Western Plastic Surgery Associates is planning on opening a cosmetic plastic sur
ID: 464631 • Letter: W
Question
Western Plastic Surgery Associates is planning on opening a cosmetic plastic surgery center in either Honolulu, San Francisco, or Seattle. There is a 60 percent chance that the demand for plastic surgery in the United States will increase in the near future, a 25 percent chance that the number will remain the same, and a 15 percent chance that the number will decrease. The developer estimates that the following prots would result from each decision given each set of economic conditions. Location Increase (0.60) Same (0.25) Decrease (0.15) Honolulu $1,102,000 $856,000 $502,000 San Francisco $720,000 $640,000 $602,000 Seattle $800,000 $702,000 $220,000 Find the best decision using the following: a. Develop a payo table for this situation. b. Find the following: 1. Maximax 2. Maximin 3. Equal likelihood 4. Minimax regret c. Can you create a sensitivity graph comparing the dierent alternatives as the probabilities of increase, same, and decrease change? Why or why not?
Explanation / Answer
Economic Conditions
Probabilites
0.6
0.25
0.15
Maximum
Minimum
Average (Equally likelihood)
Location Alternatives
Increased Demand
No change in demand
Deacrease in Demand
Honolulu
$1,102,000
$856,000
$502,000
$1,102,000
$502,000
$820,000
San Francisco
$720,000
$640,000
$602,000
$720,000
$602,000
$654,000
Seattle
$800,000
$702,000
$220,000
$800,000
$220,000
$574,000
Maximax decision rule:
This approach selects the alternative which maximizes the maximum payoff among all events
Maximum payoffs of Honolulu, San Francisco, and Seattle locations are ($1,102,000, $720,000, $800,000) respectively.
Maximum payoff among the alternative’s maximum payoff is $1,102,000 for the Location Honolulu.
Thus, alternative of locating at Honolulu maximizes the maximum payoff among all events.
Maximin Decision Rule:
This approach selects the alternative which maximizes the minimum payoff among all events.
Minimum payoffs of Honolulu, San Francisco, and Seattle locations are ($502,000, $602,000, $220,000) respectively.
Maximum payoff among the alternative’s minimum payoff is $220,000 for the Location Seattle.
Thus, alternative of locating at Seattle maximizes the minimum payoff among all events.
Equally-likely criteria:
This approach selects the alternative which maximizes the Average payoff among all the alternatives.
Average payoffs of Honolulu, San Francisco, and Seattle locations are ($820,000, $654,000, $574,000) respectively.
Maximum payoff among the alternative’s average payoff is $820,000 for the location Honolulu..
Thus, alternative of locating at Honolulu maximizes the average payoff or EMV among all events.
Regret Table:
First develop regret table by subtracting maximum payoff among the each event and subtracting each payoff of event from this value.
Regret Matrix
Economic Conditions
Probabilites
0.6
0.25
0.15
Location Alternatives
Increased Demand
No change in demand
Deacrease in Demand
Maximum
Honolulu
$0
$0
$100,000
$100,000
San Francisco
$382,000
$216,000
$0
$382,000
Seattle
$302,000
$154,000
$382,000
$382,000
MINIMAX REGRET decision rule
According to this rule select alternative which minimizes the maximum opportunity loss value of each alternative.
Maximum regret value for Honolulu, San Francisco, and Seattle locations are $100,000, $382,000, $382,000.
Minimum payoff among the alternative’s maximum opportunity loss value is $100,000 for the location Honolulu.
Thus, alternative of locating at Honolulu minimizes the maximum opportunities loss among all events.
Economic Conditions
Probabilites
0.6
0.25
0.15
Maximum
Minimum
Average (Equally likelihood)
Location Alternatives
Increased Demand
No change in demand
Deacrease in Demand
Honolulu
$1,102,000
$856,000
$502,000
$1,102,000
$502,000
$820,000
San Francisco
$720,000
$640,000
$602,000
$720,000
$602,000
$654,000
Seattle
$800,000
$702,000
$220,000
$800,000
$220,000
$574,000
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