# Supplement A Decision Making.

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Supplement A Decision Making

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.

Break-Even Analysis Quantity Total Annual Total Annual (patients) Cost (\$) Revenue (\$) (Q) (100, Q) (200Q) 0 100,000 0 , ,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)

Break-Even Analysis 400 – 300 – (2000, 400) 200 – 100 –
Total annual revenues Patients (Q) Dollars (in thousands) | | | | (2000, 400) Quantity Total Annual Total Annual (patients) Cost (\$) Revenue (\$) (Q) (100, Q) (200Q) 0 100,000 0 , ,000

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

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

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

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

Preference Matrix Threshold score = 800
Performance Weight Score Weighted Score Criterion (A) (B) (A x B) Market potential Unit profit margin Operations compatibility Competitive advantage Investment requirement Project risk Weighted score = 750 Threshold score = 800 Example A.4

Not At This Time Preference Matrix Threshold score = 800
Performance Weight Score Weighted Score Criterion (A) (B) (A x B) Market potential Unit profit margin Operations compatibility Competitive advantage Investment requirement Project risk Weighted score = 750 Threshold score = 800 Example A.4 Not At This Time

Decision Theory: Under Certainty
Alternative Low High Small facility Large facility Do nothing 0 0 Possible Future Demand If future demand will be low—Choose the small facility. Example A.5

Under Uncertainty Possible Future Demand Alternative Low High
Small facility Large facility Do nothing 0 0 Possible Future Demand Example A.6

Under Uncertainty Best of the worst Possible Future Demand
Alternative Low High Small facility Large facility Do nothing 0 0 Possible Future Demand Maximin—Small Best of the worst Example A.6

Under Uncertainty Best of the best Possible Future Demand
Alternative Low High Small facility Large facility Do nothing 0 0 Possible Future Demand Maximin—Small Maximax—Large Best of the best Example A.6

Under Uncertainty Best weighted payoff Possible Future Demand
Alternative Low High Small facility Large facility Do nothing 0 0 Possible Future Demand Maximin—Small Maximax—Large Laplace—Large Best weighted payoff Small facility 0.5(200) + 0.5(270) = 235 Large facility 0.5(160) + 0.5(800) = 480 Example A.6

Under Uncertainty Best worst regret Possible Future Demand
Alternative Low High Small facility Large facility Do nothing 0 0 Possible Future Demand Example A.6 Maximin—Small Maximax—Large Laplace—Large Minimax Regret—Large Best worst regret Regret Low Demand High Demand Small facility 200 – 200 = – 270 = 530 Large facility 200 – 160 = – 800 = 0

Under Uncertainty Possible Future Demand Alternative Low High
Small facility Large facility Do nothing 0 0 Possible Future Demand Maximin—Small Maximax—Large Laplace—Large Minimax Regret—Large Example A.6

Under Risk Possible Future Demand Alternative Low High
Small facility Large facility Do nothing 0 0 Possible Future Demand Psmall = 0.4 Plarge = 0.6 Example A.7 Alternative Expected Value Small facility 0.4(200) + 0.6(270) = 242 Large facility 0.4(160) + 0.6(800) = 544

Under Risk Highest Expected Value Possible Future Demand
Alternative Low High Small facility Large facility Do nothing 0 0 Possible Future Demand Psmall = 0.4 Plarge = 0.6 Example A.7 Alternative Expected Value Small facility 0.4(200) + 0.6(270) = 242 Large facility 0.4(160) + 0.6(800) = 544 Highest Expected Value

Under Risk Figure A.4

Perfect Information Possible Future Demand Alternative Low High
Small facility Large facility Do nothing 0 0 Possible Future Demand Psmall = 0.4 Plarge = 0.6 Example A.8 Event Best Payoff Low demand 200 High demand 800

Perfect Information Possible Future Demand Alternative Low High
Small facility Large facility Do nothing 0 0 Possible Future Demand Psmall = 0.4 Plarge = 0.6 Example A.8 Event Best Payoff Low demand 200 EVperfect = 200(0.4) + 800(0.6) = 560 High demand 800 EVimperfect = 160(0.4) + 800(0.6) = 544

Perfect Information Possible Future Demand Alternative Low High
Small facility Large facility Do nothing 0 0 Possible Future Demand Psmall = 0.4 Plarge = 0.6 Example A.8 Event Best Payoff Low demand 200 EVperfect = 200(0.4) + 800(0.6) = 560 High demand 800 EVimperfect = 160(0.4) + 800(0.6) = 544 Value of perfect information = \$560,000 - \$544,000

Decision Trees 1 2 Figure A.5 = Event node = Decision node
Ei = Event i P(Ei) = Probability of event i 1st decision Possible 2nd decision Payoff 1 Payoff 2 Payoff 3 Alternative 3 Alternative 4 Alternative 5 E1 [P(E1)] E2 [P(E2)] E3 [P(E3)] Alternative 1 Alternative 2 1 2 Figure A.5

Decision Trees 2 1 3 Example A.9 Low demand [0.4] \$200 \$223
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

Decision Trees 0.3(20) + 0.7(220) 2 1 3 Example A.9 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

Decision Trees 0.3(20) + 0.7(220) 2 1 3 \$160 Example A.9
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

Decision Trees 2 1 3 \$160 Example A.9 Low demand [0.4] \$200 \$223
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

Decision Trees 0.4(200) + 0.6(270) 0.4(160) + 0.6(800) 2 \$270 1 3 \$160
(\$160) Low demand [0.4] \$270 \$160 Small facility Large facility Low demand [0.4] Don’t expand Expand Do nothing Advertise \$200 \$223 \$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

Decision Trees 0.4(200) + 0.6(270) 0.4(160) + 0.6(800) \$242 2 \$270 1 3
(\$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 \$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)

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

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

Solved Problem 3 To determine the payoff amounts:
Payoff Scenarios 1: 2: 3: Event 1 Event 2 Event 3 Probabilities----> Low Medium High Order 25 dozen 625 Order 60 dozen 100 1500 Order 130dozen -950 450 3250 Do nothing 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

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) (.33) (.33) = 1023 130 dozen: -950(.33) + 450(.33) (.33) = 907

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

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: \$ \$1500 = \$1750 Maximum regret of 130 dozen occurs if demand is low: \$ \$950 = \$1575 The minimum of regrets is ordering 130 dozen!

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