A Container Loading Problem MILP-Based Heuristics Solved by CPLEX: An Experimental Analysis

Abstract

The issue of placing small boxes orthogonally, generally with the possibility of rotations, into a big box, maximizing the loaded volume, is usually referred to as the container loading problem. Despite its being notoriously of an NP-hard typology, a number of algorithms work out this problem very efficiently. The task becomes, nonetheless, even more challenging when additional conditions have to be taken account of. In such cases, a modeling-based approach is supposedly the most suitable and this definitely holds, in particular, when balancing requirements are posed. These, indeed, entail constraints of strong global impact that can hardly be coped with by sequential procedures, based on a step by step incremental loading of items.

MIP (Mixed Integer Programming) models relevant to the container loading problem or possible extensions of it are available in specialized literature. A dedicated MILP (Mixed Integer Linear Programming) formulation, supporting an overall heuristic approach, addressed to non-standard packing issues, is discussed in another chapter of this book. Hereinafter, some relevant computational aspects are looked into, restricting the consideration to the container loading problem, as per its classical statement. An ad hoc heuristics, derived from the above-mentioned overall approach, is outlined. The use of IBM ILOG CPLEX as an MILP optimizer is considered. Case studies concerning the solution of the MILP model tout court, when the instances involved are not of a large-scale nature, are reported first. Outcomes relevant to the ad hoc heuristics are further shown through a number of difficult instances. Examples of container loading issues, involving also balancing conditions, are additionally provided.