Data Science7 min read

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

Cyril Noirot

Lead Data Scientist

May 15, 2025

About the author

Cyril Noirot

Lead Data Scientist

Freelance data scientist. I design and ship decision systems — forecasting, pricing, marketing measurement, optimization — for teams making high-stakes calls.

From lifecycle limits to markdown rules: The product constraints behind retail profit optimization

Why retailers can't escape markdown pricing—a deep dive into the lifecycle, inventory, and pricing constraints that shape modern retail optimization strategies

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Markdown Pricing Optimization: Stochastic Programming for Retail

How retailers transform predictive demand models into prescriptive pricing decisions through stochastic programming, jointly optimizing markdown prices and inventory allocation under uncertainty

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Why price elasticity is the most difficult parameter to estimate in retail analytics

A deep dive into why measuring price elasticity remains the biggest challenge in demand modeling, from data scarcity and endogeneity to seasonal confounding—and how modern techniques address these challenges

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