Evacuation Contraflow Problems with Not Necessarily Equal Transit Time on Anti-parallel Arcs

An evacuation planning problem provides a plan for existing road topology that sends maximum number of evacuees from risk zone to the safe destination in minimum time period during disasters. The problems with different road network attributes have been studied, and solutions have been proposed in literature. Evacuation planning problems with network contraflow approach, reversing the direction of traffic flow on lanes, with the same transit time on anti-parallel arcs have also been extensively studied. The approach, due to its lane-direction reversal property, can be taken as a potential remedy to mitigate congestion and reduce casualties during emergencies. In this paper, we propose a mathematical optimization contraflow model for the evacuation problem with the case where there may exist different transit time on anti-parallel arcs. We also propose analytical solutions to a few variants of problems, such as maximum dynamic contraflow problem and earliest arrival contraflow problem in which arc reversal capability is allowed only once at time zero. We extend the solution to solve the problems with continuous time settings by applying the natural relation between discrete time flows and continuous time flows. The solution procedures are based on application of temporally repeated flows (TRFs) on modified network, and they solve the problems optimally in strongly polynomial time.