Freight transport using additional railcars attached to intercity passenger trains with transshipment and railcar circulation: Tabu-search-based Lagrangian heuristic

Developing under-exploited passenger rail networks is emerging as an alternative for freight transport. In light of this, we investigate a long-haul freight mode in which additional railcars for carrying shipments are attached to passenger trains, and the shipments can transfer among the trains at intermediate stops. To coordinate space–time schedules of shipments and railcars, we construct a two-level space–time network: one level captures the departure, transshipment, and arrival of shipments; whereas the other level depicts the holding, reshuffling, and repositioning of railcars. Incorporating variables of space–time arc selection and constraints concerning shipment (un-) loading, locomotive pulling capacity, supply–demand coupling, and flow conservation on networks, a binary integer model is established to minimize the total travel cost of both railcars and shipments. The primal problem is decomposed using Lagrangian relaxation. Lagrangian multipliers and dual bounds are approximated by solving the Lagrangian dual. We devise a primal heuristic based on tabu search for expediting high-quality solutions. Numerical experiments demonstrate computational performance and managerial insights.