Decision Making Supplement A
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1 Decision Making Supplement A
2 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.
3 Break-Even Analysis 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)
4 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.
5 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 $100 per patient. What is the break-even quantity for this service? Q = F / (p - c) = 100,000 / ( ) = 1,000 patients
6 Hospital Example Example A.1 A.1 continued 400 Dollars (in thousands) Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100, Q) (200Q) 0 100, , , Patients (Q)(
7 Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100, Q) (200Q) 0 100, , , (2000, 400) Dollars (in thousands) Total annual revenues Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100, Q) (200Q) 0 100, , , Patients (Q)(
8 Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100, Q) (200Q) 0 100, , , (2000, 400) Dollars (in thousands) Total annual revenues Total annual costs Fixed costs (2000, 300) Patients (Q)(
9 Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100, Q) (200Q) 0 100, , , (2000, 400) Profits Dollars (in thousands) Loss Total annual revenues Total annual costs Break-even even quantity Fixed costs (2000, 300) Patients (Q)(
10 pq (F + cq) 200(1500) [100, (1500)] 400 $50,000 Sensitivity Analysis Example A.2 Profits Dollars (in thousands) 300 Total annual revenues Loss Total annual costs Forecast = 1,500 Fixed costs Patients (Q)(
11 Application A.1
12 Q TR = pq TC = F + cq Application A.1 Solution
13 Application A.1 Solution pq = F + cq Q TR = pq TC = F + pq
14 Two Processes and Make-or 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.
15 Q = F m F b c b c m Breakeven for Two Processes Example A.3 12,000 2,400 Q =
16 Q = F m F b c b c m Breakeven for Two Processes Example A.3 Q = 19,200 salads
17 Application A.2 Q = F m F b c b c m = $300,000 $0 $9 $7 = 150,000
18 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.
19 Preference Matrix Example A.4 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
20 Preference Matrix Example A.4 continued Threshold score = 800 Score does not meet the threshold and is rejected. 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 d score = 750
21
22 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.
23 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.
24 Alternatives Low Events (Uncertain Demand) High Small facility Large facility Do nothing 0 0 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)
25 Alternatives Low Events (Uncertain Demand) High Small facility Large facility Do nothing 0 0 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)
26 Laplace (Assumed equal probabilities) Example A.6 c. Multiply each payoff by the probability of occurrence of its associated event. Events Alternatives Low High (0.5) (0.5) Small facility Large facility Do nothing * *0.5 = * *0.5 = 480 Select the alternative with the highest weighted payoff.
27 Alternatives Low MiniMax Regret Example A.6 d. Events (Uncertain Demand) High Small facility Large facility Do nothing 0 0 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).
28 Alternatives MiniMax Regret Example A.6 d. continued Low Events (Uncertain Demand) High Small facility Large facility Do nothing 0 0 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.)
29 Alternatives MiniMax Regret Example A.6 d. continued Low Events (Uncertain Demand) High Small facility Large facility Do nothing 0 0 Building a large facility offers the least regret. Regret Matrix Alternatives Low Events High Small facility Large facility 40 0 Do nothing MaxRegret
30 Expected Value Decision Making under Risk Example A.7 Multiply each payoff by the probability of occurrence of its associated event. Events Alternatives Low High (0.4) (0.6) Small facility Large facility Do nothing * *0.6 = * *0.6 = 544 Select the alternative with the highest weighted payoff.
31 Example A.7 Expected Value Analysis
32 Decision Trees 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.
33 Decision Trees = Event node = Decision node 1st decision Alternative Alternative Alternative Alternative 2 E 1 & Probability Probability E 1 & Probability E 2 & Probability E 3 & Probability Possible 2nd decision E 2 & Probability E 3 & Probability Payoff 1 Payoff 2 Payoff 3 Alternative 3 Alternative 4 Alternative 5 Payoff 1 Payoff 2 Payoff 1 Payoff 2 Payoff 3
34 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.
35 Small Small facility facility 1 Large facility Large facility Drawing the Tree Example A.8
36 Drawing the Tree Example A.8 continued Low demand [0.4] $200 1 Small Small facility facility High High demand demand [0.6] [0.6] 2 Don t t expand Expand $223 $270 Large Large facility facility
37 Completed Drawing Example A.8 Low demand [0.4] $200 1 Small Small facility facility Large Large facility facility High High demand demand [0.6] [0.6] Low Low demand demand [0.4] [0.4] 2 3 Don t t expand Expand Do nothing Advertise $223 $270 $40 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] $800
38 Solving Decision #3 Example A.8 Low demand [0.4] $200 Small Small facility facility High High demand demand [0.6] [0.6] 2 Don t t expand Expand $223 $270 1 Large Large facility facility Low Low demand demand [0.4] [0.4] 3 Do nothing Advertise $6 + $154 = $160 $ x $20 = $6 Modest response [0.3] Sizable response [0.7] $20 $ x $220 = $154 High demand [0.6] $800
39 Solving Decision #3 Example A.8 Low demand [0.4] $200 1 Small Small facility facility Large Large facility facility High High demand demand [0.6] [0.6] Low Low demand demand [0.4] [0.4] 2 3 $160 Don t t expand Expand Do nothing Advertise $223 $270 $40 $160 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] $800
40 Solving Decision #2 Example A.8 Low demand [0.4] $200 1 Small Small facility facility Large Large facility facility High High demand demand [0.6] [0.6] Low Low demand demand [0.4] [0.4] 2 $270 3 $160 Don t t expand Expand Do nothing Advertise $223 $270 $40 $160 Expanding has a higher value. Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] $800
41 Solving Decision #1 Example A.8 $242 Low demand [0.4] $200 x 0.4 = $80 1 Small Small facility facility Large Large facility facility High High demand demand [0.6] [0.6] Low Low demand demand [0.4] [0.4] 2 $270 3 $160 Don t t expand Expand Do nothing Advertise $223 $270 $40 $160 $242 x 0.6 = $162 Modest response [0.3] Sizable response [0.7] $20 $220 High demand [0.6] $800
42 Solving Decision #1 Example A.8 $242 Low demand [0.4] $200 1 Small Small facility facility Large Large facility facility High High demand demand [0.6] [0.6] Low Low demand demand [0.4] [0.4] 2 $270 3 $ x $160 = $64 Don t t expand Expand Do nothing Advertise $223 $270 $40 $160 Modest response [0.3] Sizable response [0.7] $20 $220 $544 High demand [0.6] $800 x 0.6 = $480
43 Solving Decision #1 Example A.8 Low demand [0.4] $200 1 $544 Small Small facility facility Large Large facility facility $242 High High demand demand [0.6] [0.6] Low Low demand demand [0.4] [0.4] 2 $270 3 $160 Don t t expand Expand Do nothing Advertise $223 $270 $40 $160 Modest response [0.3] Sizable response [0.7] $20 $220 $544 High demand [0.6] $800
44 Application A.6 OM Explorer Solution
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