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Chapter 3 Decision Analysis Homework Answers

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1 Chapter 3Decision Analysis

2 Learning ObjectivesAfter completing this chapter, students will be able to:List the steps of the decision-making processDescribe the types of decision-making environmentsMake decisions under uncertaintyUse probability values to make decisions under risk

3 Learning ObjectivesAfter completing this chapter, students will be able to:Develop accurate and useful decision treesRevise probabilities using Bayesian analysisUse computers to solve basic decision-making problemsUnderstand the importance and use of utility theory in decision making

4 Introduction What is involved in making a good decision?
Decision theory is an analytic and systematic approach to the study of decision makingA good decision is one that is based on logic, considers all available data and possible alternatives, and the quantitative approach described here

5 The Six Steps in Decision Making
Clearly define the problem at handList the possible alternativesIdentify the possible outcomes or states of natureList the payoff or profit of each combination of alternatives and outcomesSelect one of the mathematical decision theory modelsApply the model and make your decision

6 Thompson Lumber Company
Step 1 – Define the problemExpand by manufacturing and marketing a new product, backyard storage shedsStep 2 – List alternativesConstruct a large new plantA small plantNo plant at allStep 3 – Identify possible outcomesThe market could be favorable or unfavorable

7 Thompson Lumber Company
Step 4 – List the payoffsIdentify conditional values for the profits for large, small, and no plants for the two possible market conditionsStep 5 – Select the decision modelDepends on the environment and amount of risk and uncertaintyStep 6 – Apply the model to the dataSolution and analysis used to help the decision making

8 Thompson Lumber Company
STATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)Construct a large plant200,000–180,000Construct a small plant100,000–20,000Do nothingTable 3.1

9 Types of Decision-Making Environments
Type 1: Decision making under certaintyDecision maker knows with certainty the consequences of every alternative or decision choiceType 2: Decision making under uncertaintyThe decision maker does not know the probabilities of the various outcomesType 3: Decision making under riskThe decision maker knows the probabilities of the various outcomes

10 Decision Making Under Uncertainty
There are several criteria for making decisions under uncertaintyMaximax (optimistic)Maximin (pessimistic)Criterion of realism (Hurwicz)Equally likely (Laplace)Minimax regret

11 UNFAVORABLE MARKET ($)
MaximaxUsed to find the alternative that maximizes the maximum payoffLocate the maximum payoff for each alternativeSelect the alternative with the maximum numberSTATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)MAXIMUM IN A ROW ($)Construct a large plant200,000–180,000Construct a small plant100,000–20,000Do nothingMaximaxTable 3.2

12 UNFAVORABLE MARKET ($)
MaximinUsed to find the alternative that maximizes the minimum payoffLocate the minimum payoff for each alternativeSelect the alternative with the maximum numberSTATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)MINIMUM IN A ROW ($)Construct a large plant200,000–180,000Construct a small plant100,000–20,000Do nothingMaximinTable 3.3

13 Criterion of Realism (Hurwicz)
A weighted average compromise between optimistic and pessimisticSelect a coefficient of realism Coefficient is between 0 and 1A value of 1 is 100% optimisticCompute the weighted averages for each alternativeSelect the alternative with the highest valueWeighted average = (maximum in row)+ (1 – )(minimum in row)

14 Criterion of Realism (Hurwicz)
For the large plant alternative using  = 0.8 (0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000For the small plant alternative using  = 0.8 (0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000STATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)CRITERION OF REALISM ( = 0.8)$Construct a large plant200,000–180,000124,000Construct a small plant100,000–20,00076,000Do nothingRealismTable 3.4

15 Equally Likely (Laplace)
Considers all the payoffs for each alternativeFind the average payoff for each alternativeSelect the alternative with the highest averageSTATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)ROW AVERAGE ($)Construct a large plant200,000–180,00010,000Construct a small plant100,000–20,00040,000Do nothingEqually likelyTable 3.5

16 Minimax RegretBased on opportunity loss or regret, the difference between the optimal profit and actual payoff for a decisionCreate an opportunity loss table by determining the opportunity loss for not choosing the best alternativeOpportunity loss is calculated by subtracting each payoff in the column from the best payoff in the columnFind the maximum opportunity loss for each alternative and pick the alternative with the minimum number

17 Minimax Regret Opportunity Loss Tables STATE OF NATURE
FAVORABLE MARKET ($)UNFAVORABLE MARKET ($)200,000 – 200,0000 – (–180,000)200,000 – 100,0000 – (–20,000)200,000 – 00 – 0Opportunity Loss TablesTable 3.6STATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)Construct a large plant180,000Construct a small plant100,00020,000Do nothing200,000Table 3.7

18 UNFAVORABLE MARKET ($)
Minimax RegretSTATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)MAXIMUM IN A ROW ($)Construct a large plant180,000Construct a small plant100,00020,000Do nothing200,000MinimaxTable 3.8

19 Decision Making Under Risk
Decision making when there are several possible states of nature and we know the probabilities associated with each possible stateMost popular method is to choose the alternative with the highest expected monetary value (EMV)EMV(alternative i) = (payoff of 1st state of nature) x (prob. of 1st state of nature)+ (payoff of 2nd state of nature) x (prob. of 2nd state of nature)+ …+ (payoff of last state of nature) x (prob. of last state of nature)

20 EMV for Thompson Lumber
Each market has a probability of 0.50Which alternative would give the highest EMV?The calculations areEMV (large plant) = (0.50)($200,000) + (0.50)(–$180,000)= $10,000EMV (small plant) = (0.50)($100,000) + (0.50)(–$20,000)= $40,000EMV (do nothing) = (0.50)($0) + (0.50)($0)= $0

21 EMV for Thompson Lumber
STATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)EMV ($)Construct a large plant200,000–180,00010,000Construct a small plant100,000–20,00040,000Do nothingProbabilities0.50Largest EMVTable 3.9

22 Expected Value of Perfect Information (EVPI)
EVwPI (Expected Value with Perfect Information) is the long run average return if we have perfect information before a decision is madeEVwPI = (best payoff for 1st SoN)x P1st SoN+ (best payoff for 2nd SoN)x P2nd SoN+ … + (best payoff for nth SoN)x Pnth SoNEVPI (Expected Value of Perfect Information) places an upper bound on what you should pay for additional informationEVPI = EVwPI – Maximum EMV

23 Expected Value of Perfect Information (EVPI)
Scientific Marketing, Inc. offers analysis that will provide certainty about market conditions (favorable)Additional information will cost $65,000Is it worth purchasing the information?

24 Expected Value of Perfect Information (EVPI)
ALTERNATIVESSTATE OF NATUREEMV($)FAVORABLEMARKET ($)UNFAVORABLE MARKET ($)Construct a large plant200,000-180,00010,000Construct a small plant100,000-20,00040,000Largest EMVDo nothingProbabilities0.5Best alternative for favorable state of nature is build a large plant with a payoff of $200,000Best alternative for unfavorable state of nature is to do nothing with a payoff of $0EVwPI = ($200,000)(0.50) + ($0)(0.50) = $100,000The maximum EMV without additional information is $40,000EVPI = EVwPI – Maximum EMV= $100,000 - $40,000 = $60,000

25 Expected Value of Perfect Information (EVPI)
Best alternative for favorable state of nature is build a large plant with a payoff of $200,000Best alternative for unfavorable state of nature is to do nothing with a payoff of $0EVwPI = ($200,000)(0.50) + ($0)(0.50) = $100,000The maximum EMV without additional information is $40,000EVPI = EVwPI – Maximum EMV= $100,000 - $40,000= $60,000So the maximum Thompson should pay for the additional information is $60,000

26 Expected Opportunity Loss
Expected opportunity loss (EOL) is the cost of not picking the best solutionFirst construct an opportunity loss tableFor each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these togetherMinimum EOL will always result in the same decision as maximum EMVMinimum EOL will always equal EVPI

27 Opportunity Loss Table
STATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)Construct a large plant200,000–180,000Construct a small plant100,000–20,000Do nothingBestBestSTATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)Construct a large plantMax ,000 = 0Max – (-180,000) = 180,000Construct a small plantMax ,000 = 100,000Max – (-20,000) = 20,000Do nothingMax - 0 = 200,000Max – 0 = 0Opportunity loss table

28 Expected Opportunity Loss
Opportunity loss tableSTATE OF NATUREALTERNATIVEFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)EOLConstruct a large plant180,00090,000Construct a small plant100,00020,00060,000Do nothing200,000Probabilities0.50Minimum EOLTable 3.10EOL (large plant) = (0.50)($0) + (0.50)($180,000)= $90,000EOL (small plant) = (0.50)($100,000) + (0.50)($20,000)= $60,000EOL (do nothing) = (0.50)($200,000) + (0.50)($0)= $100,000

29 Summary Risk (1) Construct a large plant 200,000 Best payoff for
ALTERNATIVESSTATE OF NATUREEMV= payoff 1 * P1st SoN + … + payoff n * Pnth SoNEVwPI= (best payoff for 1st SoN)x P1st SoN+… + (best payoff for nth SoN)x Pnth SoNEVPI=EVwPI – Maximum EMVFAVORABLEMARKET ($)UNFAVORABLE MARKET ($)Construct alarge plant200,000Best payoff for1st SoN-180,00010,000100,000(=200,000x0.5+ 0x0.5)60,000(=100,000-40,000)small plant-20,00040,000Largest EMVDo nothingbest payoff for2nd SoNProbabilities0.5

30 UNFAVORABLE MARKET ($)
Summary Risk (2)Original TableOpportunity Loss TableALTERNATIVESSTATE OF NATUREEOLFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)Construct alarge plant200,000best payoff for 1st SoN-180,000=200, ,000180,000=0-(-180,000)90,000=0x ,000x0.5small plant100,000-20,000=200, ,00020,000=0-(-20,000)60,000Minimium EOL=100,000x0.5+20,000x0.5Do nothingbest payoff for 2nd SoN=200,000-0=0-0=200,000x0.5+0x0.5Probabilities0.5

31 Sensitivity AnalysisSensitivity analysis examines how our decision might change with different input dataFor the Thompson Lumber exampleP = probability of a favorable market(1 – P) = probability of an unfavorable market

32 Sensitivity Analysis Construct a large plant 200,000 -180,000
ALTERNATIVESSTATE OF NATUREEMV= Payoff 1 * P1st SoN + Payoff 2 * P2nd SoN + … + Payoff n * Pnth SoNFAVORABLE MARKET ($)UNFAVORABLE MARKET ($)Construct alarge plant200,000-180,000= $200,000P – $180,000(1 – P)= $380,000P – $180,000small plant100,000-20,000= $100,000P – $20,000(1 – P)= $120,000P – $20,000Do nothing= $0P – $0(1 – P)= $0Probabilitiesp(1-p)

33 Sensitivity Analysis $300,000 $200,000 $100,000 –$100,000 –$200,000
–$100,000–$200,000EMV ValuesEMV (large plant)Point 1Point 2EMV (small plant)EMV (do nothing).167.6151Values of PFigure 3.1

34 Sensitivity Analysis Figure 3.1 $300,000 $200,000 $100,000 –$100,000
–$100,000–$200,000EMV ValuesEMV (large plant)EMV (small plant)EMV (do nothing)Point 1Point 2.167.6151Values of P

35 Sensitivity Analysis Point 1: EMV(do nothing) = EMV(small plant)
EMV(small plant) = EMV(large plant)

36 Sensitivity Analysis BEST ALTERNATIVE RANGE OF P VALUES Do nothing
Less than 0.167Construct a small plant0.167 – 0.615Construct a large plantGreater than 0.615Figure 3.1$300,000$200,000$100,000–$100,000–$200,000EMV ValuesEMV (large plant)EMV (small plant)EMV (do nothing)Point 1Point 2.167.6151Values of P

37 Using Excel QM to Solve Decision Theory Problems
Program 3.1A

38 Using Excel QM to Solve Decision Theory Problems
Program 3.1B

39 Homework 03Prob. 3.16, 3.18, 3.19, 3.22, 3.26, 3.27

3-2Alternative 2 30,000 –20,000 Alternative 3 0 0 The Laplace (equally likely) solution is computed averaging the payoffs for each alternative and choosing the best. The results are shown below. Alternatives 1 and 2 both give the highest average return of $5,000. Average (alternative 1) = [$50,000 + (–$40,000)]/2 = $5,000 Average (alternative 2) = [$30,000 + (–$20,000)]/2 = $5,000 Average (alternative 3) = 0 The maximin decision (pessimistic) maximizes the minimum payoff outcome for every alternative: these are –40,000; –20,000; and 0. Therefore, the decision is to do nothing. The maximax decision (optimistic) maximizes the maximum payoff for any alternative: these maximums are 50,000; 30,000; and 0. Therefore, the decision is to purchase the large robot (alternative 1). The Hurwicz approach uses a coefficient of realism value of 0.7, and a weighted average of the best and the worst payoffs for each alternative is computed. The results are as follows: Weighted average (alternative 1) = ($50,000)(0.7) + (–$40,000)(0.3) = $23,000 Weighted average (alternative 2) = ($30,000)(0.7) + (–$20,000)(0.3) = $15,000 Weighted average (alternative 3) = 0 The decision would be alternative 1. The minimax regret decision minimizes the maximum opportunity loss. The opportunity loss table for Goleb is as follows: Favorable Unfavorable Maximum Alternatives Market Market in Row Rob1 0 40,000 40,000 Rob2 20,000 20,000 20,000 Nothing 50,000 0 50,000 The alternative that minimizes the maximum opportunity loss is the Rob2. This is due to the $20,000 in the last column in the table above. Rob1 has a maximum opportunity loss of $40,000,

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