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PLANNING UNDER UNCERTAINTY REGRET THEORY. MINIMAX REGRET ANALYSIS Motivating Example  Traditional way Maximize Average … select A  Optimistic decision.

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Presentation on theme: "PLANNING UNDER UNCERTAINTY REGRET THEORY. MINIMAX REGRET ANALYSIS Motivating Example  Traditional way Maximize Average … select A  Optimistic decision."— Presentation transcript:

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 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)

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

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

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

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

10 MINIMAX REGRET ANALYSIS Limitations on Regret Theory  May select different preferences if one of the alternatives was excluded or a new alternative is added. $1000 - $1050 = 50 $100 - $150 = 50 s1s1 s2s2 s3s3 Max. Regret A10005 B99954099 C0100200 D150850150  It is not necessary that equal differences in profit would always correspond to equal amounts of regret:  A small advantage in one scenario may lead to the loss of larger advantages in other scenarios.

11 CONCLUSION  Minimizing the average regret instead of minimizing the maximum.  Measure relative regret instead of absolute regret: 1050-1000 = 50150-100 = 50 versus instead of: s1s1 s2s2 s3s3 Max. Regret A10005 B99954099 C0100200 D150850150 Suggested improvements to minimax-regret criterion: Upper Regret 52.5 97 150 117.5 Avrg. Regret 35 78 100 78.3  Minimizing the upper regret average instead of the maximum only.


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