The growing demand for rail transportation has intensified the need for designing an optimal and sustainable network to facilitate freight movement with minimal cost, time, and environmental impact. A key challenge in this domain is wagon failures and the resulting delays, underscoring the critical importance of timely and preventive maintenance. In this study, major stations are considered as hubs where defective wagons are consolidated and repaired. To address the multifaceted requirements of rail transport systems, a robust multi-objective mathematical model has been developed, incorporating economic and environmental objectives alongside social responsibility components, specifically, enhancing customer satisfaction (by reducing transit time) and improving employment opportunities as primary decision-making criteria. For solving the model, an enhanced epsilon-constraint method is employed for small-scale instances, while a combination of the weighted-sum approach and the Benders decomposition algorithm is applied to large-scale problems. Subsequently, a sensitivity analysis is conducted to evaluate the stability of solutions against variations in key parameters. Sensitivity analysis shows that wagon capacity is the most influential parameter, as increasing it significantly reduces infrastructure, transportation, inspection, and reward costs. Demand is another highly sensitive factor, directly affecting the number of hubs, locomotives, and the overall network size. Within the tested ranges, the model remained stable and no infeasibility was observed. Numerical results demonstrate that the proposed model not only exhibits high efficacy in managing rail transport networks but also simultaneously fulfills sustainability, economic, and social objectives.
The key innovations of this research include:
- Implementing hub stations within rail networks specifically for handling defective wagons,
- Incorporating environmental and social considerations into wagon collection protocols,
- Minimizing freight delivery delays through optimized repair logistics,
- Developing a sustainable multi-objective mathematical model for wagon collection and repair operations.
Despite the extensive literature on hub location and intermodal transportation systems, several significant research gaps remain. First, the application of hub stations specifically for managing defective freight wagons within rail networks has not been systematically investigated. Second, previous studies rarely incorporate environmental and social considerations, such as pollution reduction and job creation, into the collection and repair processes for defective wagons. Third, existing models do not explicitly address the minimization of freight delivery delays caused by wagon failures. Finally, no comprehensive sustainability–oriented multi–objective optimization framework has been proposed for simultaneously managing the collection, inspection, and repair of defective wagons in railway transportation systems.
The increasing reliance on rail transportation for freight movement has intensified the importance of efficient maintenance and repair systems for railway equipment. Wagon failures can lead to cascading operational disruptions, increased costs, and environmental impacts. Although previous research has addressed hub location design and transportation network optimization, the integration of maintenance logistics, sustainability considerations, and delay reduction remains largely unexplored. To address these limitations, this study proposes a novel multi–objective hub location–allocation model designed specifically for managing defective wagons in rail transportation networks. The model integrates economic efficiency, environmental sustainability, and social responsibility into a unified optimization framework while incorporating inspection processes under uncertainty. By applying robust optimization techniques and scalable solution approaches, the proposed framework provides practical insights for designing resilient and sustainable rail maintenance networks.
The steadily increasing demand for rail freight transportation has highlighted the pressing need for designing an efficient, sustainable, and resilient network, one capable of minimizing transportation costs, delays, and environmental impacts. A major challenge in rail network operations is wagon failures, which lead to significant delivery delays and diminished customer satisfaction. Operational reports and empirical data indicate that wagon failures account for a substantial portion of disruptions in rail transport systems. Addressing this challenge requires implementing preventive maintenance strategies and designing efficient processes for managing and relocating defective wagons. A key solution in this regard involves establishing a network of selected stations as repair hubs, where defective wagons are consolidated, unloaded, and serviced. This approach prevents complete train stoppages in case of failures, ensuring continuity in freight movement. Enhancing wagon maintenance processes can significantly reduce failure rates, derailments, and delays, ultimately improving network reliability, capacity, and productivity.
The present study develops a robust multi-objective optimization model that integrates various sustainability dimensions including economic, environmental, and social indicators to optimize hub location and defective wagon routing. The model incorporates customer satisfaction (through reduced delivery times) and employment generation as key social responsibility metrics in decision-making. Furthermore, accounting for variations in station demand levels, stations with superior technical and logistical infrastructure are designated as primary hubs to optimize defective wagon transfers, thereby reducing repair costs and downtime.
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The growing demand for rail freight underscores the necessity for designing efficient, resilient maintenance networks—particularly when wagon failures can disrupt entire supply chains. This research develops a multi-objective mathematical model for optimal repair station (hub) placement that simultaneously addresses economic, environmental, and social dimensions. Selected hubs function as consolidation, unloading, and repair centers, enabling defective wagon removal without halting trains. This structure reduces repair durations, enhances customer satisfaction, and improves system reliability while high-capacity wagons decrease locomotive needs, operational costs, and emissions. Social responsibility metrics (delivery time reduction and employment generation) are incorporated to reflect the model’s societal dimension.
For small-scale problems, an enhanced epsilon-constraint method was implemented, while large-scale instances employed
decomposition with weighted sum approaches, yielding efficient optimal solutions. Sensitivity analyses confirmed significant impacts of wagon capacity, demand fluctuations, and infrastructure costs on network structure, hub selection, and objective values. Robust optimization techniques incorporating uncertainty parameters enhanced real-world applicability.
Collectively, these findings demonstrate that intelligent multi-objective maintenance network design enhances rail transport productivity and sustainability while reducing operational disruptions, improving service quality, lowering costs, and strengthening corporate social responsibility. The results provide theoretical foundations and practical tools for policymakers, rail managers, and logistics planners developing resilient, sustainable networks.
While this study advances hub location-allocation modeling for rail networks, several constraints merit acknowledgment. The model’s reliance on static demand assumptions and predefined failure distributions may not fully reflect the dynamic uncertainties inherent in real-world operations, such as fluctuating cargo volumes or unexpected disruptions. Computational scalability, though addressed through
decomposition, remains untested for continental-scale networks, and the robustness framework could be enhanced to capture extreme scenarios like infrastructure failures. Practical implementation may also face hurdles, including data granularity gaps for parameters like environmental impacts and unmodeled institutional barriers (e.g., cross-regional policy alignment). These limitations underscore opportunities to integrate adaptive demand modeling, hybrid uncertainty techniques, and stakeholder-driven constraints in future work.
Future research directions should focus on extending the model to incorporate multimodal transport (road, air, maritime), implementing metaheuristic algorithms for larger-scale problems, and applying data-driven or fuzzy programming approaches for managing complex uncertainties.
Referencia:
Heidari, A., Khalilzadeh, M., Jolai, F., & Ziari, M. (2026). A multi-objective mathematical model for hub location-allocation with inspection under uncertainty: A Benders decomposition approach. Transportation Research Interdisciplinary Perspectives, 38, Article 102112. https://doi.org/10.1016/j.trip.2026.102112
