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) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 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) | | | | 500 1000 1500 2000 (2000, 400) Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000

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) | | | | 500 1000 1500 2000 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 – | | | | 500 1000 1500 2000 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) | | | | 500 1000 1500 2000 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) | | | | 500 1000 1500 2000 Fixed costs Profits Loss Forecast = 1,500 pQ – (F + cQ) 200(1500) – [100,000 + 100(1500)] = $50,000

Preference Matrix Threshold score = 800 Performance Weight Score Weighted Score Criterion (A) (B) (A x B) Market potential 30 8 240 Unit profit margin 20 10 200 Operations compatibility 20 6 120 Competitive advantage 15 10 150 Investment requirement 10 2 20 Project risk 5 4 20 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 30 8 240 Unit profit margin 20 10 200 Operations compatibility 20 6 120 Competitive advantage 15 10 150 Investment requirement 10 2 20 Project risk 5 4 20 Weighted score = 750 Threshold score = 800 Example A.4 Not At This Time

Decision Theory: Under Certainty Alternative Low High Small facility 200 270 Large facility 160 800 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 200 270 Large facility 160 800 Do nothing 0 0 Possible Future Demand Example A.6

Under Uncertainty Best of the worst Possible Future Demand Alternative Low High Small facility 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 = 0 800 – 270 = 530 Large facility 200 – 160 = 40 800 – 800 = 0

Under Uncertainty Possible Future Demand Alternative Low High Small facility 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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 200 270 Large facility 160 800 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) | | | | | | | | 1 2 3 4 5 6 7 8 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) + 1500(.33) + 1500(.33) = 1023 130 dozen: -950(.33) + 450(.33) + 3250(.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: 625 1500 3250

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!

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