The Vehicle Routing Problem with Discrete Split Delivery and Time Windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles’ capacity and customer time windows. The delivery request of a customer consists of several discrete items which cannot be split further. The problem belongs to the class of split delivery problems since each customer’s demand can be split in orders, i.e. feasible combinations of items, and each customer can be visited by more than one vehicle. In this work, we model the DSDVRPTW as a mixed integer linear program, assuming that all feasible orders are known in advance and that each vehicle can serve at most one order per customer. Remarkably, service time at customer’s location depends on the serviced combination of items, which is a modeling feature rarely found in literature. We present a branch-and-price algorithm, analyzing the implications of the classical Dantzig-Wolfe reformulation. Preliminary computational results on instances based on Solomon’s data set are discussed.