Integrating freight flows with scheduled public transportation services creates attractive business opportunities as the same transportation needs can be met with fewer operating costs. The pickup and delivery problem with time windows and scheduled lines (PDPTW-SL) aims at routing a given set of vehicles to transport freight requests from their origins to their corresponding destinations, where the requests can use scheduled passenger transportation services as a part of their journeys. We describe the PDPTW-SL as an arc-based mixed-integer program. Computational results on a set of small-size instances provide a clear understanding of the benefits of using scheduled line services as a part of freight's journey.
The Pickup and Delivery Problem with Time Windows and Scheduled Lines (PDPTW-SL) consists of routing and scheduling a set of vehicles, by integrating them with scheduled public transportation lines, to serve a set of freight requests within their time windows. This paper presents an exact solution approach based on a branch-and-price algorithm. A path-based set partitioning formulation is used as the master problem, and a variant of the elementary shortest path problem with resource constraints is solved as the pricing problem. In addition, the proposed algorithm can also be used to solve the PDPTW with transfers (PDPTW-T) as a special case. Results of extensive computational experiments confirm the efficiency of the algorithm: it is able to solve small-and medium-size instances to optimality within reasonable execution time. More specifically, our algorithm solves the PDPTW-SL with up to 50 requests and the PDPTW-T with up to 40 requests on the considered instances.
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