An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints

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 and 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 branchand-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