PLANNING UNDER UNCERTAINTY REGRET THEORY

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

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

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.

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

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

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

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

MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory

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 s1 s2 s3 Max. Regret A 100 5 B 99 95 40 C 200 D 150 85 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.

Suggested improvements to minimax-regret criterion: CONCLUSION Suggested improvements to minimax-regret criterion: Minimizing the average regret instead of minimizing the maximum. s1 s2 s3 Max. Regret A 100 5 B 99 95 40 C 200 D 150 85 Avrg. Regret 35 78 100 78.3 Upper Regret 52.5 97 150 117.5 Minimizing the upper regret average instead of the maximum only. Measure relative regret instead of absolute regret: 1050-1000 = 50 150-100 = 50 versus instead of: