A branch-and-cut-and-price approach for the pickup and delivery problem with shuttle routes

The Pickup and Delivery Problem with Shuttle routes (PDPS) is a special case of the Pickup and Delivery Problem with Time Windows (PDPTW) where the trips between the pickup points and the delivery points can be decomposed into two legs. The first leg visits only pickup points and ends at some delivery point. The second leg is a direct trip – called a shuttle – between two delivery points. This optimization problem has practical applications in the transportation of people between a large set of pickup points and a restricted set of delivery points.