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Macroscopic evacuation plans for natural disasters

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


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, 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.

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

  2. Bureau de recherches géologiques et minières.


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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).

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Correspondence to Ismaila Abderhamane Ndiaye.



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

Fig. 12
figure 12

Impacted area for Vesubie scenario over the whole city of Nice

Fig. 13
figure 13

Impacted area for Vesubie scenario over the city center of Nice

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

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Ndiaye, I.A., Neron, E. & Jouglet, A. Macroscopic evacuation plans for natural disasters. OR Spectrum 39, 231–272 (2017).

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  • Natural disaster
  • Pedestrian evacuation
  • Macroscopic model
  • Duration criterion
  • Safety criterion
  • Dynamic network