Exploiting Packing Components in General-Purpose Integer Programming Solvers

TL;DR

This paper presents a compact reformulation of multi-dimensional packing problems within integer programming, enabling efficient solutions for large-scale instances with up to ten million boxes.

Contribution

It introduces a reformulation based on Allen–Burke–Marecek discretisation to improve the efficiency of solving packing problems in general-purpose integer programming solvers.

Findings

Successfully solved instances with up to 10 million boxes.

Reformulation improves computational efficiency.

Demonstrates applicability to large-scale packing problems.

Abstract

The problem of packing boxes into a large box is often a part of a larger problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution centers and stores, such that the furniture fits inside. Such problems are often formulated and sometimes solved using general-purpose integer programming solvers. This chapter studies the problem of identifying a compact formulation of the multi-dimensional packing component in a general instance of integer linear programming, reformulating it using the discretisation of Allen--Burke--Marecek, and and solving the extended reformulation. Results on instances of up to 10000000 boxes are reported.