Science China Mathematics

, Volume 61, Issue 11, pp 2079–2100 | Cite as

Efficient contraflow algorithms for quickest evacuation planning

  • Urmila Pyakurel
  • Hari Nandan Nath
  • Tanka Nath Dhamala


The optimization models and algorithms with their implementations on flow over time problems have been an emerging field of research because of largely increasing human-created and natural disasters worldwide. For an optimal use of transportation network to shift affected people and normalize the disastrous situation as quickly and Efficiently as possible, contraflow configuration is one of the highly applicable operations research (OR) models. It increases the outbound road capacities by reversing the direction of arcs towards the safe destinations that not only minimize the congestion and increase the flow but also decrease the evacuation time significantly. In this paper, we sketch the state of quickest flow solutions and solve the quickest contraflow problem with constant transit times on arcs proving that the problem can be solved in strongly polynomial time O(nm2(log n)2), where n and m are number of nodes and number of arcs, respectively in the network. This contraflow solution has the same computational time bound as that of the best min-cost flow solution. Moreover, we also introduce the contraflow approach with load dependent transit times on arcs and present an Efficient algorithm to solve the quickest contraflow problem approximately. Supporting the claim, our computational experiments on Kathmandu road network and on randomly generated instances perform very well matching the theoretical results. For sufficiently large number of evacuees, about double flow can be shifted with the same evacuation time and about half time is sufficient to push the given flow value with contraflow reconfiguration.


evacuation planning contra flow flow over time quickest flow load dependent transit time 


90B10 90C27 68Q25 90B06 90B20 


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This work was supported by Deutscher Akademischer Austauschdienst (German Academic Exchange Service) Partnership Program (with University of Kaiserslautern, Germany and Mindanao State University, Iligan Institute of Technology, Iligan, Philippines) and AvH Research Group Linkage Program (with Technische Universität Bergakademie Freiberg) in Graph Theory and Optimization at Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal. The first author was supported by the AvH Foundation for the Georg Forster Research Fellowship for post doctoral researchers at Technische Universität Bergakademic Freiberg Germany. The authors thank the anonymous referees for their valuable suggestions to improve the quality of this work.


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

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

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