Skip to main content

Advertisement

Springer Nature Link
Log in

Macroscopic evacuation plans for natural disasters

A lexicographical approach for duration and safety criteria: Lex((Q|S) Flow)

  • Regular Article
  • Published:
OR Spectrum Aims and scope Submit manuscript

Abstract

Since the 1990s, problems regarding the evacuation of persons have been extensively studied in the literature. The proposed models can be classified into two main categories: macroscopic and microscopic models. The DSS_Evac_Logistic project (2015, http://projets.li.univ-tours.fr/dssvalog/?lang=en) is interested in the evacuation of people in the context of flooding, burning or seismic events for which insecurity, capacity, and time to cross roads vary over time. We consider the problem of large-scale evacuation of medium-sized cities, in situations where the evacuees must change their place of residence for a period ranging from several days to several months. As a part of this project, we assume as solved the problem of selecting a set of starting points and shelter locations. We develop discrete macroscopic models and methods that incorporate the risk and safety that are inherent in the context studied for evacuating persons. The problem that needs to be addressed is to determine the minimum overall evacuation time while minimizing the risk incurred by evacuees (i.e., maximize the amount of unharmed persons). In this context, we first propose a pseudopolynomial method, which is based on the shortest augmenting paths, without using a time-expanded network to tackle the earliest arrival flow and the quickest flow problems no-wait with time-dependent data. Then, we extend this approach to consider the safety criterion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. \({ Lex}({ Quickest}|{ Safest})~{ Flow}.\)

  2. Bureau de recherches géologiques et minières.

References

  • Aronson JE (1989) A survey of dynamic network flows. Ann Oper Res 20(1):1–66

    Article  Google Scholar 

  • Baumann N (2007) Evacuation by earliest arrival flows. Ph.D. thesis

  • Baumann N, Skutella M (2009) Earliest arrival flows with multiple sources. Math Oper Res 34(2):499–512

    Article  Google Scholar 

  • Borrmann A, Kneidl A, Köster G, Ruzika S, Thiemann M (2012) Bidirectional coupling of macroscopic and microscopic pedestrian evacuation models. Saf Sci 50(8):1695–1703 (Evacuation and Pedestrian Dynamics)

  • Bretschneider S (2012) Mathematical models for evacuation planning in urban areas, vol 659. Springer Science & Business Media, Berlin

  • Burkard RE, Dlaska K, Klinz B (1993) The quickest flow problem. Z Oper Res 37(1):31–58

    Google Scholar 

  • Chalmet LG, Francis RL, Saunders PB (1982) Network models for building evacuation. Fire Technol 18(1):90–113. doi:10.1007/BF02993491

  • Coutinho-Rodrigues JA, Tralhão L, Alçada-Almeida L (2012) Solving a location-routing problem with a multiobjective approach: the design of urban evacuation plans. J Trans Geogr 22:206–218

  • Disser Y, Skutella M (2015) The simplex algorithm is np-mighty. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp 858–872. SIAM

  • DSS_Evac_Logistic: Decision support system for large-scale evacuation logistics. http://projets.li.univ-tours.fr/dssvalog/?lang=en. Accessed 16 Nov 2015

  • Fleischer L, Skutella M (2007) Quickest flows over time. SIAM J Comput 36(6):1600–1630

    Article  Google Scholar 

  • Ford L, Fulkerson DR (1962) Flows in networks, vol 1962. Princeton University Press, Princeton

  • Göttlich S, Kühn S, Ohst JP, Ruzika S, Thiemann M (2011) Evacuation dynamics influenced by spreading hazardous material. NHM 6(3):443–464

    Article  Google Scholar 

  • Groß M, Skutella M (2015) A tight bound on the speed-up through storage for quickest multi-commodity flows. Oper Res Lett 43(1):93–95

    Article  Google Scholar 

  • Hamacher H, Heller S, Klein W, Köster G, Ruzika S (2011) A sandwich approach for evacuation time bounds. In: Peacock RD, Kuligowski ED, Averill JD (eds) Pedestr Evac Dyn. Springer, US, pp 503–513

    Chapter  Google Scholar 

  • Hamacher HW, Tjandra SA (2002) Mathematical modeling of evacuation problems: a state of the art. In: Schreckenberg, M, Sharma SD (eds) Pedestrian and Evacuation Dynamics, pp 227–266. Springer, Berlin

  • Hamacher HW, Tjandra SA (2003) Earliest arrival flows with time-dependent data. Tech. Rep. 88, Fachbereich Mathematik—TU Kaiserslautern. https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1449. Accessed 16 Nov 2015

  • Hoppe B, Tardos E (2000) The quickest transshipment problem. Math Oper Res 25(1):36–62

    Article  Google Scholar 

  • INSEE: Population data. http://www.insee.fr. Accessed 16 Nov 2015

  • Jarvis JJ, Ratliff HD (1982) Notesome equivalent objectives for dynamic network flow problems. Manag Sci 28(1):106–109

    Article  Google Scholar 

  • Klüpfel H, Meyer-König T, Wahle J, Schreckenberg M (2001) Microscopic simulation of evacuation processes on passenger ships. In: Bandini S, Worsch T (eds) Theory and practical issues on cellular automata. Springer, London, pp 63–71

    Chapter  Google Scholar 

  • Köhler E, Möhring RH, Spenke I (2008) Quickest flows: a practical model. Technische Universität, Berlin

  • Lämmel G, Klüpfel H, Nagel K (2011) Risk minimizing evacuation strategies under uncertainty. In: Peacock RD, Kuligowski ED, Averill JD (eds) Pedestr Evac Dyn. Springer, US, pp 287–296

    Chapter  Google Scholar 

  • Lemoine A, Bernardie S, Brivois O, De Martin F, Desramaut N, Le Roy S, Monfort Climent D, Negulescu C, Pedreros R, Sedan O, Chan Vong Q, Vagner A, Foerster E (2014) Ligurian earthquake: Seismic and tsunami scenario modeling, from hazard to risk assessment towards evacuation planning. In: 2nd European conference on earthquake engineering and seismology : 2ECEES 2014. Istanbul, Turkey

  • Miller-Hooks E, Patterson SS (2004) On solving quickest time problems in time-dependent, dynamic networks. J Math Modell Algorithms 3(1):39–71

    Article  Google Scholar 

  • Opasanon S, Miller-Hooks E (2009) The safest escape problem. J Oper Res Soc 60(12):1749–1758

    Article  Google Scholar 

  • OpenStreetMap: Openstreetmap data for provence alpes-cote-d’azur (including nice city). http://download.geofabrik.de/europe/france/provence-alpes-cote-d-azur.html. Accessed 16 Nov 2015

  • OpenStreetMap: Openstreetmap website. http://openstreetmap.fr. Accessed 16 Nov 2015

  • Powell WB, Jaillet P, Odoni A (1995) Stochastic and dynamic networks and routing. Handb Oper Res Manag Sci 8:141–295

    Article  Google Scholar 

  • Rosen JB, Sun SZ, Xue GL (1991) Algorithms for the quickest path problem and the enumeration of quickest paths. Comput Oper Res 18(6):579–584

    Article  Google Scholar 

  • Schmidt M, Skutella M (2014) Earliest arrival flows in networks with multiple sinks. Discrete Appl Math 164:320–327

    Article  Google Scholar 

  • Tjandra SA (2003) Dynamic network optimisation with application to the evacuation problem. Ph.D. thesis

  • Wayne KD (1999) Generalized maximum flow algorithms. Ph.D. thesis, Citeseer

  • Yuan F, Han LD (2010) A multi-objective optimization approach for evacuation planning. Proc Eng 3:217–227

    Article  Google Scholar 

Download references

Acknowledgments

We thank the anonymous reviewers for their helpful comments that helped shaping this paper. This research has been supported by the French National Agency of Research as ANR-11-SECU-002-01 (CSOSG 2011).

Author information

Authors and Affiliations

  1. Université François-Rabelais de Tours, LI EA 6300, OC CNRS 6305, Tours, France

    Ismaila Abderhamane Ndiaye & Emmanuel Neron

  2. Université de Technologie de Compiègne, HEUDIASYC UMR CNRS 7253, Compiègne, France

    Antoine Jouglet

Authors
  1. Ismaila Abderhamane Ndiaye
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Emmanuel Neron
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Antoine Jouglet
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Ismaila Abderhamane Ndiaye.

Appendix

Appendix

See Figs. 11, 12 and 13, and Tables 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 and 17.

Fig. 11
figure 11

Example of a time-expanded network

Full size image
Fig. 12
figure 12

Impacted area for Vesubie scenario over the whole city of Nice

Full size image
Fig. 13
figure 13

Impacted area for Vesubie scenario over the city center of Nice

Full size image
Table 7 Consumption of edges at each time point t
Full size table
Table 8 Safety of each chosen path and the number of people involved at each time point t
Full size table
Table 9 Status of flow memory at time point \(t=3\)
Full size table
Table 10 Status of flow memory at time point \(t=4\)
Full size table
Table 11 Status of flow memory at time point \(t=5\)
Full size table
Table 12 Status of flow memory at time point \(t=6\)
Full size table
Table 13 Status of flow memory at time point \(t=7\)
Full size table
Table 14 Status of flow memory at time point \(t=8\)
Full size table
Table 15 Status of flow memory at time point \(t=9\)
Full size table
Table 16 Status of flow memory at time point \(t=10\)
Full size table
Table 17 Status of flow memory at time point \(t=11\)
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ndiaye, I.A., Neron, E. & Jouglet, A. Macroscopic evacuation plans for natural disasters. OR Spectrum 39, 231–272 (2017). https://doi.org/10.1007/s00291-016-0451-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00291-016-0451-1

Keywords