A GRASP x ELS for the vehicle routing problem with three-dimensional loading constraints

This paper addresses an extension of the Capacitated Vehicle Routing Problem where the client demand consists of three-dimensional weighted items (3L-CVRP). The objective is to design a set of trips for a homogenous fleet of vehicles based on a depot node which minimizes the total transportation cost. Items in each vehicle trip must satisfy the three-dimensional orthogonal packing constraints. A GRASP ELS algorithm is proposed to compute the best possible solution. We propose a new method to address the 3D packing which allows items to be rotated or not. It is based on a relaxation of the 3D problem in which items coordinates are first computed before getting compatible z-coordinates. Additional techniques are used to reduce as much as possible the time to check the 3D packing feasibility of trips. The effectiveness of our approach is evidenced through computational experiments on 3L-CVRP instances from the literature. New realistic instances are also proposed. These instances are based on the 96 French districts and encompass both small scale instances and large scale instances with up to 200 nodes