Annals of Operations Research

, Volume 283, Issue 1–2, pp 591–612 | Cite as

Partial contraflow with path reversals for evacuation planning

  • Urmila PyakurelEmail author
  • Hari Nandan Nath
  • Tanka Nath Dhamala
S.I.: Applications of OR in Disaster Relief Operations


The challenges in evacuation planning have been vital because of rapid disasters and limited road capacity. Contraflow strategy is very effective and widely accepted approach for the optimal use of available road network in evacuation management that increases the outward road capacities from the disastrous areas towards the safe destinations. Modeling the contraflow problem mathematically, there are available a number of efficient solution algorithms in literature, however, in general, the problem is still computationally quite hard. In this paper, we introduce the partial contraflow approach, in the abstract network setting with flow on paths and adapt the previous contraflow solution techniques to save unused capacities of road segments (elements) which can be used for supplying other facilities during emergency. We present efficient algorithms to solve the maximum static, lex-maximum static, maximum dynamic and earliest arrival partial contraflow problems on an abstract network. We also present an approximation algorithm to solve 2-value approximate earliest arrival transshipment partial contraflow problem for multi-terminal abstract network. Implementation of the partial contraflow reconfiguration leads to a significant improvement in increasing the flow values, decreasing the evacuation time, and utilizing the unused capacities of paths for humanitarian logistics and vehicle movements.


Evacuation planning Partial contraflow Abstract flow Switching property Flow maximization 



The authors acknowledge the supports of DAAD Partnership Program and AvH Research Group Linkage Program in Graph Theory and Optimization at Central Department of Mathematics, Tribhuvan University. Additionally, the first author thanks AvH Foundation for supporting the postdoctoral research at TU Bergakademie Freiberg, Germany and the second author thanks UGC Nepal for PhD research fellowship. The authors would also like to thank the anonymous referees and the editor for their valuable suggestions to improve the quality of this paper.


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Copyright information

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

Authors and Affiliations

  • Urmila Pyakurel
    • 1
    Email author
  • Hari Nandan Nath
    • 2
  • Tanka Nath Dhamala
    • 1
  1. 1.Central Department of MathematicsTribhuvan UniversityKathmanduNepal
  2. 2.Department of Mathematics, Bhaktapur Multiple CampusTribhuvan UniversityBhaktapurNepal

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