Emergency evacuation problem for a multi-source and multi-destination transportation network: mathematical model and case study

  • Jianghua Zhang
  • Yang Liu
  • Yingxue ZhaoEmail author
  • Tianhu Deng
S.I.: RealCaseOR


Disasters such as earthquake or tsunami can easily take the lives of thousands of people and millions worth of property in a fleeting moment. A successful emergency evacuation plan is critical in response to disasters. In this paper, we seek to investigate the multi-source, multi-destination evacuation problem. First, we construct a mixed integer linear programming model. Second, based on K shortest paths and user equilibrium, we propose a novel algorithm (hereafter KPUE), whose complexity is polynomial in the numbers of nodes and evacuees. Finally, we demonstrate the effectiveness of algorithm KPUE by a real evacuation network in Shanghai, China. The numerical examples show that the average computation time of the proposed algorithm is 95% less than that of IBM ILOG CPLEX solver and the optimality gap is no more than 5%.


Emergency evacuation Disasters and accidents User equilibrium Shortest path 



The first author’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. 71201093, 71571111), the Innovation Method Fund of China (Grant No. 2018IM020200), and the Fundamental Research Funds of Shandong University (Grant No. 2018JC055). The corresponding and third author’s work was partially supported by the National Natural Science Foundation of China (Grant Nos. 71871063, 71371052). The authors also would like to thank the Qilu Young Scholars and Tang Scholars of Shandong University for financial and technical supports.

Supplementary material


  1. Anon. (1984). Formulations of the DYNEV and I-DYNEV traffic simulation models used in ESF. Technical report, Federal Emergency Management Agency.Google Scholar
  2. Bish, D. R., & Sherali, H. D. (2013). Aggregate-level demand management in evacuation planning. European Journal of Operational Research, 224(1), 79–92.CrossRefGoogle Scholar
  3. Blake, E., & Zelinsky, D. (2017). National hurricane center tropical cyclone report: Hurricane Harvey. AL092017 August.Google Scholar
  4. Burkard, R. E., Dlaska, K., & Klinz, B. (1993). The quickest flow problem. Zeitschrift für Operations Research, 37(1), 31–58.Google Scholar
  5. Campos, V., Bandeira, R., & Bandeira, A. (2012). A method for evacuation route planning in disaster situations. Procedia-Social and Behavioral Sciences, 54, 503–512.CrossRefGoogle Scholar
  6. Chalmet, L., Francis, R., & Saunders, P. (1982). Network models for building evacuation. Management Science, 28(1), 86–105.CrossRefGoogle Scholar
  7. Chen, P. H., & Feng, F. (2009). A fast flow control algorithm for real-time emergency evacuation in large indoor areas. Fire Safety Journal, 44(5), 732–740.CrossRefGoogle Scholar
  8. Cherkassky, B. V., Goldberg, A. V., & Radzik, T. (1996). Shortest paths algorithms: Theory and experimental evaluation. Mathematical Programming, 73(2), 129–174.CrossRefGoogle Scholar
  9. Chiu, Y. C., & Zheng, H. (2007). Real-time mobilization decisions for multi-priority emergency response resources and evacuation groups: Model formulation and solution. Transportation Research Part E: Logistics and Transportation Review, 43(6), 710–736.CrossRefGoogle Scholar
  10. Chiu, Y. C., Zheng, H., Villalobos, J., & Gautam, B. (2007). Modeling no-notice mass evacuation using a dynamic traffic flow optimization model. IIE Transactions, 39(1), 83–94.CrossRefGoogle Scholar
  11. Choi, T. M., Cheng, T., & Zhao, X. (2016). Multi-methodological research in operations management. Production and Operations Management, 25(3), 379–389.CrossRefGoogle Scholar
  12. Contreras, I., Fernández, E., & Reinelt, G. (2012). Minimizing the maximum travel time in a combined model of facility location and network design. Omega, 40(6), 847–860.CrossRefGoogle Scholar
  13. Cova, T. J., & Johnson, J. P. (2003). A network flow model for lane-based evacuation routing. Transportation Research Part A: Policy and Practice, 37(7), 579–604.Google Scholar
  14. Dhingra, V., & Roy, D. (2015). Modeling emergency evacuation with time and resource constraints: A case study from gujarat. Socio-Economic Planning Sciences, 51, 23–33.CrossRefGoogle Scholar
  15. Eppstein, D. (1998). Finding the k shortest paths. SIAM Journal on computing, 28(2), 652–673.CrossRefGoogle Scholar
  16. Floridajobs. (2010). Florida keys local hurricane policies.
  17. Gupta, A., & Yadav, P. K. (2004). SAFE-R: A new model to study the evacuation profile of a building. Fire Safety Journal, 39(7), 539–556.CrossRefGoogle Scholar
  18. Hamacher, H. W., & Tjandra, S. A. (2002). Mathematical modelling of evacuation problems: A state of art. Pedestrian and evacuation dynamics (pp. 227–266). Berlin: Springer.Google Scholar
  19. He, X., Zheng, H., & Peeta, S. (2015). Model and a solution algorithm for the dynamic resource allocation problem for large-scale transportation network evacuation. Transportation Research Part C: Emerging Technologies, 59, 233–247.CrossRefGoogle Scholar
  20. Heintz, J., & Mahoney, M. (2012). Guidelines for design of structures for vertical evacuation from tsunamis. Technical report, Federal Emergency Management Agency.Google Scholar
  21. Hobeika, A. G., & Kim, C. (1998). Comparison of traffic assignments in evacuation modeling. IEEE Transactions on Engineering Management, 45(2), 192–198.CrossRefGoogle Scholar
  22. Hoppe, B., & Tardos, É. (2000). The quickest transshipment problem. Mathematics of Operations Research, 25(1), 36–62.CrossRefGoogle Scholar
  23. Knabb, R. D., Brown, D. P., & Rhome, J. R. (2006). Tropical cyclone report, hurricane Rita, 18–26 September 2005. National Hurricane Center.Google Scholar
  24. Kretz, T., Lehmann, K., & Hofsäß, I. (2014). User equilibrium route assignment for microscopic pedestrian simulation. Advances in Complex Systems, 17(02), 1450,010.CrossRefGoogle Scholar
  25. Latin, A. (2016). Hurricane matthew: Haiti south ’90% destroyed’.
  26. Leo, G., Lodi, A., Tubertini, P., & Di Martino, M. (2016). Emergency department management in Lazio, Italy. Omega, 58, 128–138.CrossRefGoogle Scholar
  27. Lim, G. J., Zangeneh, S., Baharnemati, M. R., & Assavapokee, T. (2012). A capacitated network flow optimization approach for short notice evacuation planning. European Journal of Operational Research, 223(1), 234–245.CrossRefGoogle Scholar
  28. Liu, H. X., Ban, J. X., Ma, W., & Mirchandani, P. B. (2007). Model reference adaptive control framework for real-time traffic management under emergency evacuation. Journal of Urban Planning and Development, 133(1), 43–50.CrossRefGoogle Scholar
  29. Lu, Q., George, B., & Shekhar, S. (2005). Capacity constrained routing algorithms for evacuation planning: A summary of results In SSTD (pp. 291–307). Springer.Google Scholar
  30. Lu, Q., Huang, Y., & Shekhar, S. (2003). Evacuation planning: A capacity constrained routing approach. Intelligence and Security Informatics, 64, 959–959.Google Scholar
  31. Murray-Tuite, P., & Wolshon, B. (2013). Evacuation transportation modeling: An overview of research, development, and practice. Transportation Research Part C: Emerging Technologies, 27, 25–45.CrossRefGoogle Scholar
  32. Paul, N. R., Lunday, B. J., & Nurre, S. G. (2017). A multiobjective, maximal conditional covering location problem applied to the relocation of hierarchical emergency response facilities. Omega, 66, 147–158.CrossRefGoogle Scholar
  33. Pursals, S. C., & Garzón, F. G. (2009). Optimal building evacuation time considering evacuation routes. European Journal of Operational Research, 192(2), 692–699.CrossRefGoogle Scholar
  34. Pyakurel, U., Dhamala, T. N., & Dempe, S. (2017). Efficient continuous contraflow algorithms for evacuation planning problems. Annals of Operations Research, 254(1–2), 335–364.CrossRefGoogle Scholar
  35. RSS. (2015). Report for 2014 shanghai stampede.
  36. Saadatseresht, M., Mansourian, A., & Taleai, M. (2009). Evacuation planning using multiobjective evolutionary optimization approach. European Journal of Operational Research, 198(1), 305–314.CrossRefGoogle Scholar
  37. Sayyady, F., & Eksioglu, S. D. (2010). Optimizing the use of public transit system during no-notice evacuation of urban areas. Computers and Industrial Engineering, 59(4), 488–495.CrossRefGoogle Scholar
  38. Sheffi, Y., Mahmassani, H., & Powell, W. B. (1982). A transportation network evacuation model. Transportation Research Part A: General, 16(3), 209–218.CrossRefGoogle Scholar
  39. Southworth, F. (1991). Regional evacuation modeling: A state-of-the-art review. New York: Center for Transportation Analysis, OAK Ridge National Laboratory.CrossRefGoogle Scholar
  40. Stepanov, A., & Smith, J. M. (2009). Multi-objective evacuation routing in transportation networks. European Journal of Operational Research, 198(2), 435–446.CrossRefGoogle Scholar
  41. Üster, H., Wang, X., & Yates, J. T. (2018). Strategic evacuation network design (send) under cost and time considerations. Transportation Research Part B: Methodological, 107, 124–145.CrossRefGoogle Scholar
  42. Xie, C., & Turnquist, M. A. (2011). Lane-based evacuation network optimization: An integrated lagrangian relaxation and tabu search approach. Transportation Research Part C: Emerging Technologies, 19(1), 40–63.CrossRefGoogle Scholar
  43. Xinhua. (2015). Typhoon chan-hom lands in e china, wreaks havoc.
  44. Zhang, X., & Chang, G. I. (2014). A dynamic evacuation model for pedestrian–vehicle mixed-flow networks. Transportation Research Part C: Emerging Technologies, 40, 75–92.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jianghua Zhang
    • 1
  • Yang Liu
    • 1
  • Yingxue Zhao
    • 2
    Email author
  • Tianhu Deng
    • 3
  1. 1.School of ManagementShandong UniversityJinanChina
  2. 2.School of International Trade and EconomicsUniversity of International Business and EconomicsBeijingChina
  3. 3.Department of Industrial EngineeringTsinghua UniversityBeijingChina

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