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?
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 |
The quality control manager for Porter Inc. must decide whether to accept, further analyze or reject...
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