Marketing-mix optimisation: choosing on a frontier, not a fragile optimum.
Evidence status
What was reproduced, and what it does not prove.
The public CSV and the Python run verify the six plans and their dominance status according to the three documented criteria. They verify neither the scenarios, nor the media responses, nor the optimality of a market allocation.
- Technical specification of the teaching optimisation frontier, specification in French (opens in a new tab)
v1, 31 August 2026 · CC BY 4.0 · specification in French · Method document written by marketing-mix.net. The figures are illustrative: they are not market measurements.
Key distinctions
Three conditions before calculating.
Frontier rather than ranking
A plan is dominated if another offers more contribution with less risk. The non-dominated plans form the frontier; the choice between them depends on risk appetite, reversibility and execution capacity.
Explicit constraints
Minimum presence, capacity, contracts, inventory, coverage and pace of change belong to the model. A constraint added after the computation makes the theoretical optimum unexecutable and hides its real cost.
Robustness
The central scenario is insufficient when curves and synergies are poorly known. Minimax regret, robust optimisation or weighted scenarios show which plans stay acceptable without pretending to know a perfect distribution.
Method
Building an optimised and governable recommendation
- 01Define objective and guardrails
Choose contribution, customers or long-term value and state the horizon; add risk limits, capacity, exposure by channel, mix coherence and minimum learning.
- 02Generate the scenarios
Vary response, adstock, margin, costs, competition and synergies; keep the plausible correlations so as to avoid a stress made of incompatible assumptions.
- 03Trace the frontier
Optimise under each level of risk and eliminate the dominated plans; compute expected contribution, lower bound, maximum regret, number of changes and distance to the observed support.
- 04Select and sequence
Choose the point whose marginal gain offsets the additional risk; deploy in tranches, follow the active constraints and update the curves before crossing an unobserved zone.
The contribution–risk frontier of allocations
Six plans are compared by expected contribution, loss in the low scenario, complexity and maximum regret; a robust plan dominates the status quo.
Giving up €38k of expected gain protects €210k in the low scenario
Six allocations distribute €1.5M between video, search, social, CRM and retail. The "central maximum" plan forecasts €520k of contribution, a loss of €160k in the low scenario and a maximum regret of €245k. The "robust" plan forecasts €482k, a minimum gain of €50k and a maximum regret of €118k.
Expected cost of robustness: 520 − 482 = €38k. Protection in the low scenario: 50 − (−160) = €210k. Protection-to-expected-cost ratio = 210 ÷ 38 = 5.53. The robust plan requires three changes above 20%, against five for the central maximum, and stays within the observed support on four channels out of five.
The central maximum is not retained. The robust plan sacrifices 7.3% of central gain to remove the extreme loss, reduce regret and ease execution. A learning tranche is reserved for the channel outside the support.
Acceptance conditions
What must be true to act.
- 01
Any dominated plan is discarded before discussion.
- 02
The low scenario, the maximum regret and the distance to the support are published.
- 03
Operational constraints belong to the model, not to the final correction.
- 04
Decisions outside the support are sequenced as experiments.
Limits
What this analysis does not prove.
- The frontier depends on the scenarios and can omit a structural risk.
- Unstable response functions produce an illusory precision of optimisation.
- Organisational complexity is hard to convert into a single penalty.
References
Works cited.
- Ben-Tal, A., El Ghaoui, L. & Nemirovski, A. (2009), Robust Optimization.
- Bertsimas, D. & Sim, M. (2004), “The Price of Robustness”, Operations Research, 52(1), 35–53.
- Savage, L. J. (1951), “The Theory of Statistical Decision”, Journal of the American Statistical Association, 46(253), 55–67.