The following decision evaluation matrix gives the expected

The following decision evaluation matrix gives the expected savings in maintenance costs (in thousands of dollars) for three policies of preventative maintenance and three levels of operation of equipment. Given the probabilities of each level of operation, P1=0.3, P2=0.25, and P=0.45, determine the best policy based on the most probable future criteria. Also, determine the best policy under uncertainty, using the Laplace ryke, the Maximax rule, and the Hurwicz rule with alpha=0.2 (#43, pg 203)

L1 L2 L3

M1 10 20 30

M2 22 26 26

M3 40 30 15

Solution

Expected savings

E(M1) =10*0.3+20*0.25+30*0.45 =21.5

E(M2) =22*0.3+26*0.25+26*0.45 =24.8

E(M3)=40*0.3+30*0.25+15*0.45 =26.25

the best policy based on the most probable future criteria is M3

Laplace ryke method

              L1    L2 L3                     Expected Payoff

M1 10 20 30                        (10+20+30)/3 =20

M2 22 26 26                      (22+26+26)/3 =24.67

M3 40 30 15                        (40+30+15)/3 =28.33

M3 is best on this basis

Maximax rule

   L1 L2 L3             maximum of row

M1 10 20 30                    30

M2 22 26 26                    26

M3 40 30 15                    40

M3 has payoff 40 s

Hurwicz rule

L1 L2 L3      max of row              min of row           P=0.2*Max +0.8*Min

M1 10 20 30       30                                10                         6+8 =14

M2 22 26 26       26                                22                        22.8

M3 40 30 15       40                                15                        20

M2 is best policy by this rule