PLANNING UNDER UNCERTAINTY

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# PLANNING UNDER UNCERTAINTY - PowerPoint PPT Presentation

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.

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Presentation Transcript

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

Uncertainty Free

Optimal Profit

Here & Now (HN)

Wait & See (WS)

MINIMAX REGRET ANALYSIS

Two-Stage Stochastic Programming Using Regret Theory

MINIMAX REGRET ANALYSIS

Two-Stage Stochastic Programming Using Regret Theory

where:

subject to:

,

subject to:

,

where:

subject to:

,

subject to:

,

MINIMAX REGRET ANALYSIS

Two-Stage Stochastic Programming Using Regret Theory

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

• 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.

versus

1050-1000 = 50

150-100 = 50

versus

CONCLUSION

Suggested improvements to minimax-regret criterion:

• Minimizing the average regret instead of minimizing the maximum.
• Minimizing the upper regret average instead of the maximum only.
• Measure relative regret instead of absolute regret: