In this chapter, you learned to: Define the terms state of nature, event, decision alternatives, payoff, and utility; organize information in a payoff table or a decision tree; compute opportunity loss and utility function; find an optimal decision alternative based on a given decision criterion; assess the expected value of additional information.
19 1 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 19 2 When you have completed this chapter, you will be able to: Define the terms state of nature, event, decision alternatives, payoff, and utility Organize information in a payoff table or a decision tree Compute opportunity loss and utility function Find an optimal decision alternative based on a given decision criterion Assess the expected value of additional information Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Terminology 19 3 Classical Statistics … focuses on estimating a parameter, such as the population mean, constructing confidence intervals, or hypothesis testing … (Bayesian statistics) is concerned with Statistical Decision Theory determining which decision, from a set of possible decisions, is optimal. Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. E lements of a Decision 19 4 Available choices Available choices There are … possible alternatives or acts There are three three States of Nature States of Nature components components …these are future events that are not to any to any under the control of the decision maker decision decision making making Payoffs Payoffs situation: situation: …numerical gain to the decision maker for each combination of decision alternative and state of nature Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Terminology 19 5 Payoff Table Payoff Table …is a listing of all possible combinations of decision alternatives and states of nature Expected Payoff or or Expected Payoff Expected Monetary Value Expected Monetary Value (EMV) (EMV) …is the Expected Value for each decision Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. A business example A business example 19 6 Nortel is considering introducing a new wireless Nortel is considering introducing a new wireless telecommunication device into the market. telecommunication device into the market. They are considering three alternatives: They are considering three alternatives: I. Build a new full scale plant for I. Build a new full scale plant for manufacturing the new product manufacturing the new product II. Build a medium size plant II. Build a medium size plant III. Do not market the product III. Do not market the product If they decide to market the product, the annual profit will If they decide to market the product, the annual profit will depend on the market response to the product. depend on the market response to the product. Suppose preliminary market analysis indicates that the market Suppose preliminary market analysis indicates that the market response to the product may be highly favourable, response to the product may be highly favourable, moderately favourable, or unfavourable. moderately favourable, or unfavourable. What decision should they make? What decision should they make? Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Available Choices Available Choices I.I II II 19 7 Build a new full scale plant D1 Build a new full scale plant D1 Build a medium size plant D2 Build a medium size plant D2 III Do not market the product D3 Do not market the product D3 III Market response to the product may be Market response to the product may be highly favourable S1 highly favourable S1 moderately moderately favourable S2 favourable S2 unfavourable S3 unfavourable S3 Payoff Table Payoff Table (Values … Millions of dollars) (D1) (D2) (D3) Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. (S1) 400 80 (S2) 20 60 (S3) 800 50 19 8 …determine the payoff value for each decision alternative …choose the alternative for which the associated payoff value is maximum Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. NonProbabilistic Criteria NonProbabilistic Criteria 19 9 We don’t have any information about the We don’t have any information about the probabilities of the 3 states of nature, probabilities of the 3 states of nature, except that they are each nonzero except that they are each nonzero Maximin Criterion Maximin Criterion Note the minimum payoff Note the minimum payoff for each decision for each decision alternative alternative Select the decision for which this is maximum Payoff Table Payoff Table (Values … Millions of dollars) (D1) (D2) (D3) (S1) 400 80 (S2) 20 60 This Pessimistic view results in Decision 3 This Pessimistic view results in Decision 3 … do not market the product … do not market the product Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. (S3) 800 50 NonProbabilistic Criteria NonProbabilistic Criteria 19 10 We don’t have any information about the We don’t have any information about the probabilities of the 3 states of nature, except probabilities of the 3 states of nature, except that they are each nonzero that they are each nonzero Maximax Criterion Maximax Criterion Payoff Table Payoff Table Note the maximum payoff Note the maximum payoff for each decision for each decision alternative alternative (Values … Millions of dollars) Select the decision for which this maximum payoff is maximum (D1) (D2) (D3) (S1) (S2) (S3) 400 80 20 60 800 50 This Optimistic view results in Decision 1 This Optimistic view results in Decision 1 … build a new full scale plant … build a new full scale plant Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. NonProbabilistic Criteria NonProbabilistic Criteria 19 11 The PessimisticOptimistic Index The PessimisticOptimistic Index Criterion of Hurwicz Criterion of Hurwicz Choose a number alpha between 0 and 1 Choose a number alpha between 0 and 1 (called the pessimisticoptimistic index) (called the pessimisticoptimistic index) (S1) (S2) (S3) 400 20 800 (D2) 80 60 50 (D3) 0 Payoff Table Payoff Table (D1) The value for each decision alternative is then: The value for each decision alternative is then: Alpha (minimum payoff) + (1alpha)(maximum payoff) Alpha (minimum payoff) + (1alpha)(maximum payoff) Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Continued… NonProbabilistic Criteria NonProbabilistic Criteria 19 12 The PessimisticOptimistic Index The PessimisticOptimistic Index Criterion of Hurwicz Criterion of Hurwicz (S1) (S2) (S3) 400 20 800 (D2) 80 60 50 (D3) 0 Payoff Table Payoff Table (D1) Let alpha = 0.4 Alpha (minimum payoff) + (1alpha)(maximum payoff) Alpha (minimum payoff) + (1alpha)(maximum payoff) For D1: (0.4)(800)+(0.6)(400) = $ 80 million For D2: (0.4)(50)+(0.6)(80) = $ 28 million For D3: (0.4)(0)+(0.6)(0) = $ 0 million This view results in D Decision ecision 22 – …build a medium sized plant – …build a medium sized plant This view results in Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Probabilistic Criteria Probabilistic Criteria 19 13 We assume that we have prior information We assume that we have prior information about the pprobabilities of the 3 states of nature robabilities of the 3 states of nature about the (usually based on historical data or (usually based on historical data or subjective estimates) subjective estimates) Expected Monetary Value Expected Monetary Value Criterion Criterion 0.4 0.5 0.1 (S1) (S2) (S3) (D1) 400 20 800 (D2) 80 60 50 (D3) 0 Payoff Table Payoff Table Select the Select the decision decision for which this for which this is maximum is maximum Calculate the EMV for each decision alternative Calculate the EMV for each decision alternative Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Continued… Probabilistic Criteria Probabilistic Criteria 19 14 Expected Monetary Value Expected Monetary Value Criterion Criterion 0.4 0.5 0.1 (S1) (S2) (S3) (D1) 400 20 800 (D2) 80 60 50 (D3) 0 Payoff Table Payoff Table Select the Select the decision for decision for which this is which this is maximum maximum EMV (D1): (0.4)(400)+(0.5)(20) +(0.1)(800) EMV (D2): (0.4)(80)+(0.5)(60)+(0.1)(50) EMV (D3): (0.4)(0)+(0.5)(0)+(0.1)(0) = $90 m = $57 m = $ 0 m This view results in Decision 1 – build a full sized plant This view results in Decision 1 – build a full sized plant Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Criteria Based on Criteria Based on Opportunity Loss (Regret) Opportunity Loss (Regret) 19 15 … 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 taking the difference between the optimal decision for each state of nature and the other decision alternatives Suppose that Nortel decided to build a medium sized medium sized plant… plant… Suppose that Nortel decided to build a If market conditions are very favourable (S1), then what If market conditions are very favourable (S1), then what is the expected profit? is the expected profit? Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Criteria Based on Criteria Based on Opportunity Loss (Regret) Opportunity Loss (Regret) 19 16 Suppose that Nortel decided to build a medium sized plant… Suppose that Nortel decided to build a medium sized plant… If market conditions are highly favourable are highly favourable (S1), (S1), If market conditions then what is the expected profit? then what is the expected profit? Payoff Table (S1) (S2) (S3) Payoff Table Expected Profit (D1) 400 20 800 (D2) 80 60 50 (D3) 0 But, had they known in advance that the market conditions But, had they known in advance that the market conditions would be favourable, they would have gone with D1 would be favourable, they would have gone with D1 and achieved an expected profit of $400 million! and achieved an expected profit of $400 million! Therefore, there is an Opportunity Loss Opportunity Loss of $320 million of $320 million Therefore, there is an Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Criteria Based on Criteria Based on Opportunity Loss (Regret) Opportunity Loss (Regret) 19 17 Suppose that Nortel decided to build a medium sized plant… Suppose that Nortel decided to build a medium sized plant… If market conditions are moderately favourable are moderately favourable (S2), (S2), If market conditions then what is the expected profit? then what is the expected profit? Payoff Table (S1) (S2) (S3) Payoff Table Expected Profit (D1) 400 20 800 (D2) 80 60 50 (D3) 0 Therefore, there is an Opportunity Loss Opportunity Loss of $0 of $0 Therefore, there is an million they actually gained $40 million ($60 $20)! million they actually gained $40 million ($60 $20)! Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Opportunity Loss Opportunity Loss Table Table 19 18 Pessimistic Criterion Pessimistic Criterion These are the worst case scenarios for each decision alternative Market Response Decision (D1) (S1) (S2) (S3) 40 800 (D2) 320 0 50 (D3) 400 60 The “best” of these “worst cases” is D2 The “best” of these “worst cases” is D2 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Terminology 19 19 Value of Perfect Information i.e. …what is the worth of information known in advance before a strategy is employed? Expected Value of Perfect Information (EVPI) … is the difference between the expected payoff if the state of nature were known and the optimal decision under the conditions of uncertainty Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Terminology 19 20 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… Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Decision Tree Examples… Decision Tree Examples… (D1) (D2) Decision Decision (D3) Tree Tree (S1) 400 80 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. (S2) 20 60 (S3) 800 50 19 21 Decision Tree Examples… Decision Tree Examples… (D1) (D2) Decision Decision (D3) Tree Tree (S1) (S2) (S3) 400 80 20 60 800 50 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 19 22 Decision Tree Examples… Decision Tree Examples… (D1) (D2) Decision Decision (D3) Tree Tree (S1) (S2) (S3) 400 80 20 60 800 50 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 19 23 Test your learning… … Test your learning … … n o n o k ilcick CCl www.mcgrawhill.ca/college/lind Online Learning Centre for quizzes extra content data sets searchable glossary access to Statistics Canada’s EStat data …and much more! Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 19 24 19 25 This completes Chapter 19 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. ... under the control of the decision maker decision decision making making Payoffs Payoffs situation: situation: …numerical gain to the decision maker for each combination of ... …is the Expected Value for each decision Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. A business example A business example 19 6 Nortel is considering introducing a new wireless ... have completed this chapter, you will be able to: Define the terms state of nature, event, decision alternatives, payoff, and utility Organize information in a payoff table or a decision tree Compute opportunity loss and utility function