A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows

In the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows, the set of customers is the union of delivery customers and pickup customers. A fleet of identical capacitated vehicles based at the depot must perform all deliveries and profitable pickups while respecting time windows. The objective is to minimize routing costs, minus the revenue associated with the pickups. Five variants of the problem are considered according to the order imposed on deliveries and pickups. An exact branch-and-price algorithm is developed for the problem. Computational results are reported for instances containing up to 100 customers.