Abstract:

Urban metro systems are highly vulnerable to equipment failures and delays in spare-parts supply due to operational interdependence among stations, high passenger density, and the time-sensitive nature of services. In such systems, the shortage of critical spare parts may reduce service level, increase recovery time, and disrupt the performance of different parts of the network. On the other hand, a purely cost-oriented design may expose the network to severe operational risks under critical scenarios. This study aims to develop a risk-averse multi-objective stochastic optimization model for designing a metro spare-parts support network. The proposed framework integrates facility location, reliability-level selection, inventory management, direct shipment, horizontal transshipment, and service-loss risk control within a unified decision-making structure.

The proposed model is formulated as a two-stage, multi-period, multi-item, scenario-based mixed-integer linear programming model. In the first stage, strategic decisions are made, including the activation of support centers, the selection of reliability levels, and the activation of horizontal transshipment links. In the second stage, after the realization of operational scenarios, decisions related to procurement, direct shipment, horizontal transshipment, inventory holding, and controlled shortage are determined. To control the risk of service-level deterioration, the conditional value-at-risk criterion is incorporated into the model. The bi-objective problem is solved using the epsilon-constraint method. The numerical study is designed based on the operational structure of Tehran’s metro network and includes two central hubs, two local support centers, six demand stations, two types of spare parts, three planning periods, and four operational scenarios.

The computational results reveal a clear and interpretable trade-off between the total network cost and the risk of service-level loss. In the fully risk-averse solution, the total cost is 10,780.882, while the service-loss risk is zero. In this case, the service level remains equal to one in all scenarios, and the amount of horizontal transshipment in the critical scenario reaches 149.600 standard spare-part units. This result indicates that achieving a complete service level under critical conditions requires more extensive use of horizontal transshipment and a higher total cost. At the balanced point of the Pareto frontier, the total cost decreases to 10,681.559, while the risk value equals 0.013. At this point, the service level in the critical scenario is 0.987, and the amount of horizontal transshipment is 54.990. This solution provides a suitable balance between economic efficiency and operational resilience. In the minimum-cost solution, the total cost decreases further to 10,629.341, but the risk value increases to 0.045, and the service level in the critical scenario decreases to 0.955. In this solution, one local center is removed from the network, indicating the model’s tendency to reduce fixed costs at the expense of accepting a higher level of risk. The network design results show that all centers remain active in risk-averse solutions, whereas the network structure becomes more compact in the minimum-cost solution. Sensitivity analysis also confirms the key role of horizontal transshipment. Removing this mechanism increases the shortage in the critical scenario from 6.630 to 57.320 units, raises the risk value from 0.013 to 0.115, and reduces the service level from 0.987 to 0.885. Furthermore, central hub capacity, demand intensity in the critical scenario, and shortage penalty are identified as the most influential factors affecting network performance.





The findings indicate that a risk-averse design of a metro spare-parts support network is more capable of maintaining service level under critical conditions than a purely cost-oriented design. Combining sufficient hub capacity, appropriate reliability-level selection, and targeted horizontal transshipment can serve as an effective policy for improving the operational resilience of metro support systems.