. Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Be
ID: 465799 • Letter: #
Question
. Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars).
Demand for Service
Service
Strong
Weak
Full price
960
-20
Discount
670
320
A) What alternative is best using the maximax criterion and the estimated payoff?
B) What alternative is best using the maximin criterion and the estimated payoff?
C) What alternative is best using the equal likelihood decision criterion and the estimated payoff?
D) What alternative is best using the Hurwicz (with a = 0.4) decision criterion?
Demand for Service
Service
Strong
Weak
Full price
960
-20
Discount
670
320
Explanation / Answer
a. Maximax criteria involves selecting the alternative that maximises the maximum payoff available. Maximum profit for full price service is 960 and for discount service is 670. Thus the maximum of the two os 960. The maximum quarterly profit is 960 (in thousands of dollars). Thus under this criteria Myrtle Air Express will offer full price service, (being optimistic of strong demand). The estimated payff = $960,000
b. Maximin criteria involves selecting the minimum payoff for each criteria and then selecting the highest of these minimum payoffs.
The mimimum payoffs are -20 (full price) and 320 (discount service). Highest of these two are $320,000 and so the airline should provide discount service. Estimated payoff = $320,000
c. In the equal likelihood criteria, each state of nature are given equal weights. The states of nature here is strong demand and weak demand. Equal likelihood will assign a weight of 0.50 to each of these states.
Payoff for full price service = 960*0.5 + (-20*0.5) = 470
Payoff for discount service = 670*0.5 + 320*0.5 = 495
As the payoff of the discount service is higher at $495,000 it will be selected. Payoff = $495,000
D. a = 0.4. This is the coefficient of optimism. This means that a weight of 0.4 will be given to the condition of strong demand. Weight for the condition of weak demand = 1-a = 1-0.4 = 0.6
Using the weighted formula as used in equal likelihood criteria:
Payoff for full price service = 960*0.4 + (-20*0.6) = 372
Payoff for discount service = 670*0.4 + 320*0.6 = 460.
The maximum of the above is 460. Thus a discount service will be provided with a payoff of $460,000
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