Question

The following payoff tables represents COSTS. D1 Si 10 22 15 S2 16 18 15 S3 25 8 12 D2 D3 1) Which decision alternative should be chosen, if the decision maker uses the optimistic approach? Choose 2) Which decision alternative should be chosen, if the decision maker uses the mini-max regret approach? Choose 3) Which decision alternative should be chosen, if the decision maker uses the equal-likelihood approach? Choose 4) If the decision maker chooses D1, what is the most regret possible? Max regret = 5) If P(S1) = 25; P(S2) = 5; P(S3) = 25, then the expected value of perfect information is: EVPI =

Answer 1

Given that Տ, Di « Դո Է ԱՐԱՄ Մ Մ Մ Մ Մ \2 I probability 10.25 l os I 0.25] of perfect information: s) Expected value (EVPI ) ) Մ Մ Մ c) = 'co,5 : ծ :25 30 ) * : ) 6 + o : :Տ( | : 2 S + 8 + (-S Tercoid = 13 | b) Ev t } ) = 9: 1-568.2) + 6: 6. x 2 + 6` 2-5 | : S S + 9 + 2 8 ||Ev c »)- 16 5] +0.25(12) .ch Ev (D3) = 0.25(15) tonslis) - :7) + 7 + 3 \E (P ) = 14 ] REDMI NOTE 6 PRO MI DUAL CAMERA Մ Ն 7 / 1 Ն Ն & Ն Ն Ն Ա Ն . . : Therefore Decision chooge : Di . E V = 13 .

so EVPI = I EV WPI - Ev wo PI ) - 112 - 131 l-11-1 where EVPI = 0.25 (1) +0.5C15) + 0.2508) -2.5 +7.5t 2 - 12 is optimistic Approach .. si DI | 10 t sz | 16 2222222222nooooooooo 1 53 25 8 12 Best 10 8 1 12 K Best. 15 is choose :- D2. 2) Minimax Regret approach. S2 REDMI NOTE 6 PRO MI DUAL CAMERA

5 95-8 -176 mun 010-100 16 16-151 12 9 18 -10 8-9 : 3 = 0 C ob 15-15-O 12-8 - 4 Therefore Regret Table Salsa Maximum o 1117 Dz 12 13 10 12 Do stolis רון ו\ - Minimum mini-max regret decision Therefore, the choose Da JUUSTUTIST JET 50 tot luuu66wwroo 3) Equal - likelihood apprach. Average si sa tot 16+2 17 10 16 25 22 +18+8 = 16 REDNOTE 6 PRO MIDUAL CAMERA 22 115715112=14 K

approach s. y Therefore, the equal - likelihood choose → Dz 4) Most Regret possible: It the decision maker chooses Do, then max regret - 17 (from Regret table ) Result:- proptimi is optimistic approach = choose = D2 2) Mini-Max Regret approach choose. = D3 a) equal likelihood approach choose -> D3 4) Max regret > 17 REDMI NOTE 6 PRO MI DUAL CAMERA $ > EV PI - I