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Advances in Operations Research
Volume 2016, Article ID 7902460, 7 pages
Research Article

Continuous Time Dynamic Contraflow Models and Algorithms

Central Department of Mathematics, Tribhuvan University, P.O. Box 13143, Kathmandu, Nepal

Received 10 September 2015; Accepted 6 March 2016

Academic Editor: Konstantina Skouri

Copyright © 2016 Urmila Pyakurel and Tanka Nath Dhamala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The research on evacuation planning problem is promoted by the very challenging emergency issues due to large scale natural or man-created disasters. It is the process of shifting the maximum number of evacuees from the disastrous areas to the safe destinations as quickly and efficiently as possible. Contraflow is a widely accepted model for good solution of evacuation planning problem. It increases the outbound road capacity by reversing the direction of roads towards the safe destination. The continuous dynamic contraflow problem sends the maximum number of flow as a flow rate from the source to the sink in every moment of time unit. We propose the mathematical model for the continuous dynamic contraflow problem. We present efficient algorithms to solve the maximum continuous dynamic contraflow and quickest continuous contraflow problems on single source single sink arbitrary networks and continuous earliest arrival contraflow problem on single source single sink series-parallel networks with undefined supply and demand. We also introduce an approximation solution for continuous earliest arrival contraflow problem on two-terminal arbitrary networks.