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PLANNING UNDER UNCERTAINTY
REGRET THEORY
 by   Ahmed Aseeri December 8, 2013
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MINIMAX REGRET ANALYSIS

• Its a feeling

• measurable .

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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

• Traditional way Maximize Averageselect A
• Optimistic decision maker MaxiMax select C
• Pessimistic decision maker MaxiMmin select
  D

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MINIMAX REGRET ANALYSIS
Motivating Example

• Calculate regret
• find maximum regret
• A regret 8 _at_ low market
• C regret 9 _at_ low market
• D regret 10 _at_ high market
• B regret 7 _at_ 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
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MINIMAX REGRET ANALYSIS
Two-Stage Stochastic Programming Using Regret
Theory
where
subject to
,
subject to
,
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MINIMAX REGRET ANALYSIS
Two-Stage Stochastic Programming Using Regret
Theory
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MINIMAX REGRET ANALYSIS
Two-Stage Stochastic Programming Using Regret
Theory
where
subject to
,
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

• 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 0 5 100
B 99 95 40 99
C 0 100 200 200
D 150 85 0 150

• 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.

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CONCLUSION
Suggested improvements to minimax-regret
criterion

• Minimizing the average regret instead of
  minimizing the maximum.

Upper Regret
52.5
97
150
117.5
s1 s2 s3 Max. Regret
A 100 0 5 100
B 99 95 40 99
C 0 100 200 200
D 150 85 0 150
Avrg. Regret
35
78
100
78.3

• Minimizing the upper regret average instead of
  the maximum only.

• Measure relative regret instead of absolute
  regret

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END