Lotsize optimization leading to a $p$-median problem with cardinalities

TL;DR

The paper introduces a formalized model for lot-size optimization in fashion retail, connecting it to classical problems like p-median, and provides an ILP formulation and heuristic solutions.

Contribution

It presents a new model for lot-size optimization based on practical industry cooperation, linking it to well-known optimization problems.

Findings

Developed an integer linear programming formulation.

Proposed a primal heuristic for the problem.

Related the problem to classical optimization problems like p-median.

Abstract

We consider the problem of approximating the branch and size dependent demand of a fashion discounter with many branches by a distributing process being based on the branch delivery restricted to integral multiples of lots from a small set of available lot-types. We propose a formalized model which arises from a practical cooperation with an industry partner. Besides an integer linear programming formulation and a primal heuristic for this problem we also consider a more abstract version which we relate to several other classical optimization problems like the p-median problem, the facility location problem or the matching problem.