A two-echelon multi-trip vehicle routing problem with synchronization for an integrated water- and land-based transportation system

This study focuses on two-echelon synchronized logistics problems in the context of integrated water- and land-based transportation (IWLT) systems. The aim is to meet the increasing demand in city logistics as a result of the growth in transport activities, including parcel delivery, food delivery, and waste collection. We propose two models, a novel mixed integer linear joint model, and a logic-based Benders’ decomposition (LBBD) model, for a two-echelon problem under realistic settings such as multi-trips, time windows, and synchronization at the satellites with no storage and limited resource capacities. The objective is to optimize transfers and satellite assignments, thereby reducing overall logistics costs for street vehicles and vessels. Computational experiments demonstrate that the LBBD model is more robust in terms of solution quality and solution time on average while the added value of the LBBD is more evident when solving large-scale instances with 100 customers, reducing the overall costs by 10.6% on average and significantly reducing the fleet costs on both networks. Furthermore, we assess the effect of changing cost parameters and satellite locations in the proposed IWLT system–analyzing system behavior and suggesting potential improvements–and evaluate several system alternatives in city logistics–consisting of different transportation network designs (single- and two-echelon), vehicle types, and operational constraints. On average, the proposed two-echelon IWLT system reduces the number of kilometers traveled by vehicles at street level by ranging from 20% to 30% compared to a typical single-echelon service design that relies solely on trucks.