A scenario-based planning for the pickup and delivery problem with time windows, scheduled lines and stochastic demands

•Integration of the pickup and delivery problem with public scheduled lines, considering stochastic demands, is analyzed.•Public scheduled transportation is considered as a part of the small-sized freight’s journey.•The problem is solved using an adaptive large neighborhood search embedded into a sample average approximation method.•Computational results show considerable savings in terms of expected operating costs.

The Pickup and Delivery Problem with Time Windows, Scheduled Lines and Stochastic Demands (PDPTW-SLSD) concerns scheduling a set of vehicles to serve a set of requests, whose expected demands are known in distribution when planning, but are only revealed with certainty upon the vehicles’ arrival. In addition, a part of the transportation plan can be carried out on limited-capacity scheduled public transportation line services. This paper proposes a scenario-based sample average approximation approach for the PDPTW-SLSD. An adaptive large neighborhood search heuristic embedded into sample average approximation method is used to generate good-quality solutions. Computational results on instances with up to 40 requests (i.e., 80 locations) reveal that the integrated transportation networks can lead to operational cost savings of up to 16% compared with classical pickup and delivery systems.