A hybrid approach for a multi-compartment container loading problem

Abstract

In this paper, we address a real problem of packing boxes into a multi-compartment container, in which the boxes must be delivered to customers in a predefined route. This problem arises, for example, in the distribution of beverages (packed in “boxes”) by trucks whose container has multiple compartments. The objective is to find a feasible packing plan that minimizes the handling of boxes inside the container along the whole truck route. The following practical constraints must be met: orientation of the boxes, cargo stability, load bearing strength of the boxes and load balancing. To the best of our knowledge, this is the first study focusing on a vehicle packing problem with multi-compartment containers in the context of beverage distribution. To solve this problem, we present a hybrid approach which consists of a heuristic method based on the generation of horizontal layers and on the solution of mixed integer linear programming models. Computational tests were performed with this approach and a large variety of instances based on real data from a soft drink company. The results show that the approach is able to find feasible solutions for all instances considered under all constraints, contrary to what was observed in practice with the manual procedures available in the company. In practice, if a feasible solution is not obtained, it is necessary to change the predefined route plan and/or to consider an additional new delivery route and/or to use a solution that violates some of the constraints involved. In this sense, the proposed solution approach has good potential for being embedded into existing expert and intelligent systems for supporting the decision making process.