Multi-period Vehicle Routing Problem with Due dates

In this paper we study the Multi-period Vehicle Routing Problem with Due dates (MVRPD), where customers have to be served between a release and a due date. Customers with due dates exceeding the planning period may be postponed at a cost. A fleet of capacitated vehicles is available to perform the distribution in each day of the planning period. The objective of the problem is to find vehicle routes for each day such that the overall cost of the distribution, including transportation costs, inventory costs and penalty costs for postponed service, is minimized. We present alternative formulations for the MVRPD and enhance the formulations with valid inequalities. The formulations are solved with a branch-and-cut algorithm and computationally compared. Furthermore, we present a computational analysis aimed at highlighting managerial insights. We study the potential benefit that can be achieved by incorporating flexibility in the due dates and the number of vehicles. Finally, we highlight the effect of reducing vehicle capacity.