- 15 02/27/2018 32 States of Nature Weather related cost per hour Alternatives C
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- 15 02/27/2018 32 States of Nature Weather related cost per hour Alternatives Cold cost/day |Mild cost/day |Warm cost/day Machine 1 Machine 2 Machine 3 Machine 4 Machine 5 $50 $45 $40 $60 $45 $40 $42 $35 $25 $40 $45 $47 $54 $48 $45 A plant manager considers the operational cost per hour of five machine altematives. The cost per hour is sens cold, mild, and warm. The following table represents the operations cost per hour for each altemative-state of nature combination. itive to three potential weather conditions: weathe a. Using the optimistic criterion, which altemative is best? b. Using the pessimistic criterion, which altemative is best? c. Using the equally likely criterion, which altemative is best? d. What altemative is best, using EMV. (30 cold, 50 mild, 20 warm) e. Assuming the same percentages as d above, what is the EVP1?Explanation / Answer
(a) Using Optimistic (Maximax) criterion, decision maker selects the alternative whose Maximum payoff is the Maximum of the Maximum payoffs of all the alternatives.
Maximum payoff of Machine 1 = MAX(50,40,45) = 50
Maximum payoff of Machine 2 = MAX(45,42,47) = 47
Maximum payoff of Machine 3 = MAX(40,35,54) = 54
Maximum payoff of Machine 4 = MAX(60,25,48) = 60
Maximum payoff of Machine 5 = MAX(45,40,45) = 45
Maximum of the Maximum payoffs of all the alternatives = MAX(50,47,54,60,45) = 60. It is of Machine 4. Therefore, the best alternative is Machine 4.
(b) Using Pessimistic (Maximin) criterion, decision maker selects the alternative whose Minimum payoff is the Maximum of the Minimum payoffs of all the alternatives.
Minimum payoff of Machine 1 = MIN(50,40,45) = 40
Minimum payoff of Machine 2 = MIN(45,42,47) = 42
Minimum payoff of Machine 3 = MIN(40,35,54) = 35
Minimum payoff of Machine 4 = MIN(60,25,48) = 25
Minimum payoff of Machine 5 = MIN(45,40,45) = 40
Maximum of the Minimum payoffs of all the alternatives = MAX(40,42,35,25,40) = 42. It is of Machine 2. Therefore, the best alternative is Machine 2.
(c) Using Equally likely (Laplace) criterion, decision maker selects the alternative whose Average payoff is the Maximum of the Average payoffs of all the alternatives.
Average payoff of Machine 1 = AVERAGE(50,40,45) = 45.00
Average payoff of Machine 2 = AVERAGE(45,42,47) = 44.67
Average payoff of Machine 3 = AVERAGE(40,35,54) = 43.00
Average payoff of Machine 4 = AVERAGE(60,25,48) = 44.33
Average payoff of Machine 5 = AVERAGE(45,40,45) = 43.33
Maximum of the Average payoffs of all the alternatives = MAX(45,44.67,43,44.33,43.33) = 44.67. It is of Machine 2. Therefore, the best alternative is Machine 2.
(d) Using EMV (Expected Monetary Value) criterion, decision maker selects the alternative whose EMV is the Maximum of the EMVs of all the alternatives.
EMV of Machine 1 = (0.3*50+0.5*40+0.2*45) = 44.00
EMV of Machine 2 = (0.3*45+0.5*42+0.2*47) = 43.90
EMV of Machine 3 = (0.3*40+0.5*35+0.2*54) = 40.30
EMV of Machine 4 = (0.3*60+0.5*25+0.2*48) = 40.10
EMV of Machine 5 = (0.3*45+0.5*40+0.2*45) = 42.50
Maximum of the EMVs of all the alternatives = MAX(44,43.9,40.3,40.1,42.5) = 44. It is of Machine 1. Therefore, the best alternative is Machine 1.
(e) Expected Value with Perfect Information (EVwPI) = 0.3*MAX(50,45,40,60,45)+0.5*MAX(40,42,35,25,40)+0.2*MAX(45,47,54,48,45) = 49.80
EVw/oPI = Max EMV = 44
EVPI = EVwPI - EVw/oPI = 49.8-44 = 5.8
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