# Vulnerability evaluation of freight railway networks using a heuristic routing and scheduling optimization model

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## Abstract

Railway network is an integral part of the economy of many countries. Identifying critical network elements can help network executives to take appropriate preventive actions before the occurrence of catastrophic disruptions or to add necessary redundancy to enhance the resilience of the rail network. The criticality of an element or a link is measured by calculating the increased cost or delay when that element is disrupted. In this paper, we proposed a framework for assessing the vulnerability of the freight rail networks by introducing two bi-level models. The first model determines those critical links which have the greatest impact on the routing cost when interdicted, and the next one takes the cost of rescheduling into account, in addition to that of routing, over all origins and destinations. Rerouting effects are already well-captured by existing alternative measures, but this study allows capturing the ramifications of rescheduling measures. The trains are scheduled by a time–space framework considering customer demand, track and station capacities, and time planning horizon. To overcome the difficulty of solving bi-level models, they are converted to single level models. To verify the models and the proposed approach, we considered a case study focused on three disruption scenarios for the railway network of Iran. The accuracy of the obtained results indicates the effectiveness of the proposed methodology. In addition, our method has a very short computational time in comparison with the network scan method (a full enumeration approach).

## Keywords

Railway network Vulnerability Routing and scheduling Network scan Mixed integer programming Bi-level model Single-level model## Notes

### Acknowledgements

The author would like to thank the reviewers for their valuable comments and suggestions which helped to improve the paper. This research was supported by the Iran National Science Foundation (INSF), Project No. 94806427.

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