1. PLANNING
UNDER UNCERTAINTY
REGRET THEORY

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

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

4. MINIMAX REGRET ANALYSIS
Motivating Example
Calculate regret:
find maximum regret
A … regret = 8 @ low market
C … regret = 9 @ low market
D … regret = high market
B … regret = 7 @ medium market
MINIMAX  B
In general, gives conservative decision
but not pessimistic.

5. Two-Stage Model Optimal Profit
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)

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

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

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

9. MINIMAX REGRET ANALYSIS
Two-Stage Stochastic Programming Using Regret Theory

10. MINIMAX REGRET ANALYSIS
Limitations on Regret Theory
It is not necessary that equal differences in profit would always correspond to equal amounts of regret:
$ $1050 = 50
$100 - $150 = 50 s1 s2 s3
Max.
Regret A
100 5 B 99 95 40 C
200 D
150 85
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.

11. Suggested improvements to minimax-regret criterion:
CONCLUSION
Suggested improvements to minimax-regret criterion:
Minimizing the average regret instead of minimizing the maximum. s1 s2 s3
Max.
Regret A
100 5 B 99 95 40 C
200 D
150 85
Avrg.
Regret 35 78
100
78.3
Upper Regret
52.5 97
150
117.5
Minimizing the upper regret average instead of the maximum only.
Measure relative regret instead of absolute regret:
= 50
= 50
versus
instead of: