Question 5: A plant manager considers the operational cost per hour of five machine alternatives. The cost per hour is sensitive to three potential weather conditions: cold, mild, and warm. The following table represents the operations cost per hour for each alternative-state of nature combination: States of Nature Weather-related cost per hour Mild cost/day Alternatives EMV Cold cost/day $42 $45 $40 Warm cost/day $45 $47 $54 $48 $45 Machine 1 Machine 2 Machine 3 $40 $42 $35 Machine 4 Machine 5 $60 $45 0.3 $30 $40 0.5 0,2 Assume that for a randomly selected day, there is a 30% probability of cold weather, 50% probability of mild weather, and 20% probability of warm weather. What is the EVPI?

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Question 5: A plant manager considers the operational cost per hour of five machine alternatives. The cost per hour
is sensitive to three potential weather conditions: cold, mild, and warm. The following table represents
the operations cost per hour for each alternative-state of nature combination:
States of Nature
Weather-related cost per hour
Mild cost/day
$40
$42
$35
Alternatives
EMV
Machine 1
Machine 2
Machine 3
Cold cost/day
$42
$45
$40
Warm cost/day
$45
$47
$54
Machine 4
$60
$45
0.3
$30
$40
0.5
$48
$45
Machine 5
0.2
Assume that for a randomly selected day, there is a 30% probability of cold weather, 50% probability of mild weather, and 20% probability of warm weather. What is the EVPI?
Transcribed Image Text:Question 5: A plant manager considers the operational cost per hour of five machine alternatives. The cost per hour is sensitive to three potential weather conditions: cold, mild, and warm. The following table represents the operations cost per hour for each alternative-state of nature combination: States of Nature Weather-related cost per hour Mild cost/day $40 $42 $35 Alternatives EMV Machine 1 Machine 2 Machine 3 Cold cost/day $42 $45 $40 Warm cost/day $45 $47 $54 Machine 4 $60 $45 0.3 $30 $40 0.5 $48 $45 Machine 5 0.2 Assume that for a randomly selected day, there is a 30% probability of cold weather, 50% probability of mild weather, and 20% probability of warm weather. What is the EVPI?
Expert Solution
Step 1

The mentioned problem belongs to decision-making with probabilities category. EMV denotes the expected monetary value, which is further can be defined as the weighted average cost per day where the weights assigned to cost are their corresponding probabilities.

For Machine 1, 

EMV can be given as, EMV=(Cost per day )·P(cold weather)+(Cost per day )·P(mild weather)+(Cost per day )·P(warm weather).

Use the values mentioned in the table and substitute these values in the above mentioned formula for EMV for machine 1.

                                                                  EMV=(42 )·(0.3)+(40 )·(0.5)+(45 )·(0.2)=12.6+20+9=41.6

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