[#2] Decision Under Uncertainty | Minimax Regret criterion | Hurwicz criterion | by kauserwise

Introduction

This tutorial provides a step-by-step guide on decision-making under uncertainty, focusing on the Minimax Regret and Hurwicz criteria. These concepts are essential in operations research and help decision-makers evaluate their options when faced with uncertain outcomes.

Step 1: Understanding the Minimax Regret Criterion

The Minimax Regret criterion, also known as the Savage criterion, is used to minimize the maximum regret a decision-maker might feel after making a choice. Follow these steps to apply this criterion:

1. Identify Options: List all decision alternatives available.
2. Determine States of Nature: Identify different possible outcomes or states that could occur.
3. Construct a Payoff Table: Create a table that outlines the payoffs for each option under each state of nature.
4. Calculate Regret:
   • For each state, find the maximum payoff.
   • Subtract the payoff of each option from this maximum to find the regret for that option.
5. Identify Maximum Regret: For each option, determine the maximum regret value from the regret calculations.
6. Choose the Best Option: Select the option with the lowest maximum regret.

Practical Tip

Be careful to accurately identify the maximum payoffs to prevent miscalculating regrets.

Step 2: Applying the Hurwicz Criterion

The Hurwicz criterion, or criterion of realism, combines optimism and pessimism in decision-making. Here’s how to apply it:

1. List Alternatives and States: Just like in the previous step, identify all your options and the potential outcomes.
2. Create a Payoff Table: Similar to the Minimax Regret method, construct a table with payoffs for each option against each state of nature.
3. Determine Coefficients: Decide on a coefficient of optimism (α) which ranges from 0 to 1. A higher value indicates more optimism.
4. Calculate Weighted Payoffs:
   • For each option, calculate:
     • Optimistic payoff (highest payoff in that row)
     • Pessimistic payoff (lowest payoff in that row)
   • Combine them using the formula:
     • Weighted Payoff = (α * Optimistic Payoff) + ((1 - α) * Pessimistic Payoff)
5. Choose the Best Option: Select the option with the highest weighted payoff.

Common Pitfall

Choose your coefficient of optimism wisely. An extreme value can lead to biased decision-making.

Step 3: Real-World Applications

Both the Minimax Regret and Hurwicz criteria can be applied in various fields such as:

• Business strategy development
• Financial investments
• Project management and resource allocation
• Risk assessment in engineering projects

Conclusion

In this tutorial, we've explored the Minimax Regret and Hurwicz criteria for decision-making under uncertainty. These methods provide structured approaches to evaluate options when outcomes are unpredictable. By following the steps outlined, you can make more informed decisions in both personal and professional contexts. As a next step, consider applying these criteria to a decision you are currently facing to see how they can aid your evaluation process.