A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing

During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict w...

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Published in:	Mathematical problems in engineering Vol. 2014; no. 1
Main Authors:	Cui, Jianxun, An, Shi, Zhao, Meng
Format:	Journal Article
Language:	English
Published:	New York Hindawi Publishing Corporation 01.01.2014 John Wiley & Sons, Inc
Subjects:	Disasters Emergency procedures Evacuation Evacuations & rescues Mathematical models Mathematical problems Minimum cost Mixed integer Networks Nonlinear programming Nuclear accidents & safety Redesign Roads Routing Seismic phenomena Travel time Vehicles Windows (intervals)
ISSN:	1024-123X, 1563-5147
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Abstract	During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR) function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed-integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.
AbstractList	During real‐life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR) function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed‐integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.
Author	Zhao, Meng An, Shi Cui, Jianxun
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Cites_doi	10.1177/0361198106196400117 10.1002/1520-6750(198708)34:4<487::AID-NAV3220340404>3.0.CO;2-9 10.1016/j.tra.2011.03.008 10.1109/TKDE.2007.190722 10.1016/j.trc.2010.03.007 10.4153/CJM-1956-045-5 10.1307/mmj/1028998140 10.1016/S0965-8564(03)00007-7 10.1016/0377-2217(88)90382-7 10.3141/2091-09 10.1016/j.tre.2009.11.004 10.1061/(ASCE)0733-947X(2008)134:1(41) 10.1108/03684920910973180 10.6028/jres.073B.010 10.1016/S0965-8564(02)00015-0 10.1023/B:JMMA.0000026708.57419.6d 10.1016/j.sbspro.2012.06.1084 10.1007/BF02993491 10.1016/j.elerap.2006.12.002
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Copyright	Copyright © 2014 Jianxun Cui et al. Copyright © 2014 Jianxun Cui et al. Jianxun Cui et al. 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.
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SubjectTerms	Disasters Emergency procedures Evacuation Evacuations & rescues Mathematical models Mathematical problems Minimum cost Mixed integer Networks Nonlinear programming Nuclear accidents & safety Redesign Roads Routing Seismic phenomena Travel time Vehicles Windows (intervals)
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Title	A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing
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