The following is a payoff table giving profits for various situations States of

Question

The following is a payoff table giving profits for various situations States of Nature Alternatives Alternative 1 1 Alternative 2 Alternative 3 20 Do Nothing 100 120 180 120 140 120 100 50 The probabilities for states of nature A, B, and C are 0.3,0.5, and 0.2, respectively a. If the manager of this company is pessimistic, what alternative should he select? b. If the manager of this company is optimistic, what alternative should he select? e. If the coefficient of realism (a) is 0.80, what alternative should be selected (based on the criterion of realism)? d. If the criterion of the opportunity loss (Minimax Regret) is used, what alternative should e. Use the payoffs and the probabilities to calculate the expected monetary values (EMV). f. Calculate the expected value of perfect information (EVPT) (hint: You must calculate the g. Calculate the opportunity loss table and the expected opportunity loss (EOL). Based on be selected Based on the EMV, what alternative should the manager select? expected value with perfect information in order to determine the EVPI) EOL criterion, what alternative should be selected?

Explanation / Answer

a) we know the pessimistic(maximin):

To obtain this we 1st select minimum payoffs from each row,

so,

minimum payoff from 1st row:100

minimum payoff from 2st row:120

minimum payoff from 3st row:50

as this is best of worst approch so now we select the maximum among these minimum

i.e. pessimistic=maximin(max(100,120,50)=120

so we select the 2nd Alternative

b)we know the optimistic(maximax):

To obtain the optimistic 1st we select maximum payoff from each row

so,

maximum payoff from 1st row:180

maximum payoff from 2nd row:140

maximum payoff from 3rd row:200

as we know optimistic is best in best approch so,

optimistic=maximax(max(180,140,200)=200

so we select the 3rd alternative.

d)now we have to obtain the minimax regret:

for this we have to obtain regret=Best payoff(from ech column)-each payoff recived from that column

A B C MAX

A1 (200-100)=100 (140-120)=20 (180-180)=0 100

A2 (200-120)=80 (140-140)=0 (180-120)=60 80

A3 (200-200)=0 (140-100)=40 (180-50)=130 130

now we choose minimum from these maximum,

so, min(100,80,130)=80

this is corresponding to 2nd alternative.

so we will select 2nd alternative in this approch.

e)

To find EMV

we have given probabilities,

A B C

A1 100 120 180

A2 120 140 120

A3 200 100 50

prob. 0.3 0.5 0.2

now to obtain EMV:

0.3(100)+0.5(120)+0.2(180)=126

0.3(120)+0.5(140)+0.2(120)=130

0.3(200)+0.5(100)+0.2(50)=120

and the best EMV is 130

so we choose the 2nd alternative.

f)

Noe we calculate the EVPI

EVPI=(expected payoff with perfect information)-(expected value without perfect information)

expected value without perfect information=maximum EMV=130

to calculate expected payoff with perfect information , we choose the best payoff from each column as given below,

A B C

A1 100 120 180

A2 120 140 60

A3 200 100 50

prob. 0.3 0.5 0.2

best 200 140 180

Expected payoff with perfect information= 0.3(200)+0.5(140)+0.2(180)=166

so, EVPI=166-130=36

g)

EOL(Expected Opportunity Loss)

To calculate EOL the regret is ,

regret=bsrt payoff in perticuler state of natur-actual payoff which is recived

Regret table:

A B C

A1 (200-100)=100 (140-120)=20 (180-180)=0

A2 (200-120)=80 (140-140)=0 (180-120)=60

A3 (200-200)=0 (140-100)=40 (180-50)=130

prob 0.3 0.5 0.2

0.3(100)+0.5(20)+0.2(0)=40

0.3(80)+0.5(0)+0.2(60)=36

0.3(0)+0.5(40)+0.2(130)=46

we always choose the value with minimum EOL i.e. 36

so the maneger will choose the 2nd alternative.

Note that,

The min EOL Decision = Max EMV Decision.

EVPI=min EOL

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.