Mathematical Models for a 3D Container Packing Problem

Abstract

We address the single container packing problem of a company that has to serve its customers by first placing the products in boxes and then loading the boxes into a container. We approach the problem by developing and solving mixed-integer linear models. Our models consider geometric constraints which feature non-overlappping constraints, box orientation constraints, dimensionality constraints, relative packing position constraints and linearity constraints. We also consider extension of the models by integrating load balance as well as deviation of the center of gravity. The models have been tested on a large set of real instances involving up to 41 boxes and obtaining optimal solutions in most cases and very small gaps when optimality could not be proven.