The Pallet Loading Problem: Three-dimensional bin packing with practical constraints

Abstract

Pallet loading requires the solution of a three-dimensional bin packing problem (3DBPP) with additional requirements. In particular, vertical support and load bearing, which are not enforced in 3DBPP, are essential in practice. In this work, we provide a complete solution approach for pallet loading problems where practical constraints of vertical support, load bearing, planogram sequencing, and weight limits are fully accounted for. Using a layer based column generation approach, we tackle vertical support using second order cone programming, and satisfy load bearing through a graph representation to trace load distribution. Additionally, we use industry data to propose an instance generator that produces realistic items with practical attributes such as support surface, load capacity, weight, and planogram sequence number. Extensive numerical testing reveals the ability of the approach to find high quality solutions for industry size instances in fast computational times.