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Chapter 1 supplement - Decision analysis. In this chapter, you will learn about: Decision analysis, decision making without probabilities, decision analysis with excel, decision analysis with OM tools, decision making with probabilities, expected value of perfect information, sequential decision tree.
OPERATIONS MANAGEMENT: Creating Value Along the Supply Chain, Canadian Edition Robert S Russell, Bernard W Taylor III, Ignacio Castillo, Navneet Vidyarthi CHAPTER SUPPLEMENT Decision Analysis Supplement 1-1 Lecture Outline Decision Analysis Decision Making without Probabilities Decision Analysis with Excel Decision Analysis with OM Tools Decision Making with Probabilities Expected Value of Perfect Information Sequential Decision Tree Supplement 1-2 Decision Analysis Quantitative methods • a set of tools for operations manager Decision analysis • a set of quantitative decision-making techniques for decision situations in which uncertainty exists • Example of an uncertain situation • demand for a product may vary between and 200 units, depending on the state of market Supplement 1-3 Decision Making Without Probabilities States of nature • Events that may occur in the future • Examples of states of nature: • • high or low demand for a product good or bad economic conditions Decision making under risk • probabilities can be assigned to the occurrence of states of nature in the future Decision making under uncertainty • probabilities can NOT be assigned to the occurrence of states of nature in the future Supplement 1-4 Payoff Table Payoff table • method for organizing and illustrating payoffs from different decisions given various states of nature Payoff • outcome of a decision Supplement 1-5 Decision Making Criteria Under Uncertainty Maximax choose decision with the maximum of the maximum payoffs Maximin choose decision with the maximum of the minimum payoffs Minimax regret choose decision with the minimum of the maximum regrets for each alternative Supplement 1-6 Decision Making Criteria Under Uncertainty Hurwicz choose decision in which decision payoffs are weighted by a coefficient of optimism, alpha coefficient of optimism is a measure of a decision maker’s optimism, from (completely pessimistic) to (completely optimistic) Equal likelihood (La Place) choose decision in which each state of nature is weighted equally Supplement 1-7 Southern Textile Company Supplement 1-8 Maximax Solution Decision: Maintain status quo Supplement 1-9 Maximin Solution Decision: Expand Supplement 1-10 Minimax Regret Solution Decision: Expand Supplement 1-11 Hurwicz Criteria Decision: Expand Supplement 1-12 Equal Likelihood Criteria Decision: Expand Supplement 1-13 Decision Analysis with Excel Supplement 1-14 Decision Analysis with OM Tools Supplement 1-15 Decision Making with Probabilities Risk involves assigning probabilities to states of nature Expected value • a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence Supplement 1-16 Expected Value EV (x) = p(xi)xi n i =1 where xi = outcome i p(xi) = probability of outcome i Supplement 1-17 Decision Making with Probabilities Supplement 1-18 Decision Making with Probabilities: Excel Supplement 1-19 Expected Value of Perfect Information EVPI maximum value of perfect information to the decision maker maximum amount that would be paid to gain information that would result in a decision better than the one made without perfect information Supplement 1-20 EVPI Good conditions will exist 70% of the time choose maintain status quo with payoff of $1,300,000 Poor conditions will exist 30% of the time choose expand with payoff of $500,000 Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000 Recall that expected value without perfect information was $865,000 (maintain status quo) EVPI= $1,060,000 - 865,000 = $195,000 Supplement 1-21 Sequential Decision Trees A graphical method for analyzing decision situations that require a sequence of decisions over time Decision tree consists of Square nodes - indicating decision points Circles nodes - indicating states of nature Arcs - connecting nodes Supplement 1-22 Evaluations at Nodes Compute EV at nodes & EV(node 6)= 0.80($3,000,000) + 0.20($700,000) = $2,540,000 EV(node 7)= 0.30($2,300,000) + 0.70($1,000,000)= $1,390,000 Decision at node is between $2,540,000 for Expand and $450,000 for Sell land Choose Expand Repeat expected value calculations and decisions at remaining nodes Supplement 1-23 Decision Tree Analysis Supplement 1-24 COPYRIGHT Copyright © 2014 John Wiley & Sons Canada, Ltd All rights reserved Reproduction or translation of this work beyond that permitted by Access Copyright (The Canadian Copyright Licensing Agency) is unlawful Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd The purchaser may make back-up copies for his or her own use only and not for distribution or resale The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein ... to the occurrence of states of nature in the future Decision making under uncertainty • probabilities can NOT be assigned to the occurrence of states of nature in the future Supplement 1-4 ... decision Supplement 1-5 Decision Making Criteria Under Uncertainty Maximax choose decision with the maximum of the maximum payoffs Maximin choose decision with the maximum of the minimum payoffs... equally Supplement 1-7 Southern Textile Company Supplement 1-8 Maximax Solution Decision: Maintain status quo Supplement 1-9 Maximin Solution Decision: Expand Supplement 1-1 0 Minimax Regret Solution