Bài giảng Statistical Techniques in Business and Economics - Chapter 19 Decision Making

Chapter 19Decision MakingChapter GoalsDefine the terms state of nature, event, decision alternatives, payoff, and utilityOrganize information in a payoff table or a decision treeCompute opportunity loss and utility functionFind an optimal decision alternative based on a given decision criterionWhen you have completed this chapter, you will be able to:1234Assess the expected value of additional information5TerminologyClassical Statistics focuses on estimating a parameter, such as the population mean, constructing confidence intervals, or hypothesis testing.Statistical Decision Theory (Bayesian statistics) is concerned with determining which decision, from a set of possible decisions, is optimal. E lements of a Decision Payoffs possible alternatives or actsnumerical gain to the decision maker for each combination of decision alternative and state of naturethese are future events that are not under the control of the decision maker Available choices States of NatureThere are three components to any decision-making situation:Payoff Tableis a listing of all possible combinations of decision alternatives and states of natureTerminologyExpected Payoff or Expected Monetary Value (EMV)is the Expected Value for each decisionA business exampleNortel 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 productII. Build a medium size plantIII. Do not market the productIf 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? Available ChoicesBuild a new full scale plant D1Build a medium size plant D2Do not market the product D3Market response to the product may be highly favourable S1 moderately favourable S2 unfavourable S3(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Payoff Table(Values Millions of dollars)? Nortel's decision...?determine the payoff value for each decision alternativechoose the alternative for which the associated payoff value is maximum(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Non-Probabilistic CriteriaNote the minimum payoff for each decision alternativeWe don’t have any information about the probabilities of the 3 states of nature, except that they are each non-zeroMaximin CriterionThis Pessimistic view results in Decision 3 do not market the productSelect the decision for which this is maximumPayoff Table(Values Millions of dollars)Non-Probabilistic CriteriaNote the maximum payoff for each decision alternativeWe don’t have any information about the probabilities of the 3 states of nature, except that they are each non-zeroMaximax CriterionThis Optimistic view results in Decision 1 build a new full scale plantSelect the decision for which this maximum payoff is maximum(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Payoff Table(Values Millions of dollars)Non-Probabilistic CriteriaChoose a number alpha between 0 and 1 (called the pessimistic-optimistic index)The Pessimistic-Optimistic Index Criterion of HurwiczThe value for each decision alternative is then:Alpha (minimum payoff) + (1-alpha)(maximum payoff)(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Payoff TableContinuedThis view results in Decision 2 – build a medium sized plantFor D1: (0.4)(-800)+(0.6)(400)Let alpha = 0.4= $ -80 million For D2: (0.4)(-50)+(0.6)(80) = $ 28 millionFor D3: (0.4)(0)+(0.6)(0) = $ 0 millionNon-Probabilistic CriteriaThe Pessimistic-Optimistic Index Criterion of Hurwicz(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Payoff TableAlpha (minimum payoff) + (1-alpha)(maximum payoff)Probabilistic CriteriaCalculate the EMV for each decision alternativeWe 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 CriterionSelect the decision for which this is maximum0.40.50.1(S1)(S2)(S3)(D1)40020-800(D2)8060-50(D3)000ContinuedPayoff TableThis view results in Decision 1 – build a full sized plantEMV (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.Expected Monetary Value CriterionSelect the decision for which this is maximum0.40.50.1(S1)(S2)(S3)(D1)40020-800(D2)8060-50(D3)000Probabilistic CriteriaPayoff Table is the loss because the exact state of nature is not known at the time a decision is madethe opportunity loss is computed by taking the difference between the optimal decision for each state of nature and the other decision alternativesCriteria Based on Opportunity Loss (Regret)Suppose that Nortel decided to build a medium sized plant.If market conditions are very favourable (S1), then what is the expected profit?AnswerExpected ProfitCriteria Based on Opportunity Loss (Regret)Suppose that Nortel decided to build a medium sized plant.If market conditions are highly favourable (S1), then what is the expected profit?(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Payoff TableBut, 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 millionCriteria Based on Opportunity Loss (Regret)Expected ProfitSuppose that Nortel decided to build a medium sized plant.If market conditions are moderately favourable (S2), then what is the expected profit?(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Payoff TableTherefore, there is an Opportunity Loss of $0 million ...they actually gained $40 million ($60 - $20)!Opportunity LossTablePessimistic CriterionThese are the worst case scenarios for each decision alternativeThe “best” of these “worst cases” is D2 Market Response Decision(S1)(S2)(S3) (D1)040 800(D2)320 0 50(D3)400600TerminologyValue 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 uncertaintyTerminologySensitivity 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(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Decision TreeDecision Tree ExamplesDecision Tree(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Decision Tree Examples(S1)(S2)(S3) (D1)40020-800(D2)8060-50(D3)000Decision Tree ExamplesDecision TreeTest your learning www.mcgrawhill.ca/college/lindClick onOnline Learning Centrefor quizzesextra contentdata setssearchable glossaryaccess to Statistics Canada’s E-Stat dataand much more!This completes Chapter 19