Decision Making Supplement A

Decision Making Supplement A

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.

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)

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.

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 / (200-100) = 1,000 patients

Hospital Example Example A.1 A.1 continued 400 Dollars (in thousands) 300 200 100 Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 0 500 1000 1500 2000 Patients (Q)(

Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 400 (2000, 400) Dollars (in thousands) 300 200 100 Total annual revenues Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 0 500 1000 1500 2000 Patients (Q)(

Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 400 (2000, 400) Dollars (in thousands) 300 200 100 Total annual revenues Total annual costs Fixed costs (2000, 300) 0 500 1000 1500 2000 Patients (Q)(

Quantity Total Annual Total Annual (patients) Cost ($) Revenue ($) (Q) (100,000 + 100Q) (200Q) 0 100,000 0 2000 300,000 400,000 400 (2000, 400) Profits Dollars (in thousands) 300 200 100 Loss Total annual revenues Total annual costs Break-even even quantity Fixed costs (2000, 300) 0 500 1000 1500 2000 Patients (Q)(

pq (F + cq) 200(1500) [100,000 + 100(1500)] 400 $50,000 Sensitivity Analysis Example A.2 Profits Dollars (in thousands) 300 Total annual revenues 200 100 Loss Total annual costs Forecast = 1,500 Fixed costs 0 500 1000 1500 2000 Patients (Q)(

Application A.1

Q TR = pq TC = F + cq Application A.1 Solution

Application A.1 Solution pq = F + cq Q TR = pq TC = F + pq

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.

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

Q = F m F b c b c m Breakeven for Two Processes Example A.3 Q = 19,200 salads

Application A.2 Q = F m F b c b c m = $300,000 $0 $9 $7 = 150,000

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.

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

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 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 d score = 750

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.

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.

Alternatives Low Events (Uncertain Demand) High Small facility 200 270 Large facility 160 800 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)

Alternatives Low Events (Uncertain Demand) High Small facility 200 270 Large facility 160 800 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)

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 200 270 Large facility 160 800 Do nothing 0 0 200*0.5 + 270*0.5 = 235 160*0.5 + 800*0.5 = 480 Select the alternative with the highest weighted payoff.

Alternatives Low MiniMax Regret Example A.6 d. Events (Uncertain Demand) High Small facility 200 270 Large facility 160 800 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).

Alternatives MiniMax Regret Example A.6 d. continued Low Events (Uncertain Demand) High Small facility 200 270 Large facility 160 800 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.)

Alternatives MiniMax Regret Example A.6 d. continued Low Events (Uncertain Demand) High Small facility 200 270 Large facility 160 800 Do nothing 0 0 Building a large facility offers the least regret. Regret Matrix Alternatives Low Events High Small facility 0 530 Large facility 40 0 Do nothing 200 800 MaxRegret 530 40 800

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 200 270 Large facility 160 800 Do nothing 0 0 200*0.4 + 270*0.6 = 242 160*0.4 + 800*0.6 = 544 Select the alternative with the highest weighted payoff.

Example A.7 Expected Value Analysis

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.

Decision Trees = Event node = Decision node 1st decision Alternative Alternative 1 1 2 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

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.

Small Small facility facility 1 Large facility Large facility Drawing the Tree Example A.8

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

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

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 $40 0.3 x $20 = $6 Modest response [0.3] Sizable response [0.7] $20 $220 0.7 x $220 = $154 High demand [0.6] $800

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

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

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

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 $160 0.4 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

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

Application A.6 OM Explorer Solution