33) How does the Laplace criterion for decision making under uncertainty actually convert the situation to decision making under risk?

Using the Laplace criterion, we assume equal probability for each state of nature. Once we make this assignment of probability, the problem becomes an “under risk” scenario, i.e. one in which we know the probabilities.

38)

Laplace: scores are 70, 50 and 60 recommend A1.

Maximin: scores are 50, 20 and 30 recommend A1.

Maximax: scores are 80, 70 and 90 recommend A3.

Hurwicz, α = 0.75: scores are 72.5, 57.5 and 75.0 recommend A3.

39)

Maximin: mins of each row are 20, 20 and 10 equally recommend T1 and T2.

Maximax: maxs of each row are 35, 40 and 60 recommend T3.

Laplace: avgs of each row are 27.5, 32.5 and 31.25 recommend T2.

Minimax Regret: scores are 35, 30 and 30 equally recommend T2 and T3.

Hurwicz with α = 0.2: scores are 23, 24, 20 recommend T2.

Minimax Regret: scores are 35, 30 and 30 equally recommend T2 and T3.

Rules applied to the cost matrix will use minimization criteria, where as payoff matrix rules will use maximization criteria.

43) The following decision evaluation matrix gives the expected savings in maintenance costs (in thousands of dollars) for three policies of preventive maintenance and three levels of operation of equipment. Given the probabilities of each level of operation, P1 = 0.3, P2= 0.25, and P3=0.45, determine the best policy based on the most probable future criterion.

Also, determine the best policy under uncertainty, using the Laplace rule, the Maximax rule, and the Hurwicz rule with α = 0.2.

Based on the most probable future (L3), the best policy is M1.

Under uncertainty:

Laplace: 20, 24.67 and 28.33 recommend M3.

Maximax: 30, 26, 40 recommend M3.

Hurwicz α =0.2: 14, 22.8 and 20 recommend M2.