The vehicle routing problem with transfers

Abstract

In the vehicle routing problem (VRP), a fleet of capacitated vehicles serves a set of customers with known demands at minimum cost. The Split Delivery VRP (SDVRP), a variant of VRP, permits customer demands to be served by different vehicles, and thereby results in a significant cost reduction. In this paper, we study the VRP with transfers (VRP-T), where, as in the SDVRP, customers can be visited by multiple vehicles. However, differently from the SDVRP, customer locations can be used as transfer locations to exchange load among vehicles. We find that the routing costs can potentially be reduced by at most 50% by allowing such transfers in the VRP. We develop a two-index mixed-integer programming (MIP) model and heuristic algorithm based on $\mathrm{Multi\; -\; start\; local\; search\; (MSLS)}$. The solutions obtained by the $\mathrm{MSLS}$ are used as warm-start for the MIP and the corresponding approach is tested. Computational results indicate substantial savings in the costs incurred and the number of vehicles required when transfers are allowed. Results also suggest that transfers are at least as effective in reducing the cost as split delivery.