In this paper, we present a 0-1 mixed integer linear programming model and approaches based on this model to solve problems of packing rectangular boxes inside a container or a truck. In particular, we are only interested in the arrangement of the cargo inside the truck. We assume that the route of the truck is already known in advance and that the cargo fits inside the truck. Therefore, the objective is to find the best loading pattern ensuring that the boxes do not overlap each other inside the truck and considering the sequence that they must be unloaded in order to avoid additional handling. Computational tests with the proposed approaches were performed using the software GAMS/CPLEX with randomly generated instances and instances from the literature. The results show that the model and the approaches are consistent and properly represent the situations treated although limited to optimally solve only problems of a moderate size. However, the model and the approaches can be useful to motivate future research to solve larger and more realistic problems in practice, as well as to solve the coupled vehicle routing and container loading problem.
Cutting and packing problems; Container loading with multi-dropping; Combinatorial optimization; Mathematical modeling
