Data Science

Concavity and Network Flow in Profit Optimization: How Diminishing Returns Enable Efficient Solutions

Understanding why retail revenue functions are concave, how this property enables convex optimization, and the network flow interpretation that powers modern markdown pricing algorithms

15 mai 2025
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7 min de lecture

In retail and e-commerce, the fundamental economic principle of diminishing returns creates a powerful mathematical property: revenue concavity. This property transforms complex markdown pricing problems into tractable convex optimization problems, enabling efficient solutions through network flow algorithms.

Understanding this connection between economic intuition and mathematical structure is crucial for implementing scalable pricing systems that handle thousands of SKUs across multiple locations.

In retail and e-commerce, more inventory can always be sold—but only at lower prices. This creates a diminishing marginal return: each additional unit sold contributes less incremental revenue than the previous one.

The first few units sell at high prices and yield strong profit margins, but clearing the remaining stock requires discounts, reducing the gain per unit.

À propos de l'auteur

Cyril Noirot

Cyril Noirot

Lead Data Scientist

Data scientist freelance. Je conçois et déploie des systèmes de décision — prévision, pricing, marketing measurement, optimisation.

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