Practical constraints in the container loading problem: Comprehensive formulations and exact algorithm - Nascimento, Oliviana Xavier do; Alves de Queiroz, Thiago; Junqueira, Leonardo (Computers & operations research, 2021)
•An exact iterative algorithm solves the container loading problem.•Cuts to break symmetric solutions and an enhanced linear relaxation are proposed.•Twelve real constraints are modeled with integer linear and constraint programming paradigms.•The exact algorithm solves more than 70% of the instances within one hour.•For some real constraints, more than 90% of the instances are solved. 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.