Minimizing earliness-tardiness costs in supplier networks—A just-in-time truck routing problem

We consider a routing problem where orders are transported just-in-time from several suppliers to an original equipment manufacturer (OEM). This implies that shipments cannot be picked up before their release date when they are ready at the supplier and should be delivered as close as possible to their due date to the OEM. Every shipment may have a distinct due date but all shipments loaded onto the same truck arrive at the same time. The performance of the transportation network is optimized by finding an allocation of shipments to trucks and routes for each truck that minimizes the total earliness-tardiness cost. These penalties are caused by deviations between the truck arrival times at the OEM and the due dates of the loaded shipments. To solve the problem, we introduce a metaheuristic approach based on large neighborhood search, which we combine with an efficient local search scheme that allows the evaluation of neighborhood solutions in worst-case logarithmic time despite the nonlinear objective function. Our algorithm can find high-quality solutions to large instances with 200 shipments in less than 12 minutes of CPU time. From a practical perspective, our computational tests indicate that a too small truck fleet or very limited time differences between release and due date can dramatically affect the punctuality of the deliveries.