PLANNING UNDER UNCERTAINTY REGRET THEORY by Ahmed Aseeri

PLANNING UNDER UNCERTAINTY REGRET THEORY by Ahmed Aseeri 15 September 2020

MINIMAX REGRET ANALYSIS Ø It’s a feeling… Ø… measurable.

MINIMAX REGRET ANALYSIS Ø If chosen decision is the best Zero regret ØNothing is better than the best No negetive Regret

MINIMAX REGRET ANALYSIS Motivating Example ØTraditional way Maximize Average…select A ØOptimistic decision maker Maxi. Max … select C ØPessimistic decision maker Maxi. Mmin … select D

MINIMAX REGRET ANALYSIS Motivating Example ØCalculate regret: find maximum regret ØA … regret = 8 @ low market ØC … regret = 9 @ low market ØD … regret = 10 @ high market ØB … regret = 7 @ medium market ØMINIMAX B ØIn general, gives conservative decision but not pessimistic.

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

MINIMAX REGRET ANALYSIS Two-Stage Stochastic Programming Using Regret Theory

MINIMAX REGRET ANALYSIS Limitations on Regret Theory ØIt is not necessary that equal differences in profit would always correspond to equal amounts of regret: ØA small advantage in one scenario may lead to the loss of larger advantages in other scenarios. ØMay select different preferences if one of the alternatives was excluded or a new alternative is added. $1000 - $1050 = 50 $100 - $150 = 50 s 1 s 2 s 3 Max. Regret A 100 0 5 100 B 99 95 40 99 C 0 100 200 D 150 85 150 0

CONCLUSION Suggested improvements to minimax-regret criterion: v Minimizing the average regret instead of minimizing the maximum. v Minimizing the upper regret average instead of the maximum only. s 1 s 2 s 3 Max. Regret Avrg. Regret Upper Regret A 100 0 5 100 35 52. 5 B 99 95 40 99 78 97 C 0 100 200 150 85 78. 3 117. 5 D 150 v Measure relative regret instead of absolute regret: 0 150 versus instead of: 1050 -1000 = 50 versus 150 -100 = 50

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