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

In automated decision making processes in the online fashion industry, the'predict-then-optimize' paradigm is frequently applied, particularly formarkdown pricing strategies. This typically involves a mixed-integeroptimization step, which is crucial for maximizing profit and merchandisevolume. In practice, the size and complexity of the optimization problem isprohibitive for using off-the-shelf solvers for mixed integer programs andspecifically tailored approaches are a necessity. Our paper introduces specificheuristics designed to work alongside decomposition methods, leading toalmost-optimal solutions. These heuristics, which include both primal heuristicmethods and a cutting plane generation technique within a Lagrangiandecomposition framework, are the core focus of the present paper. We provideempirical evidence for their effectiveness, drawing on real-world applicationsat Zalando SE, one of Europe's leading online fashion retailers, highlightingthe practical value of our work. The contributions of this paper are deeplyingrained into Zalando's production environment to its large-scale catalogranging in the millions of products and improving weekly profits by millions ofEuros.