A vehicle routing problem with pickup and delivery time windows, and coordination of transportable resources

This paper addresses a pickup and delivery problem with time window constraints, using two types of delivery resources, which allows for coordination. A heavy resource (in this case a van) may carry both delivery items and one or more units of the lighter resource (foot couriers) on its single- or multi-route assignment. Foot couriers can pick up and deliver items independently, or travel with a van on its outbound and/or return leg. Coordination between resources can save time and cut costs. The optimization of this type of coordinated logistics system has received scant coverage in the literature. The objective criterion is the total cost (i.e., the sum of fixed cost and travelling cost) of both heavy and light resources. The problem is first formulated as a mixed integer program, assuming a reasonable coordination strategy. A two-stage heuristic is designed by employing both exact approaches and an ejection chain based on modifying the shortest path algorithm implemented in a dynamic network. The two-stage heuristic is compared with optimization models for an independent strategy and a partial coordination strategy on both local and simulated instances of up to 200 customers. Under certain conditions, the benefit of coordination is realized over the independent strategy in terms of lower average total cost and usage of heavy resource.