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.

Semi-flexible transit, integrating fixed-route and on-demand services, offers a demand-adaptive and cost-effective alternative for public transit users, particularly in low-demand conditions. Despite the growing interest in this system, existing approaches have failed to develop comprehensive optimization methods for managing demand fluctuations across distinct scenarios, thereby significantly constraining operational adaptability in semi-flexible transit services. To address this research gap, we propose a scenario-based optimization model that jointly determines the fleet size and master routes at the tactical level as well as sub-routes at the operational level. The objective is to minimize travel costs while ensuring service feasibility under varying passenger demand scenarios, accounting for constraints such as travel time, state changes, time windows, and route consistency. Then, an Augmented Lagrangian Relaxation under Alternating Direction Method of Multipliers (ALR-ADMM) decomposition solution framework is introduced to decouple the proposed integrated problem into three sub-problems, namely master route, sub-route and service planning problems. Numerical experiments on the Sioux-Falls network validate the proposed model and solution approach, achieving a 94.93 % reduction in computation time while maintaining an average optimality difference of 0.57 % compared to the Gurobi optimizer. Sensitivity analysis further examines the effects of vehicle capacity limits, penalty parameters, and demand stop selection, revealing their impact on computational efficiency and operational costs. The applicability of our approach is further assessed through a real-world case study on the West Jordan network, which provides evidence of the ALR-ADMM-based algorithm in terms of both solution quality and computational efficiency. Our findings illustrate the feasibility and potential of the proposed model and algorithm in navigating both the tactical and operational scheme of semi-flexible transit within modern urban transit systems.

The considerable increase in parcel deliveries has negatively impacted the accessibility and livability of cities. One solution strategy is to decouple short-distance from long-distance shipping so that last-mile transport can be performed with low-footprint vehicles. Such solutions are referred to in the literature as multi-echelon distribution systems. This study introduced a new variant of the two-echelon vehicle routing problem that considers multiple alternative transport modes as well as multiple commodities over a multi-period time horizon, where customers can obtain their commodities from any store. We referred to this problem as the two-echelon multi-commodity multimodal vehicle routing problem (MCM-2E-VRP). The objective of service providers is to minimize total generalized costs while satisfying customer requirements. We formulated this as a mathematical model based on a space–time network and introduced a random utility discrete choice model to capture variations in performance and preferences. We developed an adaptive large-neighborhood search (ALNS) algorithm to provide solutions for newly generated MCM-2E-VRP instances based on the Beijing Yizhuang transportation network. Extensive numerical experiments were conducted to verify the effectiveness of the proposed model and algorithm. A sensitivity analysis revealed some policy-relevant findings regarding the effects of store distribution and vehicle capacity.

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.

The rapid increase in e-commerce and the emergence of combined passenger/freight systems in urban areas have raised the question of how best to integrate public transport services into door-to-door deliveries. This paper develops a variant of the pickup and delivery problem, called the two-echelon pickup and delivery problem using public transport (2E-PDP-PT). In the 2E-PDP-PT, the transportation network is split into two echelons. Different vehicles are utilized across the first and second echelons to ensure distribution efficiency. Parcels are delivered by public transport with free capacity or via trucks between satellites in the first echelon, and logistics vehicles are operated in the second echelon. The satellites are located at the echelon borders to transfer commodities between echelons. The 2E-PDP-PT aims to minimize total delivery costs and improve public transport capacity utilization. We formulate a new mathematical model based on a space-time network and adopt an adaptive large neighborhood search (ALNS) algorithm for the 2E-PDP-PT. The effectiveness of the ALNS algorithm is validated using newly generated small-scale instances. Furthermore, we investigate large-scale instances based on the Beijing Yizhuang transportation network. The computations show that an average total delivery cost savings of 4.5% is feasible. In addition, we analyze the impact of demand distributions and compare the ALNS algorithm and the LNS algorithm. Finally, we conclude that dynamically integrating public transport into freight transport services can benefit both logistics companies and public transport operators.