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.