To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 3 Fundamentals of Decision Theory Models

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Learning Objectives Students will be able to: List the steps of the decision- making process Describe the types of decision- making environments Use probability values to make decisions under risk Make decisions under uncertainty, where there is risk but probability values are not known Use computers to solve basic decision-making problems

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter Outline 3.1 Introduction 3.2 The Six Steps in Decision Theory 3.3 Types of Decision-Making Environments 3.4 Decision Making Under Risk 3.5 Decision Making Under Uncertainty 3.6 Marginal Analysis with a Large Number of Alternatives and States of Nature

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Introduction Decision theory is an analytical and systematic way to tackle problems A good decision is based on logic.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ The Six Steps in Decision Theory 1)Clearly define the problem at hand 2)List the possible alternatives 3)Identify the possible outcomes 4)List the payoff or profit of each combination of alternatives and outcomes 5)Select one of the mathematical decision theory models 6)Apply the model and make your decision

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Table for Thompson Lumber

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Types of Decision- Making Environments Type 1: Decision-making under certainty decision-maker knows with certainty the consequences of every alternative or decision choice Type 2: Decision-making under risk The decision-maker does know the probabilities of the various outcomes Decision-making under uncertainty The decision-maker does not know the probabilities of the various outcomes

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Tile Replacement on the Space Shuttle

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Critical Decisions in a Nuclear World

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision-Making Under Risk Expected Monetary Value

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Table for Thompson Lumber

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Expected Value of Perfect Information (EVPI) EVPI places an upper bound on what one would pay for additional information EVPI is the expected value with perfect information minus the maximum EMV

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Expected Value With Perfect Information (EV | PI)

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Expected Value of Perfect Information EVPI = EV|PI - maximum EMV

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Expected Value of Perfect Information

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Expected Value of Perfect Information EVPI = expected value with perfect information - max(EMV) = $200,000* * $40,000 = $60,000

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Expected Opportunity Loss EOL is the cost of not picking the best solution EOL = Expected Regret

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Computing EOL - The Opportunity Loss Table

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ The Opportunity Loss Table continued

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ The Opportunity Loss Table - continued

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Sensitivity Analysis EMV(Large Plant) = $200,000P - (1- P)$180,000 EMV(Small Plant) = $100,000P - $20,000(1-P) EMV(Do Nothing) = $0P + 0(1-P)

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Sensitivity Analysis - continued Values of P EMV Values Point 1 Point 2 Small Plant Large Plant EMV

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Making Under Uncertainty Maximax Maximin Equally likely (Laplace) Criterion of Realism Minimax

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Making Under Uncertainty Maximax - Choose the alternative with the maximum output

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-25 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Making Under Uncertainty Maximin - Choose the alternative with the maximum minimum output

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-26 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Making Under Uncertainty Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum Average States of Nature AlternativeFavorable Market Unfavorable Market Avg. Construct Large Plant $200,000-$180,00010,000 Construct small plant 100,000-20,00040,000 Do nothing 000

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-27 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Making Under Uncertainty Criterion of Realism (Hurwicz): CR =  *(row max) + (1-  )*(row min) State of Nature AlternativeFavorable Market Unfavorable Market CR Construct large plant $200, ,000124,000 Construct small plant $100,000-20,00076,000 Do nothing

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-28 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Decision Making Under Uncertainty Minimax - choose the alternative with the minimum maximum Opportunity Loss States of Nature Alternative Favorable Market Unfavorable Market CR Construct a large plant 0$$180,000 Construct a small plant $100,00020,000100,000 Do nothing200,0000

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Marginal Analysis P = probability that demand is greater that or equal to a given supply 1-P = probability that demand will be less than supply MP = marginal profit ML = marginal loss Optimal decision rule is: P*MP  (1-P)*ML or

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-30 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Marginal Analysis - Discrete Distributions Steps using Discrete Distributions : PDetermine the value for P Construct a probability table and add a cumulative probability column PKeep ordering inventory as long as the probability of selling at least one additional unit is greater than P

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-31 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Café du Donut Example

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-32 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Café du Donut Example continued Marginal profit = selling price - cost = $6 - $4 = $2 Marginal loss = cost Therefore:

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-33 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Café du Donut Example continued

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-34 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Marginal Analysis Normal Distribution   = average or mean sales   = standard deviation of sales MPMP = marginal profit MLML = Marginal loss

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-35 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Marginal Analysis - Discrete Distributions Steps using Normal Distributions: Determine the value for P. Locate P on the normal distribution. For a given area under the curve, we find Z from the standard Normal table. Using we can now solve for X *    * X Z MPML P  

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-36 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Joe’s Newsstand Example A MLML = 4 MPMP = 6   = Average demand = 50 papers per day   = Standard deviation of demand = 10

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-37 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Joe’s Newsstand Example A - continued Step 1: P Step 2: Look in the Normal table for P = 0.6 (i.e., 1 – 0.4).

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-38 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Joe’s Newsstand Example A continued

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-39 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Joe’s Newsstand Example B MLML = 8 MPMP = 2   = Average demand = 100 papers per day   = Standard deviation of demand = 10

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-40 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Joe’s Newsstand Example B - continued Step 1: Step 2: Z Z = for an area of 0.80 and or:

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 3-41 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Joe’s Newsstand Example B continued