This article considers a combination of capacitated vehicle routing and three-dimensional loading, with additional constraints frequently encountered in freight transportation. It proposes a tabu search algorithm that iteratively invokes an inner tabu search procedure for the solution of the loading subproblem. The algorithm is experimentally evaluated both on instances adapted from vehicle routing instances from the literature and on new real-world instances.

We consider a special case of the symmetric capacitated vehicle routing problem, in which a fleet of K identical vehicles must serve n customers, each with a given demand consisting in a set of rectangular two-dimensional weighted items. The vehicles have a two-dimensional loading surface and a maximum weight capacity. The aim is to find a partition of the customers into routes of minimum total cost such that, for each vehicle, the weight capacity is taken into account and a feasible two-dimensional allocation of the items into the loading surface exists. The problem has several practical applications in freight transportation, and it is 𝒩𝒫-hard in the strong sense. We propose an exact approach, based on a branch-and-cut algorithm, for the minimization of the routing cost that iteratively calls a branch-and-bound algorithm for checking the feasibility of the loadings. Heuristics are also used to improve the overall performance of the algorithm. The effectiveness of the approach is shown by means of computational results.