Chapter 18 Student Lecture Notes 18-1

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1 Chapter 18 Student Lecture Notes 18-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 18 Introduction to Decision Analysis 5 Prentice-Hall, Inc. Chap 18-1 Chapter Goals After completing this chapter, you should be able to: Describe the decision environments of certainty and uncertainty Construct a payoff table and an opportunity-loss table Define and apply the expected value criterion for decision making Compute the value of perfect information Develop and use decision trees for decision making 5 Prentice-Hall, Inc. Chap 17-2 Decision Making Overview Decision Making Decision Environment Decision Criteria Certainty Nonprobabilistic Uncertainty Probabilistic 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

2 Chapter 18 Student Lecture Notes 18-2 The Decision Environment Decision Environment Certainty Uncertainty * Certainty: The results of decision alternatives are known Example: Must print 1, color brochures Offset press A: $2, fixed cost + $.24 per page Offset press B: $3, fixed cost + $.12 per page 5 Prentice-Hall, Inc. Chap 17-4 The Decision Environment Decision Environment Certainty Uncertainty * Uncertainty: The outcome that will occur after a choice is unknown Example: You must decide to buy an item now or wait. If you buy now the price is $2,. If you wait the price may drop to $1, or rise to $2,. There also may be a new model available later with better features. 5 Prentice-Hall, Inc. Chap 17-5 Decision Criteria Nonprobabilistic Decision Criteria: Decision Criteria Decision rules that can be applied if the probabilities of uncertain events are not known. * Nonprobabilistic maximax criterion maximin criterion minimax regret criterion Probabilistic 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

3 Chapter 18 Student Lecture Notes 18-3 Decision Criteria Probabilistic Decision Criteria: Consider the probabilities of uncertain events and select an alternative to maximize the expected payoff of minimize the expected loss maximize expected value minimize expected opportunity loss Decision Criteria * Nonprobabilistic Probabilistic 5 Prentice-Hall, Inc. Chap 17-7 A Payoff Table A payoff table shows alternatives, states of nature, and payoffs Profit in $1, s Prentice-Hall, Inc. Chap 17-8 Maximax Solution The maximax criterion (an optimistic approach): 1. For each option, find the maximum payoff Profit in $1, s Maximum Profit 1 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

4 Chapter 18 Student Lecture Notes 18-4 Maximax Solution The maximax criterion (an optimistic approach): 1. For each option, find the maximum payoff 2. Choose the option with the greatest maximum payoff Profit in $1, s Maximum Profit 1 2. Greatest maximum is to choose Large factory 5 Prentice-Hall, Inc. Chap 17-1 Maximin Solution The maximin criterion (a pessimistic approach): 1. For each option, find the minimum payoff Profit in $1, s Minimum Profit -1 5 Prentice-Hall, Inc. Chap Maximin Solution The maximin criterion (a pessimistic approach): 1. For each option, find the minimum payoff 2. Choose the option with the greatest minimum payoff Profit in $1, s Minimum Profit Greatest minimum is to choose Small factory 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

5 Chapter 18 Student Lecture Notes 18-5 Opportunity Loss Opportunity loss is the difference between an actual payoff for a decision and the optimal payoff for that state of nature Profit in $1, s 1-1 Payoff Table The choice has payoff for. Given, the choice of would have given a payoff of, or 11 higher. Opportunity loss = 11 for this cell. 5 Prentice-Hall, Inc. Chap Opportunity Loss Profit in $1, s Payoff Table 7 Opportunity Loss Table Opportunity Loss in $1, s 1 5 Prentice-Hall, Inc. Chap Minimax Regret Solution The minimax regret criterion: 1. For each alternative, find the maximum opportunity loss (or regret ) Opportunity Loss Table Opportunity Loss in $1, s Maximum Op. Loss Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

6 Chapter 18 Student Lecture Notes 18-6 Minimax Regret Solution The minimax regret criterion: 1. For each alternative, find the maximum opportunity loss (or regret ) 2. Choose the option with the smallest maximum loss Opportunity Loss Table Opportunity Loss in $1, s Prentice-Hall, Inc. Chap Maximum Op. Loss Smallest maximum loss is to choose Average factory Expected Value Solution The expected value is the weighted average payoff, given specified probabilities for each state of nature (.3) Profit in $1, s 1-1 Suppose these probabilities have been assessed for these states of nature 5 Prentice-Hall, Inc. Chap Expected Value Solution (.3) Profit in $1, s 1-1 Expected Values Maximize expected value by choosing Average factory Example: EV () = (.3) () = 81 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

7 Chapter 18 Student Lecture Notes 18-7 Expected Opportunity Loss Solution Opportunity Loss Table Opportunity Loss in $1, s (.3) Expected Op. Loss (EOL) Minimize expected op. loss by choosing Average factory Example: EOL () = (.3) (1) = 63 5 Prentice-Hall, Inc. Chap Cost of Uncertainty Cost of Uncertainty (also called Expected Value of Perfect Information, or EVPI) Cost of Uncertainty = Expected Value Under Certainty (EVUC) Expected Value without information (EV) so: EVPI = EVUC EV 5 Prentice-Hall, Inc. Chap 17- Expected Value Under Certainty Expected Value Under Certainty (EVUC): EVUC = expected value of the best decision, given perfect information (.3) Example: Best decision given is Profit in $1, s Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

8 Chapter 18 Student Lecture Notes 18-8 Expected Value Under Certainty Now weight these outcomes with their probabilities to find EVUC: (.3) Profit in $1, s EVUC = (.3)+1+ = Prentice-Hall, Inc. Chap Cost of Uncertainty Solution Cost of Uncertainty (EVPI) = Expected Value Under Certainty (EVUC) Expected Value without information (EV) Recall: EVUC = 124 EV is maximized by choosing, where EV = 81 so: EVPI = EVUC EV = = 43 5 Prentice-Hall, Inc. Chap Decision Tree Analysis A Decision tree shows a decision problem, beginning with the initial decision and ending will all possible outcomes and payoffs. Use a square to denote decision nodes Use a circle to denote uncertain events 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

9 Chapter 18 Student Lecture Notes 18-9 Sample Decision Tree 5 Prentice-Hall, Inc. Chap Decision Add Probabilities and Payoffs Uncertain Events (.3) -1 (.3) 1 (.3) Probabilities Payoffs 5 Prentice-Hall, Inc. Chap Fold Back the Tree EV=(.3)++(-1)=61 EV=(.3)+1+()=81 EV=(.3)++=31 (.3) (.3) (.3) Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

10 Chapter 18 Student Lecture Notes 18-1 Make the Decision EV=61 (.3) -1 EV=81 (.3) 1 Maximum EV=81 EV=31 (.3) 5 Prentice-Hall, Inc. Chap Chapter Summary Examined decision making environments certainty and uncertainty Reviewed decision making criteria nonprobabilistic: maximax, maximin, minimax regret probabilistic: expected value, expected opp. loss Computed the Cost of Uncertainty (EVPI) Developed decision trees and applied them to decision problems 5 Prentice-Hall, Inc. Chap Prentice-Hall, Inc.

Module 15 July 28, 2014

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