Urban metro networks constitute one of the most critical public transportation infrastructures, playing a central role in daily passenger mobility and overall urban functionality. Due to their complex physical structure, high passenger density, and strong operational interdependencies among stations, metro systems are highly vulnerable to sudden equipment failures and operational disruptions. Even a localized failure at a key station can rapidly propagate through the network, leading to partial line shutdowns, significant service degradation, and substantial economic and social consequences. Under such circumstances, the timely availability of spare parts and the design of a resilient maintenance network become strategically essential to ensure rapid system recovery and service continuity. However, existing studies have predominantly focused either on the topological resilience analysis of metro networks or on spare-parts supply chains considered independently from the actual physical and operational structure of metro systems. This separation creates a critical gap in addressing real-world operational challenges. The primary objective of this research is therefore to develop a comprehensive framework for designing a resilient metro maintenance network that simultaneously and coherently integrates location decisions, capacity allocation, spare-parts flows, and operational interactions among stations.



To achieve this objective, this study proposes a comprehensive mixed-integer programming model for metro spare-parts supply network design. For the first time, the proposed model integrates the physical structure of the metro network, maintenance and repair requirements, spare-parts logistics flows, and operational responses to station failures within a unified optimization framework. The model jointly determines the optimal locations of central maintenance depots, the selection of local backup stations, the appropriate reliability levels, and the design of horizontal transshipment mechanisms that allow spare parts to be transferred directly between stations. To effectively address uncertainties associated with failure severity, demand patterns, and operational conditions, a scenario-based robust optimization approach is employed. In this framework, spare-parts shortages are strictly prohibited, reflecting the critical nature of metro operations, while the objective is to minimize the expected total system cost and simultaneously control cost deviations under worst-case scenarios.



Numerical experiments conducted using real data from an urban metro network demonstrate that the simultaneous design of central depots and backup stations, combined with the activation of horizontal transshipment, has a significant positive impact on network performance. The results indicate that under normal operating conditions, spare-parts supply flows are primarily handled through the hierarchical structure of the network. However, under disruption scenarios, the model automatically activates horizontal transshipment and intelligently redistributes inventory among stations, effectively preventing shortages. This adaptive mechanism leads to a substantial reduction in station recovery times, lower operational costs in severe disruption scenarios, and a notable improvement in the overall operational resilience of the metro network. Furthermore, the robust optimization results reveal that the adopted Mulvey-type framework achieves a balanced trade-off between average system cost and worst-case performance. Beyond a certain level of conservatism, the performance across scenarios converges, indicating that further increases in robustness yield diminishing operational benefits.



Overall, the proposed framework provides a practical and implementable decision-support tool for maintenance planning and spare-parts supply management in urban metro systems. The findings demonstrate that integrating location decisions, supply flows, and horizontal transshipment within a robust optimization framework can play a crucial role in enhancing operational resilience and significantly reducing service downtime in urban metro networks.



Keywords: Metro network resilience, horizontal spare-parts transshipment, robust optimization, scenario-based modeling