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UTILITY AND DECISION MAKING 579

5 Khan Corporation is considering three options for managing its data processing operation:
continuing with its own staff, hiring an outside vendor to do the managing (referred to as
outsourcing), or using a combination of its own staff and an outside vendor. The cost of the
operation depends on future demand. The annual cost of each option (in thousands of
euros) depends on demand as follows.

Demand

Staffing Options High Medium Low
Own staff 650 650 600
Outside vendor 900 600 300
Combination 800 650 500

a. If the demand probabilities are 0.2, 0.5 and 0.3, which decision alternative will mini-mize
the expected cost of the data processing operation? What is the expected annual cost
associated with that recommendation?
b. Construct a risk profile for the optimal decision in part (a). What is the probability of the
cost exceeding E700 000?
6 The following payoff table shows the profit for a decision problem with two states of nature
and two decision alternatives.

State of Nature
Decision Alternative s 1 s 2

d 1 10 1
d 2 4 3

a. Use graphical sensitivity analysis to determine the range of probabilities of state of nature
s 1 for which each of the decision alternatives has the largest expected value.
b. Suppose P(s 1 ) ¼ 0.2 and P(s 2 ) ¼ 0.8. What is the best decision using the expected
value approach?
c. Perform sensitivity analysis on the payoffs for decision alternative d 1 . Assume the
probabilities are as given in part (b) and find the range of payoffs under states of nature
s 1 and s 2 that will keep the solution found in part (b) optimal. Is the solution more
sensitive to the payoff under state of nature s 1 or s 2 ?
7 Scot Air Express decided to offer direct service from Edinburgh to Manchester. 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 Scot 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 Manchester: strong and weak. The following table shows the
estimated quarterly profits (in thousands of £).

Demand for Service
Service Strong Weak

Full price £960 £490
Discount £670 £320

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