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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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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

instead of:

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:


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