Abstract
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.
Highlights
IntroductionImportant notion during the response phase of disaster management, attempts to find an optimal evacuation plan with a realistic flow model where each evacuee is supposed to be evacuated in a minimal time period from a risky site (source) to a safe site (sink)
An evacuation planning problem, important notion during the response phase of disaster management, attempts to find an optimal evacuation plan with a realistic flow model where each evacuee is supposed to be evacuated in a minimal time period from a risky site to a safe site
Applying Algorithm 1 for the evacuation network depicted in Figure 1. for time horizon 10, the maximum dynamic contraflow with discrete time setting is of value 52, whereas the maximum dynamic flow without contraflow is of value 30
Summary
Important notion during the response phase of disaster management, attempts to find an optimal evacuation plan with a realistic flow model where each evacuee is supposed to be evacuated in a minimal time period from a risky site (source) to a safe site (sink). Despite the long history of studies of evacuation problems with contraflow approach, there is limited implementation in real emergency evacuations due to difficulty in using commonly employed methods to duplicate traffic conditions of real contraflow lane during an emergency [1] They have been adapted for evacuating some major metropolitan regions threatened by disasters. The first mathematical optimization model for contraflow problem is due to Rebennack et al [11] They have investigated analytical solution of maximum contraflow problem with polynomial time complexity for both static and dynamic networks. We call the two directed arcs ‘anti-parallel' if they join the same pair of nodes, but in opposite directions It is crucial, in case of uneven road architecture, for example, to take contraflow models on networks with not necessarily equal transit time on anti-parallel arcs into account for preparing evacuation tasks.
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