3-1 Quantitative Analysis for Management Chapter 3 Fundamentals of Decision Theory Models

3-2 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

3-3 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

3-4 Introduction  Decision theory is an analytical and systematic way to tackle problems  A good decision is based on logic.

3-5 The Six Steps in Decision Theory  Clearly define the problem at hand  List the possible alternatives  Identify the possible outcomes  List the payoff or profit of each combination of alternatives and outcomes  Select one of the mathematical decision theory models  Apply the model and make your decision

3-6 Decision Table for Thompson Lumber 200, , , , Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($)

3-7 Types of Decision-Making Environments  Type 1: Decision-making under certainty knows with certainty  decision-maker knows with certainty the consequences of every alternative or decision choice  Type 2: Decision-making under risk knows  The decision-maker knows the probabilities of the various outcomes  Decision-making under uncertainty does not know  The decision-maker does not know the probabilities of the various outcomes

3-8 Decision-Making Under Risk n nature, of states ofnumber the to 1 j where ))P(S* (Payoff i) ativeEMV(Altern n 1j j S j     Expected Monetary Value:

3-9 Decision Table for Thompson Lumber 200, , ,000-20, Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($) 0.50 EMV 10,000 40,000 0

3-10 Expected Value of Perfect Information () Expected Value of Perfect Information (EVPI)  EVPI  EVPI places an upper bound on what one would pay for additional information  EVPI  EVPI is the expected value with perfect information minus the maximum EMV

3-11 Expected Value With Perfect Information () Expected Value With Perfect Information (EV|PI) n nature, of states ofnumber the to 1 j )P(S*j) nature of statefor outcomebest j     where (PI|EV n j 

3-12 Expected Value of Perfect Information  EVPIEV|PIEMV  EVPI = EV|PI - maximum EMV

3-13 Expected Value of Perfect Information 200,000 0 Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($) 0.50 EMV 40,000

3-14 Expected Value of Perfect Information EVPI EMV EVPI = expected value with perfect information - max(EMV) = $200,000* * $40,000 = $60,000

3-15 Expected Opportunity Loss  EOL  EOL is the cost of not picking the best solution  EOL  EOL = Expected Regret We want to maximize EMV or minimize EOL

3-16 Computing EOL - The Opportunity Loss Table

3-17 The Opportunity Loss Table continued

3-18 The Opportunity Loss Table continued

3-19 Sensitivity Analysis P1-P EMV(Large Plant) = $200,000P - (1-P)$180,000 P1-P EMV(Small Plant) = $100,000P - $20,000(1-P) P1-P EMV(Do Nothing) = $0P + 0(1-P)

3-20 Sensitivity Analysis - continued EMV (Small Plant) EMV(Large Plant)

3-21 Decision Making Under Uncertainty  Maximax  Maximin  Equally likely (Laplace)  Criterion of Realism  Minimax

3-22 Decision Making Under Uncertainty Maximax - Choose the alternative with the maximum output 200, , ,000-20, Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($)

3-23 Decision Making Under Uncertainty Maximin - Choose the alternative with the maximum minimum output 200, , ,000-20, Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($)

3-24 Decision Making Under Uncertainty Equally likely (Laplace) - Assume all states of nature to be equally likely, choose maximum EMV 200, , ,000-20, Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($) 0.50 EMV 10,000 40,000 0

3-25 Decision Making Under Uncertainty Criterion of Realism (Hurwicz): CR =  *(row max) + (1-  )*(row min) 200, , ,000-20, Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($) 0.50 CR 124,000 76,000 0

3-26 Decision Making Under Uncertainty Minimax - choose the alternative with the minimum maximum Opportunity Loss 0180, ,00020, ,000 0 Construct a large plant Construct a small plant Do nothing Favorable Market ($) Unfavorable Market ($) 0.50 Max in row 180, , ,000

3-27 Marginal Analysis  P  P = probability that demand is greater than or equal to a given supply  1-P  1-P = probability that demand will be less than supply  MPML  MP = marginal profit ML = marginal loss P*MP  (1-P)*ML  Optimal decision rule is: P*MP  (1-P)*ML  or

3-28 Marginal Analysis - Discrete Distributions  Steps using Discrete Distributions: P  Determine the value for P  Construct a probability table and add a cumulative probability column P  Keep ordering inventory as long as the probability of selling at least one additional unit is greater than P

3-29 Café du Donut Example

3-30 Café du Donut Example continued  Marginal profit = selling price - cost = $6 - $4 = $2  Marginal loss = cost  Therefore:     . MPML P     

3-31 Café du Donut Example continued

3-32 Marginal Analysis Normal Distribution   = average or mean sales   = standard deviation of sales  MP  MP = marginal profit  ML  ML = Marginal loss

3-33 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 * MPML P      * X Z

3-34 Joe’s Newsstand Example A  ML  ML = 4  MP  MP = 6   = Average demand = 50 papers per day   = Standard deviation of demand = 10

3-35 Joe’s Newsstand Example A continued  Step 1:  Step 2: Look on the Normal table for PZ P = 0.6 (i.e., )  Z = 0.25, and or:   . MPML P           * X. newspapersor ..*X * 

3-36 Joe’s Newsstand Example A continued

3-37 Joe’s Newsstand Example B  ML  ML = 8  MP  MP = 2   = Average demand = 100 papers per day   = Standard deviation of demand = 10

3-38 Joe’s Newsstand Example B continued  Step 1:  Step 2: Z Z = for an area of 0.80 and or:   . MPML P           * X. newspapersor ..X * 

3-39 Joe’s Newsstand Example B continued