A GRASP algorithm for multi container loading problems with practical constraints

We consider the multicontainer loading problem of a company that has to serve its customers by first putting the products on pallets and then loading pallets onto trucks. When a large number of units of a product have to be shipped, the company requires that homogeneous pallets, with only one product, are built first, then weakly heterogeneous pallets, in which each layer corresponds to a single product, and finally strongly heterogeneous pallets with the remaining units of the products. To be useful in practice, the solutions have to satisfy five types of constraints: geometric constraints, so that pallets are completely inside the trucks and do not overlap; weight constraints, limiting the total weight a truck can bear and the maximum weight supported by each axle; constraints limiting the position of the centre of gravity of the cargo; dynamic stability constraints, to avoid cargo displacement when the truck is moving; and constraints ensuring that the delivery dates of products are respected. We have developed a Greedy Randomized Adaptive Search Procedure, including some improvement methods tailored to the problem, among them an adaptation of ejection chains. The approach has been tested on a benchmark of real problems and it has been shown to be capable of finding high-quality, realistic solutions in short computing times. We also provide a comparison with an integer programming formulation that justifies the use of a metaheuristic algorithm.