Problem 13-09 (Algorithmic) Myrtle Air Express decided to offer direct service f
ID: 333761 • Letter: P
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 o the contribution to profit or each ype o service based upon two possible evels of deman for service to e Beach: strong and weak The Ollo in tables o e estimated quarterly profits (in thousands of dollars) Service Full price Discount Demand for service Strong Weak $1200$430 $920 $400 a. 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 outcomesExplanation / Answer
A. What is the decision to be made, what is the chance event, and what is the consequence for this problem?
Management of Myrtle Air Express has to make decision regarding air service to be provided between Cleveland and Myrtle Island. The demand of air service in future can be strong or weak. Whichever alternative is selected, depending on future demand condition the quarterly profit will change.
How many decision alternatives are there?
Management has two decision alternatives:
How many outcomes are there for the chance event?
There are two outcomes for demand of Air service:
A.
Demand for Service
Maximum payoff
Minimum payoff
Alternatives
Service
Strong (S1)
Weak (S2)
A1
Full price
$1,200.00
-$430.00
$1,200.00
-$430.00
A2
Discount
$920.00
$400.00
$920.00
$400.00
Optimistic Approach:
Under this approach decision maker will not lose an opportunity to achieve largest possible profit or payoff among the alternatives. Thus, Management should use Maximax Criterion to evaluate alternatives. For this, the decision maker takes the maximum payoff under each alternative and then selects the best of those maximum payoffs.
Maximum payoffs of Alternatives A1 and A2 are $1200 and $920respectively. Maximum payoff among the alternative’s maximum payoff is $1200 for the Full-price service alternative.
According to Optimistic Approach alternative of Full price service should be selected.
Pessimistic Approach:
Under this approach decision maker will evaluates the decision alternatives, in terms of the worst payoff that can occur or the alternative that provides the best of all possible minimum payoffs of each alternative selected. Thus, management should use Maximin criterion to evaluate alternatives. Under maximin principle, take the smallest payoff under each alternative and then select the largest of those minimum payoffs.
Minimum payoffs of alternatives are -$430 and $400 respectively.
Maximum payoff among the alternative’s minimum payoff is $400 for the alternative of discount service.
According to Conservative Approach the alternative of Discount service should be selected.
c. Minimax regret criterion:
First obtain opportunity/regret payoff table: Regret payoff is obtain by subtracting each state of nature payoff from best (minimum payoff) of its state of nature. As follows:
Demand for Service
Maximum Regret
Alternatives
Service
Strong (S1)
Weak (S2)
A1
Full price
1200 - 1200
= 0
400 – (-430) = 830
830
A2
Discount
1200 – 920 = 280
400 – 400 = 0
280
Select best (minimum) payoff among the state of nature or column and subtract it from each payoff of its state of nature or column. Then obtain worst (maximum) regret payoff for each alternative and chose best (minimum) alternative that minimizes these regrets. Maximin regret value is $280 for alternative of Discount service.
Minimax Regret Approach = discount service
B. 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.
Demand for Service
Expected Payoff
Conditional payoff
Service
Strong
Weak
Full price
$1,200.00
-$430.00
0.7 x 1200
= 840
0.3 x (-430)
= -129
840 + (-129)
= 711
Discount
$920.00
$400.00
0.7 x 920
= 644
0.3 x 400
= 120
644 + 120
= 764
Probabilities
0.7
0.3
Maximum Expected value is $764 for the alternative Discount service.
Optimal Decision = discount service
D.
Demand for Service
Expected Payoff
Conditional payoff
Service
Strong
Weak
Full price
$1,200.00
-$430.00
960
-86
874
Discount
$920.00
$400.00
736
80
816
Probabilities
0.8
0.2
Maximum Expected value is $874 for the alternative Full-price service.
Optimal Decision = FULL-PRICE service
Demand for Service
Maximum payoff
Minimum payoff
Alternatives
Service
Strong (S1)
Weak (S2)
A1
Full price
$1,200.00
-$430.00
$1,200.00
-$430.00
A2
Discount
$920.00
$400.00
$920.00
$400.00