Bài giảng Operations Management - Supplement 5: Decision Theory

Decision TheoryMcGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.You should be able to:Describe the different environments under which operations are madeDescribe and use techniques that apply to decision making under uncertaintyDescribe and use the expected-value approachConstruct a decision tree and use it to analyze a problemCompute the expected value of perfect informationConduct sensitivity analysis on a simple decision problem5S-*Student SlidesCharacteristics of decisions that are suitable for using decision theoryA set of possible future conditions that will have a bearing on the results of the decisionA list of alternatives from which to chooseA known payoff for each alternative under each possible future condition5S-*Student SlidesIdentify the possible future states of natureDevelop a list of possible alternativesEstimate the payoff for each alternative for each possible future state of natureIf possible, estimate the likelihood of each possible future state of natureEvaluate alternatives according to some decision criterion and select the best alternative5S-*Student SlidesA table showing the expected payoffs for each alternative in every possible state of naturePossible Future DemandAlternativesLowModerateHighSmall facility$10$10$10Medium facility71212Large Facility(4)216A decision is being made concerning which size facility should be constructedThe present value (in millions) for each alternative under each state of nature is expressed in the body of the above payoff table5S-*Student SlidesDecisions are sometimes made under complete uncertainty: No information is available on how likely the various states of nature are.Decision Criteria:MaximinChoose the alternative with the best of the worst possible payoffsMaximaxChoose the alternative with the best possible payoffLaplaceChoose the alternative with the best average payoff Minimax regretChoose the alternative that has the least of the worst regrets5S-*Student SlidesPossible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216The worst payoff for each alternative isSmall facility: $10 millionMedium facility $7 millionLarge facility -$4 millionChoose to construct a small facilityStudent Slides5S-*Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216The best payoff for each alternative isSmall facility: $10 millionMedium facility $12 millionLarge facility $16 millionChoose to construct a large facilityStudent Slides5S-*Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216The average payoff for each alternative isSmall facility: (10+10+10)/3 = $10 millionMedium facility (7+12+12)/3 = $10.33 millionLarge facility (-4+2+16)/3 = $4.67 millionChoose to construct a medium facilityStudent Slides5S-*Possible Future DemandAlternativesLowModerateHighSmall Facility$10$10$10Medium Facility71212Large Facility(4)216Construct a regret (or opportunity loss) tableThe difference between a given payoff and the best payoff for a state of natureRegretsAlternativesLowModerateHighSmall Facility$0$2$6Medium Facility304Large Facility14100Student Slides5S-*RegretsAlternativesLowModerateHighSmall Facility$0$2$6Medium Facility304Large Facility14100Identify the worst regret for each alternativeSmall facility $6 millionMedium facility $4 millionLarge facility $14 millionSelect the alternative with the minimum of the maximum regretsBuild a medium facilityStudent Slides5S-*Decisions made under the condition that the probability of occurrence for each state of nature can be estimatedA widely applied criterion is expected monetary value (EMV)EMVDetermine the expected payoff of each alternative, and choose the alternative that has the best expected payoffThis approach is most appropriate when the decision maker is neither risk averse nor risk seeking5S-*Student SlidesPossible Future DemandAlternativesLow (.30)Moderate (.50)High (.20)Small Facility$10$10$10Medium Facility71212Large Facility(4)216EMVsmall = .30(10) +.50(10) +.20(10) = 10EMVmedium = .30(7) + .50(12) + .20(12) = 10.5EMVlarge = .30(-4) + .50(2) + .20(16) = $3Build a medium facilityStudent Slides5S-*Decision treeA schematic representation of the available alternatives and their possible consequencesUseful for analyzing sequential decisionsComposed ofNodesDecisions – represented by square nodesChance events – represented by circular nodesBranchesAlternatives– branches leaving a square nodeChance events– branches leaving a circular nodeAnalyze from right to leftFor each decision, choose the alternative that will yield the greatest returnIf chance events follow a decision, choose the alternative that has the highest expected monetary value (or lowest expected cost)5S-*Student Slides