Efficient Solution Approach to Maximum Flow Evacuation Planning Problem without Flow Conservation Aspect

Abstract

An attempt of shifting as more people as possible and/or their logistics from a dangerous place to a safer place is an evacuation planning problem. Such problems modeled on network have been extensively studied and the various efficient solution procedures have been established. The solution strategies for these problems are based on source-sink path augmentation and the flow function satisfies the flow conservation at each intermediate node. Besides this, the network flow problem in which flow may not be conserved at node necessarily could also be used to model the evacuation planning problem. This paper proposes a model for maximum flow evacuation planning problem on a singlesource-single-sink static network with integral arc capacities with holding capability of evacuees in the temporary shelter at intermediate nodes and extends the model into the dynamic case.

Model and Solution for Non-conservation Flow Evacuation Planning Problem

“…However, the model with the non-conservation constraint allows to keep at the intermediate places besides a maximum number of evacuees to send into the sink. A preliminary solution approach, which is based on the preflow and push algorithm investigated in [7], has been proposed in [1], [2] and [10].…”

Non-conserving Flow Aspect of Maximum Dynamic Flow Problem

“…A solution procedure to the problem with single-source-single-sink network with holding capability of the flow at intermediate nodes has been proposed in [16] and [2]. The procedure is based on the time-expanded network with ∈ − ∈ … ∪ and…”

“…Khadka and Bhandari [16] and Bhandari and Khadka [2] have purposed a modification on the preflow-push algorithm with an efficient solution procedure for a static network and have extended the problem on dynamic network. The solution for later case is based on time expanded network which has been explained in Section 4 below.…”

“…This approach sends the excess flow (evacuees) that is blocked to send into the sink back to the source and deletes from entire evacuation network since the flow conservation property is not maintained at nodes. The algorithm has been modified by Khadka and Bhandari [16] and Bhandari and Khadka [2] to solve the maximum evacuation planning problem on the network with holding capability of the flow on the temporary shelter of the intermediate nodes. They proposed a relaxation to allow holding evacuees in the temporary shelter at intermediate nodes instead of sending them back to the source.…”