 6 th ed. , Mc. Graw – Hill Inc. , Singapore Kriteria penilaian: Tugas mandiri/quiz (20%), UTS (40%), UAS (40%) 21 -Nov-20 Operations Research 3

What is OR ? suhanan@ugm. ac. id ü 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. ü 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. ” ü 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. ü Operations research (OR) is a discipline explicitly devoted to aiding decision makers. ü 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 21 -Nov-20 Operations Research 4

Goal of OR suhanan@ugm. ac. id 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. 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. 21 -Nov-20 Operations Research 5

suhanan@ugm. ac. id 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. 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 21 -Nov-20 Operations Research 6

Applications of OR suhanan@ugm. ac. id 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 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. 5. Manufacturing Production scheduling 21 -Nov-20 Operations Research 7

Applications of OR …… (cont…. . ) suhanan@ugm. ac. id 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 11. Others Social and public affairs, population control, etc. 21 -Nov-20 Operations Research 8

Development of O. R. suhanan@ugm. ac. id • 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 • 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 21 -Nov-20 Operations Research 9

Phases of O. R. study suhanan@ugm. ac. id • 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 • Action phase – Implementation of the tested results of the model 21 -Nov-20 Operations Research 10

Methodology of O. R. suhanan@ugm. ac. id 1. Formulating the problem 2. Constructing the model 3. Deriving the solution – Analytical method – Numerical method – Simulation method 4. Testing the model and establish a procedure 5. Implementing the solution 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. 21 -Nov-20 Operations Research 11

2. Constructiing the model suhanan@ugm. ac. id A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. 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. 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 21 -Nov-20 Operations Research 12

3. Deriving the model (find a solution) suhanan@ugm. ac. id Development of algorithms which are techniques for solving models It may be necessary to develop new techniques specifically tailored to the problem at hand. A model that is impossible to solve may have been formulated incorrectly or burdened with too much detail. Quality of solution - Feasible solution - Satisfactory (simply working for a good result) - Optimal solution (want the best solution) 21 -Nov-20 Operations Research 13

4. Testing the model and establish a procedure - suhanan@ugm. ac. id Is the solution intuitively acceptable? Comparison with historical data Sensitivity analysis How do small changes in numbers in the model affect the final outcome? 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. 21 -Nov-20 Operations Research 14

5. Implementing the solution suhanan@ugm. ac. id • 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 21 -Nov-20 Operations Research 15

suhanan@ugm. ac. id The OR Process 21 -Nov-20 Operations Research 16

suhanan@ugm. ac. id 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 21 -Nov-20 Operations Research 17

suhanan@ugm. ac. id What is Operations Research? Operations The activities carried out in an organization. Research The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. Model An abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program. 18

Systems Approach suhanan@ugm. ac. id Include broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered. Optimal Solution A solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. Team A group of individuals bringing various skills and viewpoints to a problem. Operations Research Techniques A collection of general mathematical models, analytical procedures, and algorithms. 19