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Decision Making Supplement A. Objectives Apply break-even analysis, using both the graphic and algebraic approaches, to evaluate new products and services.

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Presentation on theme: "Decision Making Supplement A. Objectives Apply break-even analysis, using both the graphic and algebraic approaches, to evaluate new products and services."— Presentation transcript:

1 Decision Making Supplement A

2 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.

3 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)

4 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

5 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)

6 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

7 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

8 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

9 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

10 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

11 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.

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

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

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

15 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

16 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

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

18 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

19 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

20 Under Risk Figure A.4

21 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

22 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

23 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

24 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

25 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

26 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

27 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

28 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

29 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

30 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)

31 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

32 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

33 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

34 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

35 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

36 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!

37 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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