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

- 147 Downloads
- 2 Citations

## 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.

## References

- Ahuja, R.K., Cunha, C.B., Şahin, G.: Network models in railroad planning and scheduling. In: Emerging Theory, Methods, and Applications, INFORMS, pp. 54–101 (2005)Google Scholar
- Assad, A.A.: Models for rail transportation. Transp. Res. Part A Gen.
**14**(3), 205–220 (1980)CrossRefGoogle Scholar - Berdica, K.: An introduction to road vulnerability: what has beendone, is done and should be done. Transp. Policy
**9**, 117–127 (2002)CrossRefGoogle Scholar - Burdett, R., Kozan, E.: Determining operations affected by delay in predictive train timetables. Comput. Oper. Res.
**41**, 150–166 (2014)CrossRefGoogle Scholar - Cats, O., Jenelius, E.: Beyond a complete failure: the impact of partial capacity degradation on public transport network vulnerability. Transp. B Transp. Dyn., 1–20 (2016). doi: 10.1080/21680566.2016.1267596
- Dehghani, M.S., Flintsch, G., McNeil, S.: Impact of road conditions and disruption uncertainties on network vulnerability. J. Infrastruct. Syst.
**20**(3), 04014015 (2014)CrossRefGoogle Scholar - Derrible, S., Kennedy, C.: The complexity and robustness of metro networks. Physica A
**389**(17), 3678–3691 (2010)CrossRefGoogle Scholar - Gedik, R., Medal, H., Rainwater, C., Pohl, E.A., Mason, S.J.: Vulnerability assessment and re-routing of freight trains under disruptions: a coal supply chain network application. Transp. Res. Part E Logist. Transp. Rev.
**71**, 45–57 (2014)CrossRefGoogle Scholar - Jenelius, E., Mattsson, L.-G.: Road network vulnerability analysis of area-covering disruptions: a grid-based approach with case study. Transp. Res. Part A Policy Pract.
**46**(5), 746–760 (2012)CrossRefGoogle Scholar - Jenelius, E., Petersen, T., Mattsson, L.-G.: Importance and exposure in road network vulnerability analysis. Transp. Res. Part A Policy Pract.
**40**(7), 537–560 (2006)CrossRefGoogle Scholar - Khaled, A.A., Jin, M., Clarke, D.B., Hoque, M.A.: Train design and routing optimization for evaluating criticality of freight railroad infrastructures. Transp. Res. Part B Methodol.
**71**, 71–84 (2015)CrossRefGoogle Scholar - Lawley, M., et al.: A time–space scheduling model for optimizing recurring bulk railcar deliveries. Transp. Res. Part B
**42**, 438–454 (2008)CrossRefGoogle Scholar - Nemani, A.K., Ahuja, R.K.: OR models in freight railroad industry. In: Wiley Encyclopedia of Operations Research and Management Science (2011). doi: 10.1002/9780470400531.eorms0622
- Peterson, S.K., Church, R.L.: A framework for modeling rail transport vulnerability. Growth Change
**39**(24), 617–641 (2008)CrossRefGoogle Scholar - RAI: Year Book of Railway, Overview report. In: Bureau of Transportation Statistics–Department of Transportation, Iran (2014)Google Scholar
- Rodríguez-Núñez, E., García-Palomares, J.C.: Measuring the vulnerability of public transport networks. J. Transp. Geogr.
**35**, 50–63 (2014)CrossRefGoogle Scholar - Scott, D.M., Novak, D.C., Aultman-Hall, L., Guo, F.: Network robustness index: a new method for identifying critical links and evaluating the performance of transportation networks. J. Transp. Geogr.
**14**(3), 215–227 (2006)CrossRefGoogle Scholar - Sherali, H.D., Suharko, A.B.: A tactical decision support system for empty railcar management. Transp. Sci.
**32**(4), 306–329 (1998)CrossRefGoogle Scholar - Sherali, H.D., Tuncbilek, C.H.: Static and dynamic time-space strategic models and algorithms for multilevel rail-car fleet management. Manage. Sci.
**43**(2), 235–250 (1997)CrossRefGoogle Scholar - Taylor, M.A.: Remoteness and accessibility in the vulnerability analysis of regional road networks. Transp. Res. Part A Policy Pract.
**46**(5), 761–771 (2012)CrossRefGoogle Scholar - Taylor, M.A., Sekhar, S.V., D’Este, G.M.: Application of accessibility based methods for vulnerability analysis of strategic road networks. Netw. Spat. Econ.
**6**(3–4), 267–291 (2006)CrossRefGoogle Scholar - Wang, Z., Chan, A.P., Yuan, J., Xia, B., Skitmore, M., Li, Q.: Recent advances in modeling the vulnerability of transportation networks. J. Infrastruct. Syst.
**21**(2), 06014002 (2014)CrossRefGoogle Scholar - Williams, H.P.: Model building in mathematical programming. Wiley, New York (2013)Google Scholar
- Zhang, Z., Li, X., Li, H.: A quantitative approach for assessing the critical nodal and linear elements of a railway infrastructure. Int. J. Crit. Infrastruct. Prot.
**8**, 3–15 (2015)CrossRefGoogle Scholar