Problem 1
Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Advance sales are so small that Weiss has no way to estimate the demand for the red roses. She buys roses for $15 per dozen and sells them for $40 per dozen. Pay-off table for the problem is given below.
Demand for Red Roses
Alternative Low (25 dozen) Medium (60 dozen) High (130 dozen)
Do nothing 0 0 0
Order 25 dozen 300,000 300,000 300,000
Order 60 dozen 100,000 600,000 600,000
Order 130 dozen -100,000 400,000 900,000
Probability 0.3 0.4 0.3
(Krajewski, L., Ritzman, L., & Malhotra, M. (2007). Operations Mangement (8th ed.). Upper Saddle Reiver, NJ: Prentice Hall)
What is the decision based on each of the following criteria? Show work in making the decision for each criterion.
a) EMV approach
b) EOL approach
a) For the EMV approach, we need to calculate the Expected Monetary Value for each decision alternative and select the one with the highest value.
To calculate the EMV, we multiply the payoff for each demand scenario by its corresponding probability and sum them up for each decision alternative.
EMV(Do nothing) = (0 x 0.3) + (0 x 0.4) + (0 x 0.3) = 0
EMV(Order 25 dozen) = (300,000 x 0.3) + (300,000 x 0.4) + (300,000 x 0.3) = 300,000
EMV(Order 60 dozen) = (100,000 x 0.3) + (600,000 x 0.4) + (600,000 x 0.3) = 420,000
EMV(Order 130 dozen) = (-100,000 x 0.3) + (400,000 x 0.4) + (900,000 x 0.3) = 400,000
Based on the EMV approach, the decision would be to Order 60 dozen, as it has the highest EMV of 420,000.
b) For the EOL approach, we need to calculate the Expected Opportunity Loss for each decision alternative and select the one with the lowest value.
To calculate the EOL, we subtract the EMV of each decision alternative from the highest EMV value.
EOL(Do nothing) = EMV(Order 60 dozen) - EMV(Do nothing) = 420,000 - 0 = 420,000
EOL(Order 25 dozen) = EMV(Order 60 dozen) - EMV(Order 25 dozen) = 420,000 - 300,000 = 120,000
EOL(Order 130 dozen) = EMV(Order 60 dozen) - EMV(Order 130 dozen) = 420,000 - 400,000 = 20,000
Based on the EOL approach, the decision would be to Order 130 dozen, as it has the lowest EOL of 20,000.
a) To make the decision based on the EMV (Expected Monetary Value) approach, we need to calculate the expected value for each alternative. The expected value is calculated by multiplying the pay-offs by their respective probabilities and summing them up.
For the "Do nothing" alternative:
Expected value = (0 * 0.3) + (0 * 0.4) + (0 * 0.3) = 0
For the "Order 25 dozen" alternative:
Expected value = (300,000 * 0.3) + (300,000 * 0.4) + (300,000 * 0.3) = 300,000
For the "Order 60 dozen" alternative:
Expected value = (100,000 * 0.3) + (600,000 * 0.4) + (600,000 * 0.3) = 420,000
For the "Order 130 dozen" alternative:
Expected value = (-100,000 * 0.3) + (400,000 * 0.4) + (900,000 * 0.3) = 430,000
Based on the EMV approach, the decision would be to "Order 130 dozen" as it has the highest expected value of 430,000.
b) To make the decision based on the EOL (Maximum Likelihood) approach, we need to identify the maximum pay-off for each demand level and select the alternative with the highest maximum pay-off.
For the "Do nothing" alternative, the maximum pay-off is 0.
For the "Order 25 dozen" alternative, the maximum pay-off is 300,000.
For the "Order 60 dozen" alternative, the maximum pay-off is 600,000.
For the "Order 130 dozen" alternative, the maximum pay-off is 900,000.
Based on the EOL approach, the decision would be to "Order 130 dozen" as it has the highest maximum pay-off of 900,000.