Model Answer
0 min readIntroduction
In the realm of management and decision science, organizations frequently encounter situations where the outcome of a decision is uncertain, dependent on future events known as ‘states of nature’. Decision-making under uncertainty necessitates employing specific criteria to guide the selection of the most appropriate course of action. Several such criteria exist, each reflecting a different attitude towards risk. This question requires the application of three such criteria – Maximax, Maximin, and Hurwicz – to a given payoff table to determine the optimal alternative. These techniques are fundamental to rational decision-making in complex environments.
Understanding the Decision Criteria
Before applying the criteria, let's define each one:
- Maximax Criterion (Optimistic Approach): This criterion assumes the decision-maker is optimistic and selects the alternative that offers the highest possible payoff, assuming the best possible state of nature occurs.
- Maximin Criterion (Pessimistic Approach): This criterion assumes the decision-maker is pessimistic and selects the alternative that offers the highest of the worst possible payoffs. It focuses on minimizing potential losses.
- Hurwicz's Criterion (Compromise Approach): This criterion represents a balance between optimism and pessimism. It assigns a weight (degree of optimism, α) to the best possible payoff and (1-α) to the worst possible payoff for each alternative. The weighted average is then calculated, and the alternative with the highest weighted average is selected.
Applying the Criteria to the Payoff Table
The given payoff table is:
| States of Nature | Alternatives A1 | Alternatives A2 | Alternatives A3 |
|---|---|---|---|
| E1 | 190 | 186 | 182 |
| E2 | 164 | 162 | 166 |
| E3 | 142 | 144 | 174 |
(A) Maximax Criterion
Identify the maximum payoff for each alternative:
- A1: Max payoff = 190 (under E1)
- A2: Max payoff = 186 (under E1)
- A3: Max payoff = 174 (under E3)
The alternative with the highest maximum payoff is A1 (190). Therefore, A1 is selected under the Maximax criterion.
(B) Maximin Criterion
Identify the minimum payoff for each alternative:
- A1: Min payoff = 142 (under E3)
- A2: Min payoff = 144 (under E3)
- A3: Min payoff = 166 (under E2)
The alternative with the highest minimum payoff is A3 (166). Therefore, A3 is selected under the Maximin criterion.
(C) Hurwicz's Criterion
Given the degree of optimism (α) = 0.7, the degree of pessimism is (1-α) = 0.3.
Calculate the weighted average for each alternative:
- A1: (0.7 * 190) + (0.3 * 142) = 133 + 42.6 = 175.6
- A2: (0.7 * 186) + (0.3 * 144) = 130.2 + 43.2 = 173.4
- A3: (0.7 * 174) + (0.3 * 166) = 121.8 + 49.8 = 171.6
The alternative with the highest weighted average is A1 (175.6). Therefore, A1 is selected under Hurwicz's criterion.
Conclusion
In conclusion, the application of different decision criteria yields varying results. The Maximax criterion, reflecting optimism, selected alternative A1. The Maximin criterion, embodying pessimism, favored alternative A3. Hurwicz’s criterion, with a degree of optimism of 0.7, also selected A1. This demonstrates that the choice of criterion significantly impacts the decision, reflecting the decision-maker’s risk appetite and beliefs about the future. Understanding these criteria is crucial for effective decision-making in uncertain environments.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.