MGT613 ASSIGNMENT 1 SOLUTION 2023 | MGT613 ASSIGNMENT 1 FALL 2023 | MGT613 ASSIGNMENT 1 2023 | PRODUCTION/OPERATIONS MANAGEMENT | VuTech
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Question:
Decision theory is the best approach in decision making when the outcomes linked with different alternatives are not certain. The Pay-off table makes decisions easy in this uncertain situation for the operations managers. Managers use this approach in decision making related to inventory, location and capacity-based decision for their production processes.
The following table depicts the expected payoffs related to different alternatives for each possible state of nature:
Table: Possible Future Demand
|
Possible Future Demand (in thousand) |
|
|||
|
Alternatives |
Low |
Moderate |
|
High |
|
Small Facility |
45,000 |
45,000 |
|
45,000 |
|
Medium Facility |
36,000 |
51,000 |
|
51,000 |
|
Large Facility |
(8000) |
12,000 |
|
63,000 |
Considering the given payoff table, determine which alternative would be chosen under each of the following strategies?
- Maximin (Marks: 3)
- Maximax (Marks: 3)
- Laplace (Marks: 4)
Solution:
1. Maximin:
Maximin is a conservative decision-making strategy where the decision-maker selects the alternative that maximizes the minimum payoff for each alternative.
For each alternative, find the minimum payoff and then select the alternative with the maximum of these minimum payoffs.
Small Facility: Minimum payoff = 45,000
Medium Facility: Minimum payoff = 36,000
Large Facility: Minimum payoff = (8000)
The maximin values are as follows:
Small Facility: 45,000
Medium Facility: 36,000
Large Facility: (8000)
Decision:
The maximin strategy would choose the Large Facility because it has the maximum minimum payoff.
2. Maximax:
Maximax is an optimistic decision-making strategy where the decision-maker selects the alternative that maximizes the maximum payoff for each alternative.
For each alternative, find the maximum payoff and then select the alternative with the maximum of these maximum payoffs.
Small Facility: Maximum payoff = 45,000
Medium Facility: Maximum payoff = 51,000
Large Facility: Maximum payoff = 63,000
The maximax values are as follows:
Small Facility: 45,000
Medium Facility: 51,000
Large Facility: 63,000
Decision:
The maximax strategy would choose the Large Facility because it has the maximum payoff.
3. Laplace:
Laplace is a decision-making strategy where the decision-maker assigns equal probabilities to all possible states of nature and calculates the expected payoff for each alternative.
The expected payoff for each alternative is calculated as the average of the payoffs for each state of nature.
Small Facility: (45,000 + 45,000 + 45,000) / 3 = 45,000
Medium Facility: (36,000 + 51,000 + 51,000) / 3 = 46,000
Large Facility: ((-8,000) + 12,000 + 63,000) / 3 = 22,333.33
The Laplace values are as follows:
Small Facility: 45,000
Medium Facility: 46,000
Large Facility: 22,333.33
Decision:
The Laplace strategy would choose the Medium Facility because it has the highest expected payoff.
OR
|
Strategy |
Small Facility |
Medium Facility |
Large Facility |
|
Maximin |
45,000 |
36,000 |
-8,000 |
|
Maximax |
45,000 |
51,000 |
63,000 |
|
Laplace |
45,000 |
46,000 |
22,333.33 |
Decision:
Maximin: Choose the Large Facility.
Maximax: Choose the Large Facility.
Laplace: Choose the Medium Facility.