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# Decision Theory

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Operations Management.
Source of reference Operations Management by Stevenson, 10e.

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### Decision Theory

1. 1. CHAPTER Supplement to 5 Decision Theory Prepared by: Group 2 / BA 10 / G 4:00PM – 5:15PM / C507 Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
2. 2. Learning Objectives: Describe the different environments under which operations decisions are made. Describe and use techniques that apply to decision making under uncertainty. Describe and use the expectedvalue approach. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
3. 3. Learning Objectives: Construct a decision tree and use it to analyze a problem. Compute the expected value of perfect information. Conduct sensitivity analysis on a simple decision problem. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
4. 4. Introduction : Decision Theory A general approach to decision making that is suitable to a wide range of operations management decisions: Capacity planning Product and service design Equipment selection Location planning Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
5. 5. Decision Theory characterized as follows: Set of future conditions Decision Theory Known payoff alternatives List of alternatives Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
6. 6. To use this approach, a decision maker would employ this process: Step 1 Identify possible future conditions or state of nature Step 2 Develop a list of possible alternatives Step 3 Determine the payoff associated with each alternative for every possible future condition Step 4 Estimate the likelihood of each possible future conditions Step 5 Evaluate alternatives based to some decision criterion, and select the best alternative Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
7. 7. The information for a decision is often summarized in a payoff table. Payoff Table Table showing the expected payoffs for each alternative in every possible state of nature. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
8. 8. Payoff Table: Example 1.0 POSSIBLE FUTURE DEMAND Alternatives Small Facility Medium Facility Large Facility Low Moderate \$10* \$10 7 (4) 12 2 High \$10 12 16 *Present value in \$ millions. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
9. 9. Causes for Poor Decisions Mistakes in decision process Bounded Rationality Suboptimization Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
10. 10. Mistakes in Decision Process  It happens because of mistakes on the following decisions steps: 1 • Identify the problem. 2 • Specify the objectives and criteria for solution. 3 • Develop suitable alternatives. 4 • Analyze and compare alternatives. 5 • Select the best alternative. 6 • Implement the solution. 7 • Monitor to see that desired result is achieved. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
11. 11. Bounded Rationality Limitations on decision making caused by costs, human abilities, time, technology, and availability of information. Because of these limitations, managers can’t always expect to reach decisions that are optimal in the sense of providing the best possible outcome. They might instead, resort to a satisfactory solution. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
12. 12. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
13. 13. Decision Environments Environment in which it is impossible to asses the likelihood of various future events. Environment in which relevant parameters have known values. Environment at which certain future events have probable outcomes. Risk Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
14. 14. Decision Making Under Certainty When it is known for certain which is of the possible future conditions will happen, just choose the alternative that has the best payoff under the state of nature. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
15. 15. Decision Making Under Certainty Example 2.0 POSSIBLE FUTURE DEMAND Alternatives Low Small Facility \$10* \$10 \$10 7 12 12 (4) 2 16 Medium Facility Large Facility Moderate High *Present value in \$ millions. What will you choose to build if the demand will be low, moderate and high?  If the demand will be low, just choose the small facility with a payoff of \$10 Million.  If the demand is moderate choose to build a medium facility with a payoff \$12 Million.  If the demand is high just build large facility with a \$16 Million. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
16. 16. Decision Making Under Uncertainty Decisions are sometimes made under complete uncertainty. No information is available on how likely the various states of nature are: Maximin Choose the alternative with the best of the worst possible payoff. Maximax Choose the alternative with the best possible payoff. Laplace Choose the alternative with the best average period of any of the alternatives. Minimax Regret Choose the alternative that has the least of worst regrets. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
17. 17. Decision Making Under Uncertainty Example 3.1 POSSIBLE FUTURE DEMAND Alternatives Low Small Facility \$10* \$10 \$10 7 12 12 (4) 2 16 Medium Facility Large Facility Moderate High *Present value in \$ millions. Using the maximin approach what will we choose? The worst payoffs for the alternatives are: Small Facility : \$10 million Medium Facility : 7 million Large Facility : (4) million Hence, since \$10 million is the best we choose to build a small facility. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
18. 18. Decision Making Under Uncertainty Example 3.2 POSSIBLE FUTURE DEMAND Alternatives Low Small Facility \$10* \$10 \$10 7 12 12 (4) 2 16 Medium Facility Large Facility Moderate High *Present value in \$ millions. Using the maximax approach what will we choose? The best payoffs for the Small Facility Medium Facility Large Facility alternatives are: : \$10 million : 12 million : 16 million The best overall payoff is the \$16 million on the third row. Hence, the maximax criterion leads to building a large facility. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
19. 19. Decision Making Under Uncertainty Example 3.3 POSSIBLE FUTURE DEMAND Low Moderate High \$10* \$10 \$10 Alternatives Small Facility Medium Facility 7 Large Facility (4) *Present value in \$ millions. 12 2 12 16 Using the laplace approach what will we choose? Row in Total Row Average (in \$ Million ) (in \$ Million) \$30 \$10.00 31 10.33 14 4.67 Because the medium facility has the highest average, it would be chosen under the Laplace criterion. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
20. 20. Decision Making Under Uncertainty Example 3.4 POSSIBLE FUTURE DEMAND Alternatives Small Facility Medium Facility Large Facility Low Moderate High \$10* \$10 \$10 7 12 12 (4) 2 16 *Present value in \$ millions. Using the minimax regret approach what will we choose? Regrets (in \$ Millions) Alternatives Low Moderate High Worst Small Facility \$0 \$2 \$6 \$6 Medium Facility 3 0 4 4 Large Facility 14 10 0 14 The best of these worst regrets would be chosen using a minimax regret. The lowest regret is 4, which is for medium facility, Hence, it would be chosen. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
21. 21. Decision Making Under Risk Decisions made under the condition that the probability of occurrence for each state of nature can be estimated A widely applied criterion is expected monetary value (EMV). Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
22. 22. Decision Making Under Risk EMV Determine the expected payoff of each alternative, and choose the alternative that has the best expected payoff This approach is most appropriate when the decision maker is neither risk averse nor risk seeking Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
23. 23. Decision Making Under Risk Example 4.0 POSSIBLE FUTURE DEMAND Alternatives Low Small Facility \$10* \$10 \$10 7 12 12 (4) 2 16 Medium Facility Large Facility Moderate High *Present value in \$ millions. Using the EMV criterion, identify the best alternative for these probabilities: low=.30,moderate=.50 and high=.20. EVSmall = EVMedium = EVLarge = .30(\$10)+.50(\$10)+.20(\$10) = .30(\$7) +.50(\$12)+.20(\$12) = .30(\$-4) +.50(\$2) +.20(\$16) = \$10 \$10.5 \$3 Hence, choose the medium facility because it has the highest expected value. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
24. 24. Decision Trees Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
25. 25. Decision Trees Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
26. 26. Decision Trees Example 5.0 Determine the product of the chance probabilities and their respective payoffs of the branches and the expected value of each initiative: Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
27. 27. Decision Trees Build Small Low Demand High Demand .4(\$40) = .6(\$55) = \$16 \$33 Build Large Low Demand High Demand .4(\$50) = .6(\$70) = \$20 \$42 ______________________________________________________________________ Build Small \$16 + \$33 = \$49 Build Large \$20 + \$42 = \$62 Hence, the choice should be to build the large facility because it has a larger expected value than the small facility. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
28. 28. Expected Value of Perfect Information (EVPI) The difference between the expected payoff with perfect information and the expected payoff under risk. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
29. 29. Expected Value of Perfect Information (EVPI) There are two ways to determine EVPI: Expected Payoff Under Certainty Expected Payoff Under Risk EVPI or Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
30. 30. Expected Value of Perfect Information (EVPI) Example 6.1 (Using the first method) .30(\$10) + .50(\$12) + .20(\$16) = \$12.2 The expected payoff risk based on Example 4.0 is \$10.5. EVPI = \$12.2 - \$10.5 = \$1.7 Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
31. 31. Expected Value of Perfect Information (EVPI) Example 6.2 (Using the second method) Using the table of regrets in Example 3.4, we can compute the expected regret for each alternative. Thus: Small Facility .30(0) + .50(2) + .20(6) = 2.2 Medium Facility .30(3) + .50(0) + .20(4) = 1.7 Large Facility .30(14)+.50(10)+.20(0) = 9.2 The lowest expected regret is 1.7. Therefore, EVPI = 1.7.
32. 32. Sensitivity Analysis Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.
33. 33. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.