An integer programming based heuristic approach to the three-dimensional packing problem

The problem of packing a set of boxes into a container (e.g., a truck) has prompted research efforts that have produced various solution techniques. Most published work, however, concentrates on the one- and two-dimensional packing problem. Very little has been published in the area of three-dimensional packing. Potential applications of this packing situation include loading of shipping containers or trucks, warehouse design, etc. The present research investigates a three-dimensional packing problem where one tries to pack various types of boxes (with different sizes) in various types of containers with the objective that the total cost of containers used is minimized. This article presents a heuristic algorithm based on an integer programming formulation of this problem.