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Published byAllyson Burnsworth Modified about 1 year ago

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PLANNING UNDER UNCERTAINTY REGRET THEORY

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

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

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MINIMAX REGRET ANALYSIS Motivating Example Calculate regret: find maximum regret A …regret = low market C …regret = low market D …regret = high market B …regret = medium market MINIMAX B In general, gives conservative decision but not pessimistic.

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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)

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

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

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

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MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory

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MINIMAX REGRET ANALYSIS Limitations on Regret Theory May select different preferences if one of the alternatives was excluded or a new alternative is added. $ $1050 = 50 $100 - $150 = 50 s1s1 s2s2 s3s3 Max. Regret A10005 B C D 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.

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CONCLUSION Minimizing the average regret instead of minimizing the maximum. Measure relative regret instead of absolute regret: = = 50 versus instead of: s1s1 s2s2 s3s3 Max. Regret A10005 B C D Suggested improvements to minimax-regret criterion: Upper Regret Avrg. Regret Minimizing the upper regret average instead of the maximum only.

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