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Decisions-optimistic, conservative, minimax regret

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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).

(see chart in attached file)

a. If nothing is known about the probabilities of the chance outcomes, determine the recommended decision using the optimistic, conservative, and minimax regret approaches.

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.

c. 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?
d. Use sensitivity analysis to determine the range of demand probabilities for which each of the decision alternatives has the largest expected value.

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The solution recommends decisions under uncertainty using optimistic, conservative, minimax regret criteria and when probabilities are known using expected value.

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Management Decisions (Stats problems 3, 4): optimistic strategy, conservative strategy, utility,

(See attached file for full problem description)

3. The table shows both prospective profits and losses for a company, depending on what decision is made and what state of nature occurs. Use the information to determine what the company should do.

s1 s2 s3
d1 30 80 -30
d2 100 30 -40
d3 -80 -10 120
d4 20 20 20

a. if an optimistic strategy is used.
b. if a conservative strategy is used.
c. if minimax regret is the strategy.

4. Dollar Department Stores has the opportunity of acquiring either 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores, and its president estimates P(s1) = .4, P(s2) = .3, P(s3) = .1, and P(s4) = .2. The utility has also been estimated. Given the payoffs (in $1,000,000's) and utility values below, which decision should Dollar make?

Payoff Table

State Of The Economy
Over The Next 5 Years
Decision s1 s2 s3 s4

d1 -- buy 10 leases 10 5 0 -20
d2 -- buy 5 leases 5 0 -1 -10
d3 -- buy 3 leases 2 1 0 - 1
d4 -- do not buy 0 0 0 0

Utility Table

Payoff (in $1,000,000's) +10 +5 +2 +1 0 -1 -10 -20
Utility +10 +5 +2 +1 0 -1 -20 -50

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