Problem 3-1 Maria Rojas is considering the possibility of opening a small dress
ID: 2740668 • Letter: P
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Problem 3-1 Maria Rojas is considering the possibility of opening a small dress shop on Fairbanks Avenue, a few blocks from the university. She has located a good mall that attracts students. Her options are to open a small shop, a medium-sized shop, or no shop at all. The market for a dress shop can be good, average, or bad. The probabilities for these three possibilities are 0.2 for a good market, 0.5 for an average market, and 0.3 for a bad market. The net profit or loss for the medium-sized and small shops for the various market conditions are given in the following table. Building no shop at all yields no loss and no gain. a. What do you recommend? b. Calculate the EVPI. c. Develop the opportunity loss table for this situation. What decisions would be made using the mini- max regret criterion and the minimum EOL criterion? AVERAGE BAD GOOD MARKET MARKET MARKET (S) ($0 ALTERNATIVE 40,000 75,000 25,000 Small shop Medium-sized shop 35,000 60,000 100,000 No shopExplanation / Answer
Answer a.
EMV (small shop) = 0.2*($75,000) + 0.5*($25,000) + 0.3*($-40,000) = $15,500
EMV (medium shop) = 0.2*($100,000) + 0.5*($35,000) + 0.3*($-60,000) = $19,500
EMV (do nothing) = 0.2*($0) + 0.5*($0) + 0.3*($0) = $0
Medium Shop because it has the highest EMV of $19,500.
Answer b.
Best alternative for good state of nature is opening a medium shop with a payoff of $100,000
Best alternative for average state of nature is opening a medium shop with a payoff of $35,000
Best alternative for bad state of nature is to do nothing with a payoff of $0
EVwPI = ($100,000)*0.2 + ($35,000)*0.5 + ($0)*0.3 = $37,500
The maximum EMV is $19,500
EVPI = EVwPI – Maximum EMV
EVPI = $37,500 - $19,500 = $18,000
Answer c.
Opportunity Loss Table using Mini-max Regret Criterion :
State of Nature
Alternative
Good Market
Average Market
Bad Market
Maximum in a row
Small Shop
25,000
10,000
40,000
40,000
Medium sized shop
0
0
60,000
60,000
Do Nothing
100,000
35,000
0
100,000
Opportunity Loss is calculated by subtracting each payoff in the column from the best payoff in the column.
So using Mini-max Regret Criterion, We should chose Small shop option.
Minimum EOL will always result in the same decision as EVPI.
State of Nature
Alternative
Good Market
Average Market
Bad Market
Maximum in a row
Small Shop
25,000
10,000
40,000
40,000
Medium sized shop
0
0
60,000
60,000
Do Nothing
100,000
35,000
0
100,000
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