A model-based heuristic to the vehicle routing and loading problem

In this paper a model-based heuristic approach for a typical distribution problem is presented. In order to be cost-effective, the distribution process for many customers, each of them with orders of considerable volume, should be dealt with like a combination of two well-known problems: the vehicle routing problem (VRP) and the container loading problem (CLP). This paper studies a particular integration of these two problems called the vehicle routing and loading problem (VRLP). The VRLP is an operational problem that must be solved daily by many production and distribution companies. Like the two original problems (VRP and 3D-CLP), the VRLP is NP-hard. In this work, regardless of the complexity of this problem, a mixed integer linear programming (MILP) model that characterizes the VRLP with time windows is presented and it is also used to solve the problem optimally. Then, a model-based heuristic that improves the computational time, when bigger instances need to be solved, is also presented. In order to prove the viability of the approach and the developed MILP model, tests with the benchmark instances of the VRLP were made and the results compared with other published works. Despite the long computational time needed to solve bigger instances, the VRLP model could be used to compute optimal solutions or at least good lower bounds, in order to have a base of comparison when nonexact methods are applied to the VRLP.