Question

A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff (profit in thousands of dollars) table based on whether business will be brisk, medium, or slow.

                                                                                

                                           Business Level

Decision               Brisk           Medium                Slow

────────────────────────────────────────

Buy                          90                 50                       30                                               

Rent                         50                 60                       45                                               

Lease                       40                55                       50

(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) Calculate the Hurwicz’s value for each decision if α = 0.6. What is the best decision using the Hurwicz’s criterion? What is the payoff for it?

also for this problem,,  assume that the probability of brisk business level is 0.4, the probability of medium business level is 0.4 and the probability of slow business level is 0.2.

(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 for this problem.

Answer 1

a)

Maximum of the max payoff is 90 which belongs to "Buy" Decision hence it is the best decision according to maximax criterion

Payoff for it is 90 (in thousands of dollars)

b)

Maximum of the min payoff is 45 which belongs to "Rent" Decision hence it is the best decision according to maximin

criterion

Payoff for it is 45 (in thousands of dollars)

c)

Best of the average decision is 56.66666667 which belongs to "Buy" Decision hence it is the best decision according to equal likelihood criterion

Average Payoff for it is 56.66666667 (in thousands of dollars)

d)

Minimum of the maximum regret is 20 which belongs to "Buy" Decision hence it is the best decision according to Minimax regret criterion

Regret for it is 20 (in thousands of dollars)

Formula

e)

According to Hurwicz's criterion, payoff = alpha*Max payoff+(1-alpha)*Min payoff

According to Hurwicz's criterion, payoff of "Buy" Decision = 0.6*90+(1-0.6)*30 = 66
According to Hurwicz's criterion, payoff of "Rent" Decision = 0.6*60+(1-0.6)*45 = 54
According to Hurwicz's criterion, payoff of "Lease" Decision = 0.6*55+(1-0.6)*40 = 49

Best decision is "Buy" and payoff for it is 66

a)

So, according to expected value approach best decision is "Buy" as this decision has highest expected payoff

Formula

b)

using the expected opportunity loss criterion, best decision is "Buy" as this decision has lowest expected opportunity loss

Formula

c)

value of perfect information = expected value without perfect information-expected value without perfect information

=90*0.4+60*0.4+50*0.2-62

= 8