# © 2007 Pearson Education Decision Making Supplement A.

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© 2007 Pearson Education Decision Making Supplement A

© 2007 Pearson Education Break-Even Analysis  Break-even analysis is used to compare processes by finding the volume at which two different processes have equal total costs.  Break-even point is the volume at which total revenues equal total costs.  Variable costs (c) are costs that vary directly with the volume of output.  Fixed costs (F) are those costs that remain constant with changes in output level.

© 2007 Pearson Education  “Q” is the volume of customers or units, “c” is the unit variable cost, F is fixed costs and p is the revenue per unit  cQ is the total variable cost.  Total cost = F + cQ  Total revenue = pQ  Break-even is where pQ = F + cQ (Total revenue = Total cost) Break-Even Analysis

© 2007 Pearson Education Break-Even Analysis can tell you…  If a forecast sales volume is sufficient to break even (no profit or no loss)  How low variable cost per unit must be to break even given current prices and sales forecast.  How low the fixed cost need to be to break even.  How price levels affect the break-even volume.

© 2007 Pearson Education Hospital Example Example A.1 A hospital is considering a new procedure to be offered at \$200 per patient. The fixed cost per year would be \$100,000, with total variable costs of \$100 per patient. Q = F / (p - c) = 100,000 / (200-100) = 1,000 patients What is the break-even quantity for this service?

© 2007 Pearson Education 400 – 300 – 200 – 100 – 0 – Patients (Q) Dollars (in thousands) |||| 500100015002000 QuantityTotal AnnualTotal Annual (patients)Cost (\$)Revenue (\$) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000 Hospital Example Example A.1 continued

© 2007 Pearson Education QuantityTotal AnnualTotal Annual (patients)Cost (\$)Revenue (\$) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000 400 – 300 – 200 – 100 – 0 – Patients (Q) Dollars (in thousands) |||| 500100015002000 (2000, 400) Total annual revenues QuantityTotal AnnualTotal Annual (patients)Cost (\$)Revenue (\$) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000

© 2007 Pearson Education Total annual costs Patients (Q) Dollars (in thousands) 400 – 300 – 200 – 100 – 0 – |||| 500100015002000 Fixed costs (2000, 400) (2000, 300) QuantityTotal AnnualTotal Annual (patients)Cost (\$)Revenue (\$) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000 Total annual revenues

© 2007 Pearson Education 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 QuantityTotal AnnualTotal Annual (patients)Cost (\$)Revenue (\$) (Q)(100,000 + 100Q)(200Q) 0100,0000 2000300,000400,000

© 2007 Pearson Education Total annual revenues Total annual costs Patients (Q) Dollars (in thousands) 400 – 300 – 200 – 100 – 0 – |||| 500100015002000 Fixed costs Profits Loss Sensitivity Analysis Example A.2 Forecast = 1,500 pQ – ( F + cQ ) 200(1500) – [100,000 + 100(1500)] \$50,000

© 2007 Pearson Education Application A.1

© 2007 Pearson Education Application A.1 Solution TR = pQ TC = F + cQ Q

© 2007 Pearson Education Application A.1 Solution TC = F + cQ TR = pQ Q

© 2007 Pearson Education Application A.1 Solution TR = pQ Q TC = F + pQ pQ = F + cQ pQ = F + cQ

© 2007 Pearson Education Two Processes and Make-or-Buy Decisions Two Processes and Make-or-Buy Decisions  Breakeven analysis can be used to choose between two processes or between an internal process and buying those services or materials.  The solution finds the point at which the total costs of each of the two alternatives are equal.  The forecast volume is then applied to see which alternative has the lowest cost for that volume.

© 2007 Pearson Education Breakeven for Two Processes Example A.3

© 2007 Pearson Education Q = F m – F b c b – c m Q = 12,000 – 2,400 2.0 – 1.5 Breakeven for Two Processes Example A.3

© 2007 Pearson Education Q = F m – F b c b – c m Q = 19,200 salads Breakeven for Two Processes Example A.3

© 2007 Pearson Education Application A.2 F m – F b c b – c m = Q = \$300,000 – \$0 \$9 – \$7 \$300,000 – \$0 \$9 – \$7 = \$150,000

© 2007 Pearson Education Preference Matrix   A Preference Matrix is a table that allows you to rate an alternative according to several performance criteria.   The criteria can be scored on any scale as long as the same scale is applied to all the alternatives being compared.   Each score is weighted according to its perceived importance, with the total weights typically equaling 100.   The total score is the sum of the weighted scores (weight × score) for all the criteria. The manager can compare the scores for alternatives against one another or against a predetermined threshold.

© 2007 Pearson Education PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential Unit profit margin Operations compatibility Competitive advantage Investment requirement Project risk Threshold score = 800 Preference Matrix Example A.4

© 2007 Pearson Education PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential30 Unit profit margin20 Operations compatibility20 Competitive advantage15 Investment requirement10 Project risk5 Threshold score = 800 Preference Matrix Example A.4 continued

© 2007 Pearson Education PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential308 Unit profit margin2010 Operations compatibility206 Competitive advantage1510 Investment requirement102 Project risk54 Threshold score = 800 Preference Matrix Example A.4 continued

© 2007 Pearson Education PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential308240 Unit profit margin2010200 Operations compatibility206120 Competitive advantage1510150 Investment requirement10220 Project risk5420 Threshold score = 800 Preference Matrix Example A.4 continued

© 2007 Pearson Education PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential308240 Unit profit margin2010200 Operations compatibility206120 Competitive advantage1510150 Investment requirement10220 Project risk5420 Weighted score =750 Weighted score =750 Threshold score = 800 Preference Matrix Example A.4 continued

© 2007 Pearson Education PerformanceWeightScoreWeighted Score Criterion(A)(B)(A x B) Market potential308240 Unit profit margin2010200 Operations compatibility206120 Competitive advantage1510150 Investment requirement10220 Project risk5420 Weighted score =750 Weighted score =750 Threshold score = 800 Preference Matrix Example A.4 continued Score does not meet the threshold and is rejected.

Application A.3 Repeat this process for each alternative — pick the one with the largest weighted score The concept of a weighted score

© 2007 Pearson Education Decision Theory  Decision theory is a general approach to decision making when the outcomes associated with alternatives are often in doubt.  A manager makes choices using the following process: 1.List the feasible alternatives 2.List the chance events (states of nature). 3.Calculate the payoff for each alternative in each event. 4.Estimate the probability of each event. (The total probabilities must add up to 1.) 5.Select the decision rule to evaluate the alternatives.

© 2007 Pearson Education Decision Rules  Decision Making Under Uncertainty is when you are unable to estimate the probabilities of events.  Maximin: The best of the worst. A pessimistic approach.  Maximax: The best of the best. An optimistic approach.  Minimax Regret: Minimizing your regret (also pessimistic)  Laplace: The alternative with the best weighted payoff using assumed probabilities.  Decision Making Under Risk is when one is able to estimate the probabilities of the events.  Expected Value: The alternative with the highest weighted payoff using predicted probabilities.

© 2007 Pearson Education AlternativesLowHigh Small facility200270 Large facility160800 Do nothing00 Events (Uncertain Demand) MaxiMin Decision Example A.6 a. 1.Look at the payoffs for each alternative and identify the lowest payoff for each. 2.Choose the alternative that has the highest of these. (the maximum of the minimums)

© 2007 Pearson Education AlternativesLowHigh Small facility200270 Large facility160800 Do nothing00 Events (Uncertain Demand) MaxiMax Decision Example A.6 b. 1.Look at the payoffs for each alternative and identify the “highest” payoff for each. 2.Choose the alternative that has the highest of these. (the maximum of the maximums)

© 2007 Pearson Education Laplace (Assumed equal probabilities) Example A.6 c. AlternativesLowHigh (0.5) (0.5) Small facility200270 Large facility160800 Do nothing00 Events 200*0.5 + 270*0.5 = 235 160*0.5 + 800*0.5 = 480 Multiply each payoff by the probability of occurrence of its associated event. Select the alternative with the highest weighted payoff.

© 2007 Pearson Education MiniMax Regret Example A.6 d. AlternativesLowHigh Small facility200270 Large facility160800 Do nothing00 Events (Uncertain Demand) Look at each payoff and ask yourself, “If I end up here, do I have any regrets?” Your regret, if any, is the difference between that payoff and what you could have had by choosing a different alternative, given the same state of nature (event).

© 2007 Pearson Education MiniMax Regret Example A.6 d. continued AlternativesLowHigh Small facility200270 Large facility160800 Do nothing00 Events (Uncertain Demand) If you chose a small facility and demand is low, you have zero regret. If you chose a large facility and demand is low, you have a regret of 40. (The difference between the 160 you got and the 200 you could have had.)

© 2007 Pearson Education MiniMax Regret Example A.6 d. continued AlternativesLowHigh Small facility200270 Large facility160800 Do nothing00 Events (Uncertain Demand) Alternatives LowHigh Small facility 0530 Large facility 400 Do nothing 200800 Events MaxRegret 530 40 800 Regret Matrix Building a large facility offers the least regret.

© 2007 Pearson Education Expected Value Decision Making under Risk Example A.7 AlternativesLowHigh (0.4) (0.6) Small facility200270 Large facility160800 Do nothing00 Events 200*0.4 + 270*0.6 = 242 160*0.4 + 800*0.6 = 544 Multiply each payoff by the probability of occurrence of its associated event. Select the alternative with the highest weighted payoff.

© 2007 Pearson Education Example A.7 Expected Value Analysis

© 2007 Pearson Education Application A.4

© 2007 Pearson Education Application A.4 840 – 840 = 0 840 – 370 = 470 840 – 25 = 830 1150 – 440 = 710 1150 – 220 = 930 1150 – 1150 = 0 670 – (-25) = 695 670 – 670 = 0 670 – 190 = 480 710 930 830 What is the minimax regret solution?

© 2007 Pearson Education Application A.5

© 2007 Pearson Education  Decision Trees are schematic models of alternatives available along with their possible consequences.  They are used in sequential decision situations.  Decision points are represented by squares.  Event points are represented by circles. Decision Trees

© 2007 Pearson Education = Event node = Decision node 1stdecision Possible 2nd decision Payoff 1 Payoff 2 Payoff 3 Alternative 3 Alternative 4 Alternative 5 Payoff 1 Payoff 2 Payoff 3 E 1 & Probability E 2 & Probability E 3 & Probability E 2 & Probability E 3 & Probability E 1 & Probability Alternative 1 Alternative 2 Payoff 1 Payoff 2 12 Decision Trees

© 2007 Pearson Education Decision Trees   After drawing a decision tree, we solve it by working from right to left, starting with decisions farthest to the right, and calculating the expected payoff for each of its possible paths.   We pick the alternative for that decision that has the best expected payoff.   We “saw off,” or “prune,” the branches not chosen by marking two short lines through them.   The decision node’s expected payoff is the one associated with the single remaining branch.

© 2007 Pearson Education Small facility Large facility 1 Drawing the Tree Example A.8

© 2007 Pearson Education Small facility Large facility Low demand [0.4] Don’t expand Expand \$200\$223\$270 High demand [0.6] 1 2 Drawing the Tree Example A.8 continued

© 2007 Pearson Education Small facility Large facility 1 Low demand [0.4] 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] 2 3 Completed Drawing Example A.8

© 2007 Pearson Education Solving Decision #3 Example A.8 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 x \$20 = \$6 0.7 x \$220 = \$154 \$6 + \$154 = \$160

© 2007 Pearson Education Don’t expand Expand Do nothing Advertise \$200\$223\$270\$40\$800 \$160 Low demand [0.4] Small facility Large facility Low demand [0.4] Modest response [0.3] Sizable response [0.7] \$20\$220 High demand [0.6] 1 2 3 Solving Decision #3 Example A.8 \$160

© 2007 Pearson Education \$160 Modest response [0.3] Sizable response [0.7] \$20\$220 Solving Decision #2 Example A.8 Expanding has a higher value. 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 High demand [0.6] 1 2 3 \$270

© 2007 Pearson Education \$470 x 0.4 = \$80 x 0.4 = \$80 x 0.6 = \$162 \$242 \$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 Solving Decision #1 Example A.8

© 2007 Pearson Education Solving Decision #1 Example A.8 \$242 \$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 x 0.6 = \$480 0.4 x \$160 = \$64 \$544

© 2007 Pearson Education \$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 Solving Decision #1 Example A.8 \$544

© 2007 Pearson Education Application A.6 OM Explorer Solution Application A.6 OM Explorer Solution

© 2007 Pearson Education Solved Problem 1 250 – 200 – 150 – 100 – 50 – 0 – Total revenues Total costs Units (in thousands) Dollars (in thousands) ||||||||||||||||1234567812345678||||||||||||||||1234567812345678 Break-evenquantity 3.1 \$77.7

© 2007 Pearson Education Solved Problem 4 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 \$240 \$151 \$245 \$441