Scheduling shared passenger and freight transport for an underground logistics system

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.