Question

The quality control manager for Porter Inc. must decide whether to accept, further analyze or reject a lot of incoming material used to make disposable coffee cups. Historical data indicates that there is 30% chance that the lot is poor quality, 50 % chance that the lot is fair quality and 20% chance that the lot is good quality. The payoff table below indicates the profits available depending on the decision made and the quality of the lot.

	Low Quality	Fair Quality	Good Quality
Accept	20	30	90
Further Analyze	60	70	10
Reject	80	50	40

a) Assuming profit is the only objective, what should the quality control manger do with the lot of incoming material?

b) What is the maximum amount that the manager would be willing to pay for perfect information?

Answer 1

	Payoffs table:
		Quality
		Low	Fair	Good
Decision	Accept	20	30	90
	Further analyze	60	70	10
	Reject	80	50	40
	Probabilities	0.3	0.5	0.2
	Opportunity Loss table:
		Quality
		Low	Fair	Good
Decision	Accept	60	40	0
	Further analyze	20	0	80
	Reject	0	20	50

(a)
Expected profit for Accept = 20 * 0.3 + 30 * 0.5 + 90 * 0.2 = 39
Expected profit for Further analyze = 60 * 0.3 + 70 * 0.5 + 10 * 0.2 = 55
Expected profit for Reject = 80 * 0.3 + 50 * 0.5 + 40 * 0.2 = 57
Decision: Reject the lot
(b)
EOL for Accept = 60 * 0.3 + 40 * 0.5 + 0 * 0.2 = 38
EOL for Further analyze = 20 * 0.3 + 0 * 0.5 + 80 * 0.2 = 22
EOL for Reject = 0 * 0.3 + 20 * 0.5 + 50 * 0.2 = 20
EVPI = EOL = 20