American Institute of Mathematical Sciences

January  2015, 11(1): 265-289. doi: 10.3934/jimo.2015.11.265

A survey on models and algorithms for discrete evacuation planning network problems

 1 Central Departments of Mathematics/CSIT, IOST, Tribhuvan University, Kathmandu, Nepal

Received  May 2013 Revised  January 2014 Published  May 2014

With an increasing number of large-scale natural and man-created disasters over the last decade, there is growing focus on the application of operations research techniques for humanitarian relief in the emerging field of emergency evacuation. Even though a large diversity of models have been developed, many rely on solving network-flow problems on appropriate graphs. In this survey, we give a systematic collection of network flow models used in emergency evacuation and their applications. We especially focus on results interrelating these models. Considered models include max flows and min cost flows, lexicographic flows, quickest flows, and earliest arrival flows, as well as contraflows and time-dependent problems.
Citation: Tanka Nath Dhamala. A survey on models and algorithms for discrete evacuation planning network problems. Journal of Industrial and Management Optimization, 2015, 11 (1) : 265-289. doi: 10.3934/jimo.2015.11.265
References:
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References:
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Baumann, Evacuation by Earliest Arrival Flows, Ph.D thesis, Department of Mathematics, University of Dortmund, Germany, 2007. [7] N. Baumann and M. Skutella, Solving evacuation problems efficiently, earliest arrival flows with multiple sources, in Foundations of Computer Science, FOCS '06, (2006), 399-410. doi: 10.1109/FOCS.2006.70. [8] N. Baumann and M. Skutella, Earliest arrival flows with multiple sources, Mathematics of Operations Research, 34 (2009), 499-512. doi: 10.1287/moor.1090.0382. [9] G. N. Berlin, The Use of Directed Routes for Assigning Escape Potential, National Fire Protection Association, Boston, MA, 1979. [10] D. R. Bish, Planning for a bus-based evacuation, OR Spectrum, 33 (2011), 629-654. doi: 10.1007/s00291-011-0256-1. [11] S. Bretschneider and A. Kimms, Pattern-based evacuation planning for urban areas, European Journal of Operational Research, 216 (2012), 57-69. doi: 10.1016/j.ejor.2011.07.015. [12] R. E. Burkard, K. Dlaska and H. Kellerer, The quickest disjoint flow problem, Institute of Mathematics, University of Technology, Graz, Austria, (1991), 189-191. [13] R. E. Burkard, K. Dlaska and B. Klinz, The quickest flow problem, ZOR-Methods and Models of Operations Research, 37 (1993), 31-58. doi: 10.1007/BF01415527. [14] M. Carey and E. Subrahmanian, An approach to modelling time-varying flows on congested networks, Transportation Research B, 34 (2000), 157-183. doi: 10.1016/S0191-2615(99)00019-3. [15] L. G. Chalmet, R. L. Francis and P. B. Saunders, Network models for building evacuation, Fire Technology, 18 (1982), 90-113. doi: 10.1007/BF02993491. [16] L. Chen and E. Miller-Hooks, The building evacuation problem with shared information, Naval Research Logistics, 55 (2008), 363-376. doi: 10.1002/nav.20288. [17] Y. L. Chen and Y. H. Chin, The quickest path problem, Computers and Operations Research, 17 (1990), 153-161. doi: 10.1016/0305-0548(90)90039-A. [18] W. Choi, H. W. Hamacher and S. Tufekci, Modeling of building evacuation problems by network flows with side constraints, European Journal of Operations Research, 35 (1988), 98-110. doi: 10.1016/0377-2217(88)90382-7. [19] T. N. Dhamala and U. Pyakurel, Earliest arrival contraflow problem for evacuation planning on series-parallel graph, International Journal of Operations research, 10 (2013), 1-13. [20] K. F. Doerner, W. J. Gutjahr and L. V. Wassenhove, Special issue on optimization in disaster relief, OR Spectrum, 33 (2011), 445-449. doi: 10.1007/s00291-011-0262-3. [21] Decision Support System for Large-Scale Evacuation Logistics, Homepage, 2012, http://projets.li.univ-tours.fr/dssvalog/?lang=en [22] B. Eksioglu, A.V. Vural and A. Reisman, The vehicle routing problem: A taxonomic review, Computers & Industrial Engineering, 57 (2009), 1472-1483. doi: 10.1016/j.cie.2009.05.009. [23] L. Fleischer, Universally maximum flow with piecewise-constant capacities, Networks, 38 (2001), 115-125. doi: 10.1002/net.1030. [24] L. Fleischer and E. Tardos, Efficient continuous-time dynamic network flow algorithms, Operations Research Letters, 23 (1998), 71-80. doi: 10.1016/S0167-6377(98)00037-6. [25] L. K. Fleischer, Faster algorithms for quickest transshipment problem, SIAM Journal on Optimization, 12 (2001), 18-35. doi: 10.1137/S1052623497327295. [26] L. K. Fleischer and M. Skutella, Quickest multicommodity flow problem, in Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, Springer, 2337, (2002), 36-53. doi: 10.1007/3-540-47867-1_4. [27] L. K. Fleischer and M. Skutella, Quickest flows over time, SIAM Journal on Computing, 36 (2007), 1600-1630. doi: 10.1137/S0097539703427215. [28] F. R. Ford and D. R. Fulkerson, Constructing maximal dynamic flows from static flows, Operations Research, 6 (1958), 419-433. doi: 10.1287/opre.6.3.419. [29] F. R. Ford and D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, New Jersey, 1962. [30] D. 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