The heterogeneous fleet vehicle routing problem with overloads and time windows

This paper addresses a new variant of the vehicle routing problem (VRP) with time windows, in which the vehicle fleet comprises units of different capacities and some overloads (i.e., loading vehicles above nominal capacity) are allowed. Although often encountered in practice, the problem, which we call heterogeneous fleet vehicle routing with overloads and time windows (HFVROTW), has not been previously tackled in the literature. We model it by integrating the constraint of the total trip load into the objective function, and solve it via a sequential insertion heuristic that employs a penalty function allowing capacity violations but limiting them to a variable predefined upper bound. Computational results on benchmark problems show the effectiveness of the proposed approach in reducing vehicle costs with minimal capacity violations, thus offering evidence of the significance of this VRP variant.