The Budget Split That Explains Itself

Budget allocation is a constrained optimisation problem, and Linear Programming (LP) offers a powerful byproduct: shadow prices that explain why each constraint shaped the result. The common fix for over-concentration — binary on/off variables — converts the LP into a mixed-integer program, destroying those shadow prices. Instead, slicing each channel's budget into diminishing-return bands achieves natural diversification while keeping the model a pure LP. Named constraints then report whether they bound the solution and at what cost. The approach is demonstrated with PuLP in Python, and the author has packaged the full workflow — including scenario analysis, forecasting, and constraint interpretation — into an open-source library called CLARO (pip install claro-engine).

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