Question

McBurger Inc., wants to redesign its kitchen to improve productivity and quality. Three designs, called B1, B2, and B3, are under consideration. No matter which design is used, daily demand for sandwiches at a typical McBurger restaurant is 500 sandwiches. A sandwich costs 500 baiza to produce. Non-defective sandwich sell, on average, for 1 OR per sandwich. Defective sandwich cannot be sold and are scrapped. The goal is to chose a design that maximizes the expected profit at a typical restaurant over a period of one year (365 days). Designs B1, B2, and B3 cost 40,000

3

OR, 50,000 OR, and 70,000 OR, respectively. Under design B1, there is 0.8 chance that 90 out of each 100 sandwiches are non-defective and 0.2 chance that 70 out of each 100 sandwiches are non-defective. Under design B2, there is 0.85 chance that 90 out of each 100 sandwiches are non- defective and 0.15 chance that 75 out of each 100 sandwiches are non-defective. Under design B3, there is 0.9 chance that 95 out of each 100 sandwiches are non-defective and 0.1 chance that 80 out of each 100 sandwiches are non-defective.

1. Calculate the payoff in each alternative with the corresponding states of the nature.

2. Draw the decision tree.

3. What is the expected profit level of the design that achieves the maximum expected profit level per year?

4. What is the EVPI? Give the interpretation of the result.

Answer 1

Daily expected profit level of a design K1 = 550*0.8*{(90/100)*(2.75-1.4) + (10/100)*(-1.4)} + 550*0.2*{(70/100)*(2.75-1.4) + (30/100)*(-1.4)} = $530.75

Daily expected profit level of a design K2 = 550*0.85*{(90/100)*(2.75-1.4) + (10/100)*(-1.4)} + 550*0.15*{(75/100)*(2.75-1.4) + (25/100)*(-1.4)} = $557.22

Daily expected profit level of a design K3 = 550*0.9*{(95/100)*(2.75-1.4) + (5/100)*(-1.4)} + 550*0.1*{(80/100)*(2.75-1.4) + (20/100)*(-1.4)} = $644.19

Total expected profit for K1 = 530.75*300 – 100000 = $59,255

Total expected profit for K2 = 557.22*300 – 140000 = $27166

Total expected profit for K3 = 644.19*300 – 180000 = $13256.25

So, design K1 gives maximum expected profit.