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Decision Making Chapter: Definitions, Tools, and Criteria

This chapter focuses on defining decision-making terms and concepts, organizing information in tables and trees, computing opportunity loss and utility, and making optimal decisions based on criteria. It also discusses classical and Bayesian statistics and the elements of decision theory.

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Decision Making Chapter: Definitions, Tools, and Criteria

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  1. Decision Making Chapter 19

  2. 5 1 2 3 4 Chapter Goals When you have completed this chapter, you will be able to: Definethe terms state of nature, event, decision alternatives, payoff, and utility Organizeinformation in a payoff table or a decision tree Compute opportunity loss and utility function Findan optimal decision alternative based on a given decision criterion Assess the expected value of additional information

  3. Terminology Classical Statistics … focuses on estimating a parameter, such as the population mean, constructing confidence intervals, or hypothesis testing. … (Bayesian statistics) is concerned with determining which decision, from a set of possible decisions, is optimal. Statistical Decision Theory

  4. Elements of a Decision • Available choices … possible alternatives or acts There are three components to any decision-making situation: • States of Nature …these are future events that are not under the control of the decision maker • Payoffs …numerical gain to the decision maker for each combination of decision alternative and state of nature

  5. Terminology Payoff Table …isa listing of all possible combinations of decision alternatives and states of nature Expected Payoff or Expected Monetary Value (EMV) …is the Expected Value for each decision

  6. A business example Nortel is considering introducing a new wireless telecommunication device into the market. They are considering three alternatives: I. Build a new full scale plant for manufacturing the new product II. Build a medium size plant III. Do not market the product If they decide to market the product, the annual profit will depend on the market response to the product. Suppose preliminary market analysis indicates that the market response to the product may be highly favourable, moderately favourable, or unfavourable. What decision should they make?

  7. Payoff Table (Values … Millions of dollars) Available Choices • Build a new full scale plantD1 • Build a medium size plantD2 • Do not market the product D3 Market response to the product may be highly favourable S1moderately favourable S2unfavourable S3

  8. Nortel's decision...? ? …determine the payoff value for each decision alternative …choose the alternative for which the associated payoff value is maximum

  9. Payoff Table (Values … Millions of dollars) Non-Probabilistic Criteria We don’t have any information about the probabilities of the 3 states of nature, except that they are each non-zero Maximin Criterion Note the minimum payoff for each decisionalternative Select the decision for which this is maximum This Pessimistic view results in Decision 3 … do not market the product

  10. Payoff Table (Values … Millions of dollars) Non-Probabilistic Criteria We don’t have any information about the probabilities of the 3 states of nature, except that they are each non-zero Maximax Criterion Note the maximum payoff for each decisionalternative Select the decision for which this maximum payoff is maximum This Optimistic view results in Decision 1 … builda new full scale plant

  11. Non-Probabilistic Criteria The Pessimistic-Optimistic IndexCriterion of Hurwicz Choose a number alpha between 0 and 1 (called the pessimistic-optimistic index) Payoff Table The value for each decision alternative is then: Alpha (minimum payoff) + (1-alpha)(maximum payoff) Continued…

  12. Non-Probabilistic Criteria The Pessimistic-Optimistic IndexCriterion of Hurwicz Payoff Table Let alpha = 0.4 Alpha (minimum payoff) + (1-alpha)(maximum payoff) = $ -80 million For D1: (0.4)(-800)+(0.6)(400) For D2: (0.4)(-50)+(0.6)(80) = $ 28 million For D3: (0.4)(0)+(0.6)(0) = $ 0 million This view results in Decision 2 – …build a medium sized plant

  13. Probabilistic Criteria We assume that we have prior information about the probabilities of the 3 states of nature (usually based on historical data or subjective estimates) Expected Monetary Value Criterion Payoff Table Select the decision for which this is maximum Calculate the EMV for each decisionalternative Continued…

  14. Probabilistic Criteria Expected Monetary Value Criterion Payoff Table Select the decision for which this is maximum EMV (D1): (0.4)(400)+(0.5)(20) +(0.1)(-800) = $90 m. EMV (D2): (0.4)(80)+(0.5)(60)+(0.1)(-50) = $57 m. EMV (D3): (0.4)(0)+(0.5)(0)+(0.1)(0) = $ 0 m. This view results in Decision 1 – build a full sized plant

  15. A nswer Criteria Based on Opportunity Loss (Regret) … is the loss because the exact state of nature is not known at the time a decision is made …the opportunity loss is computed by takingthe difference between the optimal decision for each state of natureand the other decision alternatives Suppose that Nortel decided to build a medium sized plant…. If market conditions are very favourable (S1), then what is the expected profit?

  16. Expected Profit Criteria Based on Opportunity Loss (Regret) Suppose that Nortel decided to build a medium sized plant…. If market conditionsare highly favourable(S1), then what is the expected profit? Payoff Table But, had they known in advance that the market conditions would be favourable, they would have gone with D1 and achieved an expected profit of $400 million! Therefore, there is an Opportunity Loss of $320 million

  17. Expected Profit Criteria Based on Opportunity Loss (Regret) Suppose that Nortel decided to build a medium sized plant…. If market conditionsare moderately favourable(S2), then what is the expected profit? Payoff Table Therefore, there is an Opportunity Loss of $0 million ...they actually gained $40 million ($60 - $20)!

  18. Opportunity Loss Table Pessimistic Criterion These are the worst case scenarios for each decision alternative The “best” of these “worst cases” is D2

  19. Terminology Value of Perfect Information i.e. …what is the worth of information known in advance beforea strategy is employed? Expected Value of Perfect Information (EVPI) … is the difference between the expected payoffif the state of naturewere knownand the optimal decisionunder the conditions of uncertainty

  20. Terminology Sensitivity Analysis … examines the effects of various probabilities for the states of nature on the expected values for the decision alternatives. Decision Trees … are useful for structuring the various alternatives. They present a picture of the various courses of action and the possible states of nature. See the following Decision Tree Examples…

  21. Decision Tree Examples… Decision Tree

  22. Decision Tree Decision Tree Examples…

  23. Decision Tree Decision Tree Examples…

  24. www.mcgrawhill.ca/college/lind for quizzes extra content data sets searchable glossary access to Statistics Canada’s E-Stat data …and much more! Test your learning… Click on… Online Learning Centre

  25. This completes Chapter 19

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