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ISMT 161: Introduction to Operations Management 4 What is the best way to solve your problem? Decision Analysis

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ISMT 161: Introduction to Operations Management Decision Analysis 4 Every decision you make uses some kind of model, whether you know it or not. 4 We will take a more systematic look at the decision process and the underlying theories.

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ISMT 161: Introduction to Operations Management The Decision Process Identify the Problem Specify objectives and the criteria for choosing a solution Develop alternatives 4 Analyze and compare alternatives

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ISMT 161: Introduction to Operations Management The Decision Process (Cont) Select the best alternative Implement the chosen alternative 4 Monitor the results

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ISMT 161: Introduction to Operations Management Causes of Poor Decisions Bounded Rationality The limitations on decision making caused by costs, human abilities, time, technology, and availability of information

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ISMT 161: Introduction to Operations Management Causes of Poor Decisions (Cont ) Suboptimization The result of different departments each attempting to reach a solution that is optimum for that department

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ISMT 161: Introduction to Operations Management Decision Environments Certainty - Environment in which relevant parameters have known values 4 Risk - Environment in which certain future events have probable outcomes 4 Uncertainty - Environment in which it is impossible to assess the likelihood of various future events

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ISMT 161: Introduction to Operations Management Decision Theory Decision Theory represents a general approach to decision making which is suitable for a wide range of operations management decisions, including: capacity planning product and service design product and service design equipment selection location planning

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ISMT 161: Introduction to Operations Management Decision Theory Elements A set of possible future conditions exists that will have a bearing on the results of the decision A list of alternatives for the manager to choose from 4 A known payoff for each alternative under each possible future condition

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ISMT 161: Introduction to Operations Management Decision Theory Process Identify possible future conditions called states of nature Develop a list of possible alternatives, one of which may be to do nothing 4 Determine the payoff associated with each alternative for every future condition

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ISMT 161: Introduction to Operations Management Decision Theory Process (Cont ’d ) If possible, determine the likelihood of each possible future condition 4 Evaluate alternatives according to some decision criterion and select the best alternative

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ISMT 161: Introduction to Operations Management Decision situations 4 under Certainty 4 under Uncertainty 4 under Risk

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ISMT 161: Introduction to Operations Management Payoff Table Possible future demand* *Present value in $ millions

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ISMT 161: Introduction to Operations Management Decision Making under Uncertainty - Some Criteria Maximin - Choose the alternative with the best of the worst possible payoffs Maximax - Choose the alternative with the best possible payoff Laplace (weighted average) - Choose the alternative with the best average payoff of any of the alternatives Minimax Regret - Choose the alternative that has the least of the worst regrets

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ISMT 161: Introduction to Operations Management Example - Maximin 4 Maximin

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ISMT 161: Introduction to Operations Management Example - Minimax regret 4 Regret table (opportunity losses) Regrets (in $ mil.)

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ISMT 161: Introduction to Operations Management Example - EMV 4 EMV - expected monetary value -The best expected value among the alternatives 4 Suppose the probabilities for the future demand are: low = 0.3, moderate =.5 and high =.2. Find the EMV for the best alternatives: EV(small) =.3(10) +.5(10) +.2(10) = 10 EV(medium) =.3(7) +.5(12) +.2(12) = 10.5 EV(large) =.3(-4) +.5(2) +.2(16) = 3 4 Thus the medium facility has the highest EV.

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ISMT 161: Introduction to Operations Management Decision Tree- Schematic representation of the alternatives and their possible consequences State of nature 1 B Payoff 1 State of nature 2 Payoff 2 Payoff 3 2 Choose A 3 Choose A 4 Payoff 6 State of nature 2 2 Payoff 4 Payoff 5 Choose A 5 Choose A 6 State of nature 1 Choose A 1 Choose A 2 1 Decision Point Chance Event

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ISMT 161: Introduction to Operations Management Expected Value of Perfect Information Expected value of perfect information - the difference between the expected payoff under certainty and the expected payoff under risk Expected value of perfect information = Expected payoff under certainty - expected payoff under risk

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ISMT 161: Introduction to Operations Management Constructing a Decision Tree 4 List all the possible alternatives of decisions 4 List all the outcomes of random events 4 Work through the possible decisions and random events chronologically 4 Fill in final outcomes and payoffs, and probability distributions of random events if necessary

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ISMT 161: Introduction to Operations Management Example (p.86, problem 4) 4 A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be $400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of $50, If a large facility is built and demand is high, the estimated net present value is $800,000. If demand turns out to be low, the net present value will be -$10,000. The probability that demand will be high is estimated to be.60 and that of low would be (a) Analyze using a tree diagram. (b) Compute the EVPI. How could this information be useful?

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ISMT 161: Introduction to Operations Management Constructing the decision tree 4 Alternatives: – build small, –build large; –expand (for high demand and build small ) –maintain (…) 4 Outcomes: low demand, high demand

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ISMT 161: Introduction to Operations Management Example (solutions) Demand low (.4) B Demand high (.6) 2 Maintain Expand Demand low (.4) Build small Build large 1 Demand high (.6) $400,000 (1) $400,000 (2) $450,000(3) - $10,000(4) $800,000(5)

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ISMT 161: Introduction to Operations Management Example (solution continued) 4 The expected net present value of the alternatives 4 (1).4 400,000 = 160,000 4 (2) can be eliminated (since its npv is less than expansion) 4 (3).6 450,000 = 270,000 4 (4).4 (-10,000) = -4,000 4 (5).6 800,000 = 480,000 4 Build small expected npv = = Build large expected npv = = Since building a large capacity has the higher expected net present value, select “build large” alternative

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ISMT 161: Introduction to Operations Management Rollback approach for EMV Demand low (.4) Demand high (.6) 2 Maintain Expand Demand low (.4) Build small Build large 1 Demand high (.6) $400,000 (1) $400,000 (2) $450,000(3) - $10,000(4) $800,000(5) 450K 430K 476K

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ISMT 161: Introduction to Operations Management Example (solution continued) 4 Expected payoff under certainty =.4(400,000) +.6(800,000) = 640,000 4 Expected payoff under risk = 476,000 4 Expected value of perfect Information = 640, ,000 = 164,000

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ISMT 161: Introduction to Operations Management Sensitivity Analysis A B C A bestC bestB best #1 Payoff#2 Payoff Sensitivity analysis: determine the range of probability for which an alternative has the best expected payoff

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