When optimizing marketing budgets in MMM, you're solving a constrained non-linear optimization problem. Mixed Integer Programming (MIP) with discretized response curves guarantees finding the global optimum through branch-and-bound algorithms.
Subject to: - Budget constraint: $\sumi Xi = B$ - Business constraints: $Li \leq Xi \leq Ui$
Before discretization, we must formulate the marketing allocation problem mathematically. This modeling phase translates business objectives and constraints into mathematical expressions.
Decision Variables: These represent budget allocation choices: - Continuous: Spend amount per channel (e.g., $X{\text{TV}}$ = TV budget) - Binary: Channel activation decisions (e.g., $zi \in \{0,1\}$ for on/off) - Discrete: Campaign count or creative versions (e.g., number of TV spots) - Semi-continuous: Zero or within range (e.g., $Xi = 0$ or $Xi \in [Li, Ui]$)
About the author
Cyril Noirot
Lead Data Scientist
Freelance data scientist. I design and ship decision systems — forecasting, pricing, marketing measurement, optimization.