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Decision Making Supplement A

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Objectives Apply break-even analysis, using both the graphic and algebraic approaches, to evaluate new products and services and different process methods. evaluate decision alternatives with a preference matrix for multiple criteria. Construct a payoff table and then select the best alternative by using a decision rule such as maximin, maximax, Laplace, minimax regret, or expected value. Calculate the value of perfect information. Draw and analyze a decision tree.

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Break-Even Analysis QuantityTotal AnnualTotal Annual (patients)Cost ($)Revenue ($) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000 Total Cost = Fixed Cost + Variable Cost * Volume sold Total Revenue = Revenue per unit * Volume Sold Revenue = Cost = pQ = F + cQ Break Even Point= Fixed Cost / (revenue – variable cost)

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Break-Even Analysis 400 – 300 – 200 – 100 – 0 – Total annual revenues Patients (Q) Dollars (in thousands) |||| 500100015002000 (2000, 400) QuantityTotal AnnualTotal Annual (patients)Cost ($)Revenue ($) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000

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Break-Even Analysis Total annual revenues Total annual costs Patients (Q) Dollars (in thousands) 400 – 300 – 200 – 100 – 0 – |||| 500100015002000 Fixed costs (2000, 400) (2000, 300) (0, 100) (0, 0)

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Break-Even Analysis Total annual revenues Total annual costs Patients (Q) Dollars (in thousands) 400 – 300 – 200 – 100 – 0 – |||| 500100015002000 Fixed costs Break-even quantity (2000, 400) (2000, 300) Profits Loss

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Sensitivity Analysis 400 – 300 – 200 – 100 – 0 – Example A.2 Total annual revenues Total annual costs Patients (Q) Dollars (in thousands) |||| 500100015002000 Fixed costs Profits Loss Forecast = 1,500

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Sensitivity Analysis 400 – 300 – 200 – 100 – 0 – Total annual revenues Total annual costs Patients (Q) Dollars (in thousands) |||| 500100015002000 Fixed costs Profits Loss Forecast = 1,500 pQ – ( F + cQ ) 200(1500) – [100,000 + 100(1500)] = $50,000

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Preference Matrix PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential308240 Unit profit margin2010200 Operations compatibility206120 Competitive advantage1510150 Investment requirement10220 Project risk5420 Weighted score =750 Threshold score = 800 Example A.4

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Preference Matrix PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential308240 Unit profit margin2010200 Operations compatibility206120 Competitive advantage1510150 Investment requirement10220 Project risk5420 Weighted score =750 Threshold score = 800 Example A.4 Not At This Time

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Decision Theory: Under Certainty Example A.5 AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand If future demand will be low—Choose the small facility.

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Under Uncertainty AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand Example A.6

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Under Uncertainty AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand Maximin—Small Best of the worst Example A.6

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Under Uncertainty AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand Maximin—Small Maximax—Large Best of the best Example A.6

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Under Uncertainty AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand Maximin—Small Maximax—Large Laplace—Large Best weighted payoff Small facility0.5(200) + 0.5(270) = 235 Large facility0.5(160) + 0.5(800) = 480 Example A.6

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Under Uncertainty AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand Example A.6 Maximin—Small Maximax—Large Laplace—Large Minimax Regret—Large Best worst regret Regret Low DemandHigh Demand Small facility200 – 200 = 0800 – 270 = 530 Large facility200 – 160 = 40800 – 800 = 0

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Under Uncertainty AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand Maximin—Small Maximax—Large Laplace—Large Minimax Regret—Large Example A.6

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Under Risk AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand P small = 0.4 P large = 0.6 Example A.7 AlternativeExpected Value Small facility0.4(200) + 0.6(270) = 242 Large facility0.4(160) + 0.6(800) = 544

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Under Risk Highest Expected Value AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand P small = 0.4 P large = 0.6 Example A.7 AlternativeExpected Value Small facility0.4(200) + 0.6(270) = 242 Large facility0.4(160) + 0.6(800) = 544

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Under Risk Figure A.4

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Perfect Information AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand P small = 0.4 P large = 0.6 Example A.8 EventBest Payoff Low demand200 High demand800

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Perfect Information AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand P small = 0.4 P large = 0.6 Example A.8 EventBest Payoff Low demand200EV perfect = 200(0.4) + 800(0.6) = 560 High demand800EV imperfect = 160(0.4) + 800(0.6) = 544

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Perfect Information AlternativeLowHigh Small facility200270 Large facility160800 Do nothing00 Possible Future Demand P small = 0.4 P large = 0.6 Example A.8 EventBest Payoff Low demand200EV perfect = 200(0.4) + 800(0.6) = 560 High demand800EV imperfect = 160(0.4) + 800(0.6) = 544 Value of perfect information = $560,000 - $544,000

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Decision Trees = Event node = Decision node E i = Event i P(E i ) = Probability of event i 1st decision Possible 2nd decision Payoff 1 Payoff 2 Payoff 3 Alternative 3 Alternative 4 Alternative 5 Payoff 1 Payoff 2 Payoff 3 E 1 [P(E 1 )] E 2 [P(E 2 )] E 3 [P(E 3 )] E 2 [P(E 2 )] E 3 [P(E 3 )] E 1 [P(E 1 )] Alternative 1 Alternative 2 Payoff 1 Payoff 2 12 Figure A.5

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Decision Trees Low demand [0.4] Small facility Large facility Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 Example A.9

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Decision Trees Low demand [0.4] Small facility Large facility Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 0.3(20) + 0.7(220) Example A.9

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Decision Trees $160 Low demand [0.4] Small facility Large facility Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 0.3(20) + 0.7(220) Example A.9

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Decision Trees $160 Low demand [0.4] $160 Small facility Large facility Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 $270 Example A.9

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Decision Trees ($160) Low demand [0.4] $270 $160 Small facility Large facility Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 0.4(200) + 0.6(270) 0.4(160) + 0.6(800) Example A.9

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Decision Trees ($160) Low demand [0.4] $270 $160 Small facility Large facility $242 $544 Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 Example A.9 0.4(200) + 0.6(270) 0.4(160) + 0.6(800)

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Decision Trees $160 Low demand [0.4] $270 $160 Small facility Large facility $544 $242 $544 Low demand [0.4] Don’t expand Expand Do nothing Advertise $200 $223 $270 $40 $800 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] 1 2 3 Example A.9

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Solved Problem 1 250 – 200 – 150 – 100 – 50 – 0 – Total revenues Total costs Units (in thousands) Dollars (in thousands) ||||||||12345678||||||||12345678 Break-even quantity 3.1 $77.7 BE Revenue = pQ Revenue = 25*3111 Revenue = $77,775

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Solved Problem 3 To determine the payoff amounts: Payoff Scenarios 1:2:3: Event 1Event 2Event 3 Probabilities-- -->LowMediumHigh Order 25 dozen 625 Order 60 dozen 1001500 Order 130dozen -9504503250 Do nothing 000 Buy roses for $15 dozen Sell roses for $40 dozen Sell 25, Order 25, = pQ – cQ = 40(25) – 15(25) =625 Sell 60, Order 130 = pQ – cQ = 40(60) – 15(130) = 450

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Solved Problem 3 Maximin – best of the worst. If demand is Low, the best alternative is to order 25 dozen. Maximax – best of the best. If demand is high, the best alternative is to order 130 dozen. Laplace – Best weighted payoff. 25 dozen: 625(.33) + 625(.33) +625(.33) = 625 60 dozen: 100(.33) + 1500(.33) + 1500(.33) = 1023 130 dozen: -950(.33) + 450(.33) + 3250(.33) = 907

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Solved Problem 3 Payoffs Event 1Event 2Event 3 Probabilities-- -->Low Regret Medium Regret High RegretMax Regret Order 25 dozen 625 0 875 625 2625 Order 60 dozen 100 525 1500 0 1750 Order 130dozen -950 1575 450 1050 3250 01575 Do nothing 0 625 0 1500 0 3250 Best Payoff:62515003250

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Solved Problem Minimax Regret –best “worst regret” Maximum regret of 25 dozen occurs if demand is high: $3250 – $625 = $2625 Maximum regret of 60 dozen occurs if demand is high: $3250 - $1500 = $1750 Maximum regret of 130 dozen occurs if demand is low: $625 - -$950 = $1575 The minimum of regrets is ordering 130 dozen!

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Solved Problem 4 Figure A.8 Bad times [0.3] Normal times [0.5] Good times [0.2] One lift Two lifts Bad times [0.3] Normal times [0.5] Good times [0.2] $256.0 $225.3 $256.0 $191 $240 $151 $245 $441

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