DECISION MAKING – under uncertainty and with probabilitiesExamples of Problem Solving Thought ProcessesAdditional Problem Solving TechniquesDecision Making Under UncertaintyThe Payoff TablePayoff TableSlide 7Decision Making with ProbabilitiesExpected Maximum ValuesExpected valueExampleSlide 12Slide 13Step One Expected Maximum ValueSlide 15Step Two Expected Maximum ValueSlide 17Step Three Expected Maximum ValueSlide 19Step 4Slide 21Slide 22Slide 23Expected Value With Perfect Information (EVPI) ExampleCalculate EVPICalculate the Value of the Perfect Information (VPI)Slide 27DECISION MAKING – UNDER UNCERTAINTY AND WITH PROBABILITIES1Examples of Problem Solving Thought Processes2• Do nothing•Forrest GumpAdditional Problem Solving Techniques•Theory of Constraints•Six Sigma•Just in Time•Lean3Decision Making Under Uncertainty4The Payoff TableA method of organizing & illustrating the payoffs from different decisions given various states of natureA payoff is the outcome of the decision – a Craps table pay off chart is an example of a payoff chart 5Payoff TableStates Of Nature(Alternatives)Decision a b1 Payoff 1/a Payoff 1/b2 Payoff 2/a Payoff 2/b67STATES OF NATUREGood Foreign Poor ForeignDECISION Competitive Conditions Competitive ConditionsExpand $ 800,000 $ 500,000Maintain status quo 1,300,000 -150,000Sell now 320,000 420,000Maximums: 1,300,000; 800,000, 420,000Minimums: 500,000; 320,000; -150,000Decision 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 8Expected Maximum Values•What is the maximum value expected for each alternative?9Expected value10EV (x) = p(xi)xini =1xi= outcome ip(xi) = probability of outcome iwhereExample•The profit level for a furniture manufacturer using three different plants 1, 2, and 3 and the economic conditions – Good, Fair, Poor1112Plant/Demand Good Fair Poor1 200 350 6002 250 350 5403 300 375 400Plant/DemandGood Fair PoorExpectedMaximumValue1 200 350 6002 250 350 5403 300 375 400Probability.4 .25 .3513Step One Expected Maximum Value•Multiply Probability x Outcome/Payoff•(.4 x 200) + (.25 x 350) + (.35 x 600)•80 + 87.5 + 210 = 377.514Plant/DemandGood Fair PoorExpectedMaximumValue1 200 350 600377.52 250 350 5403 300 375 400Probability.4 .25 .3515Step Two Expected Maximum Value•Multiply Probability x Outcome/Payoff•(.4 x 250) + (.25 x 350) + (.35 x 540)•100 + 87.5 + 189 = 376.516Plant/DemandGood Fair PoorExpectedMaximumValue1 200 350 600377.52 250 350 540376.53 300 375 400Probability.4 .25 .3517Step Three Expected Maximum Value•Multiply Probability x Outcome/Payoff•(.4 x 300) + (.25 x 375) + (.35 x 400)•120 + 93.75 + 171.5 = 353.7518Plant/DemandGood Fair PoorExpectedMaximumValue1 200 350 600377.52 250 350 540376.53 300 375 400353.75Probability.4 .25 .3519Step 4•Choose the decision with the highest Expected Maximum Value20Plant/ConditionsGood Fair PoorExpectedMaximumValue1 200 350 600377.52 250 350 540376.53 300 375 400353.75Probability.4 .25 .3521Expected Value With Perfect Information and the Value of Perfect Information•EVPI - maximum value with perfect information to the decision maker•VPI - Maximum amount that an investor would pay to purchase perfect information22Plant/ConditionsGood Fair PoorExpectedMaximumValue1 200 350 600377.52 250 350 540376.53 300 375 400353.75Probability.4 .25 .3523Expected Value With Perfect Information (EVPI) ExampleGood Economic Conditions will exist – probability = .4; Therefore choose Plant 3Fair Economic Conditions will exist – probability = .25; Therefore choose Plant 3Poor Economic Conditions will exist – probability = .35; Therefore choose Plant 124Calculate EVPI•Step 1: Good conditions = .4 x 300 = 120•Step 2: Fair conditions = .25 x 375 = 93.75•Step 3: Poor conditions = .35 x 600 = 210•Step 4: Sum values = 120 + 93.75 + 210 = 423.75•EVPI = 423.7525Calculate the Value of the Perfect Information (VPI)•VPI = EVPI – Largest EMV (without perfect information)•VPI = 423.75 – 377.5•VPI = 46.25•So what?26Questions