Understanding Minimax Regret Analysis: Theory and Application

1. PLANNING UNDER UNCERTAINTY REGRET THEORY

2. MINIMAX REGRET ANALYSIS Motivating Example • Traditional way Maximize Average…select A • Optimistic decision maker MaxiMax … select C • Pessimistic decision maker MaxiMin … select D

3. MINIMAX REGRET ANALYSIS • If chosen decision is the best  Zero regret • Nothing is better than the best  No negetive Regret

4. MINIMAX REGRET ANALYSIS Motivating Example • Calculate regret: find maximum regret • A … regret = 8 @ low market • C … regret = 9 @ low market • D … regret = 10 @ high market • B … regret = 7 @ medium market • MINIMAX B • In general, gives conservative decision but not pessimistic.

5. Two-Stage Model Optimal Profit Uncertainty Free Optimal Profit Here & Now (HN) Wait & See (WS) MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory

6. MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory where: subject to: , subject to: ,

7. where: subject to: , subject to: , MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory

8. MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory where: subject to: , subject to: ,

9. MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory

10. MINIMAX REGRET ANALYSIS Limitations on Regret Theory • It is not necessary that equal differences in profit would always correspond to equal amounts of regret: $1000 - $1050 = 50 $100 - $150 = 50 • A small advantage in one scenario may lead to the loss of larger advantages in other scenarios. • May select different preferences if one of the alternatives was excluded or a new alternative is added.

11. versus instead of: 1050-1000 = 50 150-100 = 50 versus CONCLUSION Suggested improvements to minimax-regret criterion: • Minimizing the average regret instead of minimizing the maximum. • Minimizing the upper regret average instead of the maximum only. • Measure relative regret instead of absolute regret: