Question

The produce manager at the local Pig & Whistle grocery store must determine how many pounds of bananas to order weekly. Based upon past experience, the demand for bananas is expected to be 100, 150, 200, or 250 pounds with the following probabilities: 100lbs 0.20; 150lbs 0.25, 200lbs 0.35, 250lbs 0.20. The bananas cost the store $.45 per pound and are sold for $.085 per pound. Any unsold bananas at the end of each week are sold to a local zoo for $.30 per pound. Use your knowledge of decision analysis to model and solve this problem in order to recommend how many pounds of bananas the manager should order each week

Answer 1

Solution

The solution is based on EMV criterion of Decision Making.

Back-up Theory

Expected Monetary Value Criterion

Under this criterion, for each decision option, the pay-offs under various States of Nature (SON’s) are multiplied by the respective probability to obtain the EMV for that decision option. Then, the decision option which yields the maximum EMV is selected.

Now to work out the solution,

Let Q be the order quantity (in pounds) and D be the demand also in pounds.

If D ≤ Q, quantity sold at $0.85 per pound is D and that sold at $0.30 per pond is (Q – D)

Hence the pay-off (i.e., profit) = 0.85D + (Q - D) x 0.30 – 0.45Q = 0.55D – 0.15Q ...................... (1)

If D > Q, quantity sold is always Q and hence the pay-off = (0.85 – 0.45)Q = 0.40Q ................(2)

EMV calculations are tabulated below:

Q	Pay-off				EMV
	D
	100	150	200	250
100	40.0	40.0	40.0	40.0	40.00
150	32.5	60.0	60.0	60.0	54.50
200	25.0	52.5	80.0	80.0	62.13
250	17.5	45.0	72.5	100.0	60.13
P(D)	0.20	0.25	0.35	0.20

Since EMV is maximum at $62.3 for Q = 200,

optimum order quantity is 200 pounds of bananas per week. Answer

DONE