Question

3.

A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The profit from each purchase will be determined by whether the company succeeds in getting a government military full contract, partial contract or no contract. The profit from each purchase associated with each contract outcome is shown in the following payoff table:

Purchase         Full Contract      Partial Contract     No Contract

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Drill press        $26,000    $34,000              $10,000

Lathe                 34,000                   24,000                18,000

Grinder               54,000                   22,000                20,000

4. For the problem given in Question 3, assume that the probability of a full contract is 0.5, the probability of a partial contract is 0.4, and the probability of no contract is 0.1.

(a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?

(b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?

(c) Calculate and interpret the value of perfect information.

Answer 1

For the problem given in Question 3, assume that the probability of a full contract is 0.5, the probability of a partial contract is 0.4, and the probability of no contract is 0.1.

(a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?

Expected value of Drill press = 0.5*26000 + 0.4*34000 + 0.1*10000 = 27600

Expected value of Lathe = 0.5*34000 + 0.4*24000 + 0.1*18000 = 28400

Expected value of Grinder = 0.5*54000 + 0.4*22000 + 0.1*20000 = 37800

Using expected value criterion, recommended option is Grinder

(b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?

Opportunity loss = Regret = |Best payoff - payoff received|

Below is the opportunity loss table

Expected value of opportunity loss of Drill press = 0.5*28000 + 0.4*0 + 0.1*10000 = 15000

Expected value of opportunity loss of Lathe = 0.5*20000 + 0.4*10000 + 0.1*2000 = 14200

Expected value of opportunity loss of Grinder = 0.5*0 + 0.4*12000 + 0.1*0 = 4800

Using expected opportunity loss criterion, recommended option is Grinder (minimum opportunity loss)

(c) Calculate and interpret the value of perfect information.

EVPI = expected value with perfect information - Expected value without perfect information

= (0.5*54000+0.4*34000+0.1*20000) - 37800 = 4800

EVPI = Min expected opportunity loss = 4800

EVPI denotes minimum opportunity loss value