Given is a decision payoff table and a Sub Decision Payoff Table. Use Minimax Re
ID: 361944 • Letter: G
Question
Given is a decision payoff table and a Sub Decision Payoff Table. Use Minimax Regret as an evaluation criterion to evaluate alternatives.
Future Demand
Alternatives
Low
Moderate
High
Small Facility
17
12
13
Medium Facility
12
22
21
Large Facility
5
7
15
Alternatives
Worst Regrets
Small Facility
?
Medium Facility
?
Large Facility
?
a) The worst regrets for alternative Small Facility is
b) The worst regrets for alternative Medium Facility is
c) The worst regrets for alternative Large Facility is
d) The best course of action or decision by using Minimax Regret is to select facility
Future Demand
Alternatives
Low
Moderate
High
Small Facility
17
12
13
Medium Facility
12
22
21
Large Facility
5
7
15
Explanation / Answer
The Minimax approach is basically an approach which minimises the maximum regret you can have in any given situation. A regret is basically best payoff - payoff actually received.
In the question, we are given a payoff table which I will put forth below
Future Demand
Alternatives
Low
Moderate
High
Small Facility
17
12
13
Medium Facility
12
22
21
Large Facility
5
7
15
The items on the first column are the various alternatives
The headers which give us the demand (low, medium and high) are the different states or situations the decision maker can be in.
To calculate the regret, go column wise, and subtract the cell content from the max of the column (vertically)
Future Demand
Alternatives
Low
Moderate
High
Small Facility
17 - 17= 0
22 - 12 = 10
21 - 13 = 8
Medium Facility
17-12 = 5
22 - 22 = 0
21 - 21 = 0
Large Facility
17 - 5 = 12
22 - 7 = 15
21 - 15 = 6
The new regret table is
Future Demand
Alternatives
Low
Moderate
High
Small Facility
0
10
8
Medium Facility
5
0
0
Large Facility
12
15
6
The worst regret is given by the maximum of each row. Hence,
Small Facility: worst regret is 10
Medium Facility: worst regret is 5
Large Facility: worst regret is 15
Now, by minimax method, the minimum of all these regrets is 5, which corresponds to medium facility. Hence, the best course of action is to select the medium facility.
Future Demand
Alternatives
Low
Moderate
High
Small Facility
17
12
13
Medium Facility
12
22
21
Large Facility
5
7
15
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