A small building contractor has recently experienced two successive years in which work opportunities exceeded the firm's capacity. The contractor must now make a decision on capacity for next year. Estimated profits under each of the two possible states of nature are as shown in the table below. Which alternative should be selected if the decision criterion is:

 

a. Maximax?

b. Maximin?

c. Laplace?

d. Minimax regret?

NEXT YEAR'S DEMAND

Alternative                      Low                    High                     

Do nothing                     $50*                   $60

Expand                           20                      80

Subcontract                    40                      70

Answers:

(a). Maximax Criterion: Expand

(b). Maximin Criterion: Do nothing

(c). Laplace Criterion: Both Do nothing and Subcontract

(d). Minimax Regret Criterion: Subcontract

Step-by-step explanation

(a) Maximax Criterion

Step 1: Choose the best payoff for each alternative. 

Step 2: From the best payoff of each alternatives, choose the highest value. 

In using maximax criterion, Expansion should be selected.

(b) Maximin Criterion

Step 1: Choose the worst possible payoff for each alternative.

Step 2: From the worst payoff of each alternatives, choose the highest value.

In using maximin criterion, Do nothing should be selected.

(c) Laplace Criterion

Step 1:  Determine the average payoff for each alternative.

Step 2: Choose the alternative with the best or highest average.

In using laplace criterion, Both do nothing and subcontract should be selected since they have equal average value.

(d) Minimax regret criterion

Step 1: Determine the worst regret for each alternative.

Step 2: Choose the worst regret with the highest value.

Step 3: Choose the alternative with the best worst or the lowest value.

In using minimax regret criterion, subcontract should be selected.