A construction company must decide on the size of the shopping mall, i.e. Large,
ID: 453286 • Letter: A
Question
A construction company must decide on the size of the shopping mall, i.e. Large, Medium or Small, that has to be constructed in their acquired plot in the sub-urban area of Seattle. Due to the market conditions, the number of visitors to the mall will be High, Moderate, or Low.
The level of response and the size of the mall will decide the return of investment from the mall.
The profit payoff table for management (in millions of dollars) after 5 years is provided below.
Number of visitors
Size of the mall
High
Moderate
Low
Large
25
15
–20
Medium
20
12
–10
Small
15
13
5
The probabilities are P(High) = 0.35, P(Moderate) = 0.40, and P(Low) = 0.25.
a. Use a decision tree to recommend a decision.
b. Use EVPI to determine whether the construction company should attempt to obtain a better estimate of the response.
Number of visitors
Size of the mall
High
Moderate
Low
Large
25
15
–20
Medium
20
12
–10
Small
15
13
5
Explanation / Answer
Answer-1 number of visitors Probability Expected value high 25 0.35 9.75 large moderate 15 0.4 low -20 0.25 high 20 0.35 9.3 size of mall medium moderate 12 0.4 low -10 0.25 high 15 0.35 11.7 small moderate 13 0.4 low 5 0.25 EMV for the best decision = 11.7 the ecpected value of small decision is highest therefore this si selected. Answer-2 To calculate EVPI, first calculate EPPI by choosing optimal course of action for each state of nature. Multiply conditional numbers associated with each course of action by the given probability to get weighted profit, and then add these weights. Here the conditional numbers are: Numbers probability High 25 0.35 Moderate 15 0.4 low 5 0.25 So EPPI = 16 Now EMV for the best decision = 11.7 Therefore EVPI = EPPI-EMV = 4.3
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