Marketing-mix optimisation: choose on a frontier, not a fragile optimum.
Answer:
A mathematical optimum is not automatically a good decision. It depends on curves, constraints, interactions and the selected scenario. When these are uncertain, the point maximising central value can concentrate risk and be dominated in an adverse scenario. Responsible optimisation shows the efficient frontier between expected contribution and exposure, compares regret across scenarios, values constraints and preserves room to learn.
Method and decision:
Define contribution, customers or long-term value and the horizon, then add risk, capacity, channel exposure, mix coherence and minimum-learning guardrails. Vary response, adstock, margin, costs, competition and synergies while keeping plausible correlations. Optimise at each risk level, remove dominated plans, and calculate expected contribution, lower bound, maximum regret, number of changes and distance from observed support. Select the point whose marginal gain compensates added risk; deploy in tranches and update curves before crossing unobserved territory. Choose a frontier plan whose additional gain justifies risk, regret and operating cost relative to a robust option.
Worked example:
Six allocations distribute €1.5m across video, search, social, CRM and retail. The “central maximum” expects €520k contribution, a €160k loss in the low scenario and €245k maximum regret. The “robust” plan expects €482k, minimum gain €50k and maximum regret €118k. Its expected robustness cost is 520 − 482 = €38k. Low-scenario protection is 50 − (−160) = €210k, for protection-to-expected-cost ratio 210 ÷ 38 = 5.53. The robust plan needs three changes above 20%, versus five, and remains in observed support for four of five channels. Do not select the central maximum: the robust plan gives up 7.3% central gain to eliminate the extreme loss, reduce regret and simplify execution; reserve a learning tranche for the off-support channel.
Limits:
The frontier depends on scenarios and may omit structural risk. Unstable response functions create illusory optimisation precision. Organisational complexity is difficult to turn into a single penalty.