Conventional railway planning follows a sequential approach in which rolling stock scheduling is performed only after timetables are constructed, forcing early-stage line-planning decisions to rely on simplified rolling stock cost approximations. The lack of precise cost information hampers line-plan evaluation and limits the design of cost-efficient services. This study considers rolling stock scheduling in a strategic setting, aiming to estimate fleet size and operational costs for a given line plan without solving the timetabling problem. Since predefined train services are unavailable at this level, unlike in tactical planning, we introduce a network representation incorporating shunting movements like coupling and uncoupling. To account for demand uncertainty, a two-stage stochastic programming approach is proposed, in which first-stage decisions determine fleet acquisition and second-stage decisions optimize rolling stock circulation, including shunting, under each demand scenario. Two models are developed, differing in whether the fleet size is estimated using a flow-based or circulation-based approach. The applicability of the proposed models is demonstrated using instances derived from the Dutch Intercity network. Compared to a trip-based benchmark, the circulation-based model yields more accurate cost estimates, while short and simple cycles retain most of its value at much lower computational cost. Moreover, stochastic planning better captures the procurement–service trade-off under demand uncertainty and produces more robust fleet plans than a deterministic approach. Under strong emphasis on investment costs, fleet choices are dominated by flexible, cost-effective unit types. Allowing shunting enables flexible capacity redistribution, reducing fleet requirements and investment costs while maintaining comparable service levels.

This study investigates a shared-use metro network in which passengers and freight are transported on different trains, enhancing resource utilization and promoting the sustainable growth of urban areas. From the perspective of public authorities seeking to balance the interests of all stakeholders, we address the tactical problem of determining the optimal number, stop pattern, and schedule of freight train services needed for freight delivery, while maintaining high passenger service quality by minor timetable adjustments. A non-convex mixed-integer quadratic programming model is developed to minimize freight transportation, train operational costs, and deviations in passenger train schedules. A Frank-Wolfe-based heuristic is developed with a novel gradient approximation that accounts for the hierarchy between binary and continuous decisions. The step size is defined as a discrete gap between disjoint subspaces determined by train operations, reflecting that partially shifting flow does not effectively impact the objective due to the indivisibility of train activation. Experiments are conducted based on instances generated from the Beijing Metro network. The results show that under high freight demand, dedicated freight trains cause less passenger delay than utilizing existing passenger trains. Prioritizing passenger schedules shifts freight to lower-priority lines, while incorporating a quadratic consolidation cost helps reduce fragmentation and excessive transshipments.

With the introduction of freight transportation into the passenger transit network, underground city logistics are regarded as a desirable alternative to address the challenges due to truck movements in urban freight transport. Furthermore, some metro lines suffer from low-capacity utilization because of the unbalanced demand, which provides the potential to expand the extra capacity for freight transportation. Therefore, this study integrates the train unit scheduling problem with combined transportation of passengers and freight during off-peak hours. The objective is to fully utilize the remaining capacity by not only integrating passenger and freight flows but also allowing a flexible composition such that the capacity can better meet the demand. The composition of a trip is defined as its state. A three-dimensional space–time–state network is constructed to capture the composition transitions and passenger/freight trajectories. The problem is formulated as an integer linear programming model to minimize the weighted sum of train unit operational, passenger travel, and freight travel costs. Utilizing the problem-specific characteristics, a constrained-gap-based branch-and-bound approach is developed to efficiently solve the model. The worst bound for each objective is guaranteed by introducing two gaps in the passenger- and freight-related objectives. The nodes with estimated lower bounds exceeding the designated gaps are pruned. A beam search procedure is also included to further reduce the computational complexity. The developed algorithm is tested on real-life instances from the Beijing Metro Network. The results provide insights into the benefits and applicable scenarios for integrating passenger and freight transportation. Moreover, we demonstrate that the number of train units should be carefully determined considering the tradeoff between passenger service quality and freight demand volume.

This study investigates the potential of a shared freight and passenger high-speed railway system in which different transportation resources are allowed to be shared under different sharing modes. A sharing-carriage mode is proposed and combined with a sharing-train mode to fully exploit the remaining capacity of the existing railway schedule. The manner in which these two sharing modes are jointly involved to utilize the available capacity is investigated and optimized. First, a space–time network is constructed to analyze the distribution of flow for a given train schedule. Subsequently, the influence of integrated transportation upon passenger satisfaction is included by introducing a load-factor-based penalty cost for each train. The model is first formulated as a mixed-integer program that minimizes service and routing costs and then reformulated into a path-based model. A Benders decomposition approach is proposed to decompose the problem into two subproblems. Instead of exploring every possible path for each commodity when solving the Benders subproblem, a column-pool-based approximation approach is proposed to generate feasible solutions. Finally, the proposed approach is tested on two small-scale examples and 12 scenarios from a real-world high-speed railway network. Different train load factors, penalty costs, sharing modes, and commodity volumes are investigated to demonstrate the applicability of integrated transportation. The performance of the algorithm and acceleration techniques is also analyzed.