Question

Problem 13-09 (Algorithmic)

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	$1320	-$550
Discount	$980	$440

1. What is the decision to be made, what is the chance event, and what is the consequence for this problem?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
   How many decision alternatives are there?
   
   Number of decision alternatives =
   
   How many outcomes are there for the chance event?
   
   Number of outcomes =
   
2. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative and minimax regret approaches?
   

   Optimistic approach
   Conservative approach
   Minimax regret approach

3. Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision.
   
   Optimal Decision :  
   
4. Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach?
   
   Optimal Decision :  
   
5. Determine the range of demand probabilities for which each of the decision alternatives has the largest expected value. If required, round your answer to four decimal places.
   
     is the best choice if probability of strong demand is less than or equal to . For values of  greater than , the full price service is   choice.

Answer 1

a.

The decision that has to be made is to choose between full price or discounted service.

There are two decision alternatives

There are two outcomes for the chance event

b.

Optimistic approach: this is also called maximax approach. The maximum value for each decision alternative is 1320 and 980. Among them 1320 is more optimistic. Hence we will choose Full price service.

Conservative approach: this is also called maximin approach. The minimum value for each decision alternative is -550 and 440. Among the better option is 440. Hence we will choose Discount service.

Minimax regret: if we choose full price and the demand is strong then the regret is 0. However if we choose discount and the demand is strong then the regret is 1320-980=340. Similarly if we choose full price and the demand is weak, the regret is 440-(-550) = 990. On the other hand if we choose discount and the demand is weak, there is no regret.

Now the maximum regret for Full price service decision is 990. The maximum regret for the discount service is 340. Among them the minimum regret is with discount service.

The minimax regret approach dictates that we should provide discounted service.

c.

Expected value approach: determine the sum of product between probabilities and payoffs for each decision.

Full price = 0.7*1320 + 0.3*(-550) = 759

Discount = 0.7*980 + 0.3*440 = 818

The higher value is expected with discounted service as per the expected value method and that will be the optimal decision.

d.

Recalculating using the new probabilities,

Full price = 0.8*1320 + 0.2*(-550) = 946

Discount = 0.8*980 + 0.2*440 = 872

The optimal decision now is to offer full priced service.

e.

Let the probability of strong demand be X. We have already seen that X as an equilibrium point falls between 0.7 and 0.8. Thus

X*1320 + (1-X)*(-550) = X*980 + (1-X)*440

1320X – 980X = (1-X)*(440 + 550)

340X = 990 – 990X

X = 990/(990+340) = 0.744

The equilibrium point is 0.744 probability for the strong demand.

Discounted price service is the best option if the strong demand is less than or equal to 0.744. For values greater than this, the full price is the right choice