Question

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.

Question 3 Was:

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

__________________________________________________

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

Lathe                 34,000                   24,000                18,000

Grinder               54,000                   22,000                20,000

(a) What is the best decision using the maximax criterion? What is the payoff for it?

(b) What is the best decision using the maximin criterion? What is the payoff for it?

(c) Determine the average payoff value for each decision. What is the best decision using the equal likelihood criterion? What is the average payoff for it?

(d) Determine the regret table for this problem. What is the best decision using the minimax regret criterion? What is the regret for it?

(e) What is the best decision using the Hurwicz’s criterion if α = 0.8? What is the payoff for it?

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

Full Contract Partial Contract No contract Drill Press 28000 C) 10000 Lathe 20000 10000 Grinder C) 12000 C)

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

(a) What is the best decision using the maximax criterion? What is the payoff for it?

Maximax is the optimistic criterion and maximizes the maximum pay-offs

maximum payoffs under Drill press = 34000
maximum payoffs under Lathe = 34000
maximum payoffs under Grinder = 54000

Maximum of these maximum payoffs is 54000 and that is of Grinder (Ans)

(b) What is the best decision using the maximin criterion? What is the payoff for it?

Minimum payoffs under Drill press = 10000
Minimum payoffs under Lathe = 18000
Minimum payoffs under Grinder = 20000

Maximum of these Minimum payoffs is 20000 and that is of Grinder (Ans)