# Tricks from the Trade for Large-Scale Markdown Pricing: Heuristic Cut Generation for Lagrangian Decomposition

arXiv: https://arxiv.org/abs/2404.02996 · HTML: https://mlsanity.com/paper/2404.02996/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2024.

## Built on by (most cited first, 2 of 2)

- [DeepRule: An Integrated Framework for Automated Business Rule Generation via Deep Predictive Modeling and Hybrid Search Optimization](https://mlsanity.com/paper/2512.03607/) (2025)
- [High-Frequency Pricing at Scale for E-Commerce](https://mlsanity.com/paper/2606.13741/) (2026)

## Abstract (arXiv)

In automated decision making processes in the online fashion industry, the 'predict-then-optimize' paradigm is frequently applied, particularly for markdown pricing strategies. This typically involves a mixed-integer optimization step, which is crucial for maximizing profit and merchandise volume. In practice, the size and complexity of the optimization problem is prohibitive for using off-the-shelf solvers for mixed integer programs and specifically tailored approaches are a necessity. Our paper introduces specific heuristics designed to work alongside decomposition methods, leading to almost-optimal solutions. These heuristics, which include both primal heuristic methods and a cutting plane generation technique within a Lagrangian decomposition framework, are the core focus of the present paper. We provide empirical evidence for their effectiveness, drawing on real-world applications at Zalando SE, one of Europe's leading online fashion retailers, highlighting the practical value of our work. The contributions of this paper are deeply ingrained into Zalando's production environment to its large-scale catalog ranging in the millions of products and improving weekly profits by millions of Euros.