Practical constraints in the container loading problem: Comprehensive formulations and exact algorithm

This paper addresses the Single Container Loading Problem. We present an exact approach that considers the resolution of integer linear programming and constraint programming models iteratively. A linear relaxation of the problem based on packing in planes is proposed. Moreover, a comprehensive set of mathematical formulations for twelve practical constraints that arise in this problem are discussed. These constraints include complete shipment, conflicting items, priorities, weight limit, cargo stability, load-bearing, multi-drop, load-balancing, manual loading, grouping, separation, and multiple orientations. Extensive computational experiments are carried out on instances from the literature to show the performance of the proposed approach and state how each practical constraint affects the container?s occupancy, the approach runtime, and the number of packing patterns evaluated. In general, the approach could optimally solve instances with around ten items types and a total of 110 items, besides obtaining the optimal solution for more than 70% of all instances. ? 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study addresses the Single Container Loading Problem by proposing an exact approach that iteratively solves integer linear programming and constraint programming models. Extensive computational experiments were conducted to demonstrate the performance of the proposed approach, showing that it could optimally solve instances with around ten item types and more than 70% of all instances.