Introduction to Operations Research

1. Introduction to Operations Research

2. Operations Research • Quantitative methods to support managerial decisions • The application of a scientific approach to solving management problems in order to facilitate better decision making • A philosophy of using a logical, systematic approach to decision making

3. Operations Research • Also referred as: • Operations Analysis • Management Science • Quantitative Analysis

4. Operations Research • Similar to • Systems Analysis • Systems Engineering • Industrial Engineering

5. Operations Research • OA IS NOT “READY MADE” DECISIONS

6. Operations Research • OA Provides decision makers with essential factors of the real problem and offers alternatives to approach the problem

7. History • Originated in WW II when the military turned to civilian scientists for help in resolving complex operational problems • Early warning radar • Gunnery • Convoy composition, tactics • ASW (ASWORG) • and others

8. The Evolution of OR 1990 Expert Systems and Artificial Intelligence 1980 Decision Support Systems Information Systems 1970 Goal Programming Decision Theory 1960 Network Models Dynamic Programming 1950 Linear Programming Game Theory 1940 Transportation 1930 Assignment Technique 1920 Inventory Control Queuing Theory 1910 Markov Analysis 1900

15. OPTION ADVISIORS • OptionAdvisor • Marine Corps LCOL Mislick • Land Combat LTC Manago • Simulation, Modeling and Analysis CDR Boensel • Supply Corps CDR Maher • Human Factors LCDR Shilling • International Professor Dell

16. Overview of Operations Research • Scientific Approach to Managerial Decision Making • Considers both Quantitative and Qualitative Factors Quantitative Analysis Meaningful Information Raw Data

17. The Operations Research Approach Define the Problem Develop a Model Acquire Input Data Develop a Solution Test the Solution Analyze the Results Implement the Solution

18. Define the Problem • The most important step, and often the most difficult • A clear and concise statement of the problem is essential • Must separate the symptoms from the underlying causes • Identify, observe, define

19. Define the Problem • Select those problems where quantitative analysis will do the most good • Develop specific, measurable objectives

20. Possible Problems • Conflicting viewpoints • Impact on other departments • Beginning assumptions • Solution outdated

21. Develop a Model • Models are the principle tool of management science • An abstract representation of an existing problem • Comprised of mathematical relationships used to evaluate alternative courses of action • variables • parameters • Spreadsheet-based

22. Advantages of Using Models • They are less expensive and disruptive than experimenting with the real world system • They allow quantitative analysts to ask “What if” types of questions • They are built for management problems and encourage management input

23. Advantages of Using Models • They force a consistent and systematic approach to the analysis of problems • They require managers to be specific about constraints and goals relating to a problem. • They can help reduce the time needed in decision making.

24. Possible Problems • May be expensive and time-consuming to develop and test if no textbook model applies • Are often misused and misunderstood (and feared) because of their mathematical complexity • Tend to downplay the role and value of nonquantifiable information • Often have assumptions that oversimplify the variables of the real world

25. Acquire Input Data • Essential to obtain accurate data for the model • Improper data will lead to misleading results

26. Possible Problems • Using accounting data • Validity of data

27. Develop a Solution • Involves manipulating the data to arrive at an optimal solution • Solve an equation • Trial and error • Complete enumeration • Algorithm

28. Possible Problems • Hard-to-understand mathematics • Only one answer is limiting

29. Test the Solution • Solution depends on accuracy of the input data and the model • Do results make sense?

30. Analyze the Results • Determine the implications of the solution • Conduct sensitivity analysis to determine how much the solution varies with changes in the model or input data • Model is an approximation of reality • Data may be incomplete

31. Implement the Results • Not always easy despite the potential of significant cost savings, increases in profit • Compelling reasons why the solution should be implemented may be required to overcome resistance to change

32. Models and OR Techniques Can Help: • Gain deeper insight into the nature of business relationships • Find better ways to assess values in such relationships; and • See a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions

33. THE OA METHOD • Reference: Naval Operations Analysis, Wagner Mylander, and Sanders

34. THE OA METHOD • Formulation of the Problem • Analysis of the Problem • Communicate the Results • Analyst assistance to implement result

35. THE OA METHOD • Formulation of the Problem • ID objectives of the operations decision maker • ID reasonable alternative courses of action (COA’s) • Define measures of effectiveness (MOE’s) to provide an ordering scheme of COA’s

36. THE OA METHOD • Analysis of the Problem • Construct a model (analytical or simulation), “…that is faithful to reality and amenable to analysis.” • Evaluate in terms of the MOE outcomes of the alternative courses of action • Conduct operational trials

37. THE OA METHOD • AA Fired AA not Fired • ------------------------------------------------------------------- • Attacks 331 155 • Ships Attacked 155 71 • Bombs Dropped 632 304 • Bombs which hit 50 39 • Ships Sunk 16 18 • Planes Shot Down 13 0

38. THE OA METHOD • AA Fired AA not Fired • ------------------------------------------------------------------- • Attacks 331 155 • Ships Attacked 155 71 • Bombs Dropped 632 304 • Bombs which hit 50 39 • Ships Sunk 16 18 • Planes Shot Down 13 0 • Give a concise statement of the objective.

39. THE OA METHOD • AA Fired AA not Fired • ------------------------------------------------------------------- • Attacks 331 155 • Ships Attacked 155 71 • Bombs Dropped 632 304 • Bombs which hit 50 39 • Ships Sunk 16 18 • Planes Shot Down 13 0 • State alternative courses of action

40. THE OA METHOD • AA Fired AA not Fired • ------------------------------------------------------------------- • Attacks 331 155 • Ships Attacked 155 71 • Bombs Dropped 632 304 • Bombs which hit 50 39 • Ships Sunk 16 18 • Planes Shot Down 13 0 • Identify MOE’s to be used to assess the problem

41. THE OA METHOD • AA Fired AA not Fired • ------------------------------------------------------------------- • Attacks 331 155 • Ships Attacked 155 71 • Bombs Dropped 632 304 • Bombs which hit 50 39 • Ships Sunk 16 18 • Planes Shot Down 13 0 • Analyze the problem using the appropriate MOE.

42. THE OA METHOD • Conclusions and Recommendations