Robust optimisation: choosing the scenario that limits maximum regret.
Key distinctions
Three conditions before calculating.
Coherent scenarios
A scenario combines compatible assumptions on demand, costs, competition and media response. Mixing extremes independently produces impossible worlds and a prudence without value.
Relative regret
Regret is the gap between the result of an option and the best option in the same scenario. It distinguishes a generally weak performance from a decision specifically ill-adapted.
Hard constraints
Compliance, cash, capacity and service threshold must be filtered before the ranking. A low regret does not make an unfeasible option acceptable.
Method
Building a robust decision without abandoning ambition
- 01Generate the plausible worlds
Define central scenario, low demand, competitive reaction and cost shock from documented ranges and coherent dependencies.
- 02Assess each option
Compute contribution, cash, service and constraints for every option-scenario pair with the same conventions.
- 03Compute the regrets
Subtract each result from the best result in its column, then record maximum regret, average regret and frequency of dominance.
- 04Add reversibility
Separate close options by cost of reversal, learning time and the possibility of increasing the commitment after observation.
The maximum-regret matrix
Three plans are compared across four scenarios. The balanced plan is never the best gross profit, but it limits the loss relative to the best choice in each world.
| Plan | Central | Weak demand | Competitor | Cost | Maximum regret |
|---|---|---|---|---|---|
| Aggressive | €0k | €180k | €210k | €120k | €210k |
| Balanced | €110k | €20k | €30k | €40k | €110k |
| Conservative | €240k | €0k | €0k | €0k | €240k |
The balanced plan reduces the worst regret from €210k to €110k
The aggressive plan produces €520k, €80k, €40k and €180k across four scenarios. The balanced one produces €410k, €240k, €220k and €260k. The conservative one produces €280k, €260k, €250k and €300k.
The best results by scenario are 520, 260, 250 and 300. Maximum regrets: aggressive €210k, balanced €110k, conservative €240k.
The balanced plan is retained. It gives up €110k in the central scenario but protects more against low demand, competition and cost shock.
Acceptance conditions
What must be true to act.
- 01
The scenarios represent coherent worlds and not independent extremes.
- 02
All options respect the hard constraints before comparison.
- 03
Maximum regret, average regret and central result are published together.
- 04
A reversible option is preferred when the regrets are close.
Limits
What this analysis does not prove.
- Minimax regret depends on the set of scenarios retained and ignores their probability.
- Excessive prudence can sacrifice opportunities if the adverse scenarios are barely plausible.
- Dynamic interactions and sequential learning require a multi-stage model.
References
Works cited.
- Savage, L. J. (1951), “The Theory of Statistical Decision”, Journal of the American Statistical Association.
- Ben-Tal, A. & Nemirovski, A. (1998), “Robust Convex Optimization”, Mathematics of Operations Research.
- Bertsimas, D. & Sim, M. (2004), “The Price of Robustness”, Operations Research.