Central optimisation selects the best option if every assumption occurs.
Central optimisation selects the best option if every assumption occurs. A robust decision seeks acceptable performance across several plausible worlds. Minimax regret compares each option with the choice one would have made after knowing the scenario, then retains the option with the smallest worst opportunity loss.
Decision and method.
Keep a plan that is less optimal in the central scenario when it protects contribution materially better against plausible adverse assumptions. Define coherent central, weak-demand, competitor-reaction and cost-shock worlds from documented ranges and dependencies. For every option–scenario pair, calculate contribution, cash, service and constraints using the same conventions. Filter compliance, cash, capacity and service thresholds before ranking. Subtract each outcome from the best outcome in its column; report maximum regret, mean regret, central result and dominance frequency. Break near ties by reversibility: rollback cost, learning delay and ability to increase commitment after observing results.
Worked example.
Aggressive produces €520k, €80k, €40k and €180k across four scenarios. Balanced produces €410k, €240k, €220k and €260k; conservative produces €280k, €260k, €250k and €300k. Best results are €520k, €260k, €250k and €300k. Maximum regrets are €210k aggressive, €110k balanced and €240k conservative. Retain balanced: it gives up €110k centrally but protects better against weak demand, competition and cost shock.
Checks and limits.
Scenarios must be coherent worlds, not independently combined extremes; all options must meet hard constraints; publish worst regret, mean regret and central outcome together; prefer reversibility when regrets are close. Minimax regret depends on the selected scenario set and ignores probabilities. Excessive caution can sacrifice opportunity when adverse worlds are unlikely; dynamic interaction and sequential learning need a multi-stage model.
Resources and sources.
Download the minimax-regret matrix. Related: identify decisive assumptions, compare scenarios, formalise hard constraints. Sources: Savage (1951); Ben-Tal and Nemirovski (1998); Bertsimas and Sim (2004).