# American Institute of Mathematical Sciences

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 & Management Optimization, 2015, 11 (1) : 265-289. doi: 10.3934/jimo.2015.11.265
##### References:
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##### References:
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Skutella, Solving evacuation problems efficiently, earliest arrival flows with multiple sources,, in Foundations of Computer Science, (2006), 399. 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. doi: 10.1287/moor.1090.0382. [9] G. N. Berlin, The Use of Directed Routes for Assigning Escape Potential,, National Fire Protection Association, (1979). [10] D. R. Bish, Planning for a bus-based evacuation,, OR Spectrum, 33 (2011), 629. 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. 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, (1991), 189. [13] R. E. Burkard, K. Dlaska and B. Klinz, The quickest flow problem,, ZOR-Methods and Models of Operations Research, 37 (1993), 31. 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. 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. doi: 10.1007/BF02993491. [16] L. Chen and E. Miller-Hooks, The building evacuation problem with shared information,, Naval Research Logistics, 55 (2008), 363. doi: 10.1002/nav.20288. [17] Y. L. Chen and Y. H. Chin, The quickest path problem,, Computers and Operations Research, 17 (1990), 153. 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. 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. [20] K. F. Doerner, W. J. Gutjahr and L. V. Wassenhove, Special issue on optimization in disaster relief,, OR Spectrum, 33 (2011), 445. doi: 10.1007/s00291-011-0262-3. [21] Decision Support System for Large-Scale Evacuation Logistics, Homepage, 2012,, , (). [22] B. Eksioglu, A.V. Vural and A. Reisman, The vehicle routing problem: A taxonomic review,, Computers & Industrial Engineering, 57 (2009), 1472. doi: 10.1016/j.cie.2009.05.009. [23] L. Fleischer, Universally maximum flow with piecewise-constant capacities,, Networks, 38 (2001), 115. doi: 10.1002/net.1030. [24] L. Fleischer and E. Tardos, Efficient continuous-time dynamic network flow algorithms,, Operations Research Letters, 23 (1998), 71. 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. doi: 10.1137/S1052623497327295. [26] L. K. Fleischer and M. Skutella, Quickest multicommodity flow problem,, in Integer Programming and Combinatorial Optimization, 2337 (2002), 36. 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. doi: 10.1137/S0097539703427215. [28] F. R. Ford and D. R. Fulkerson, Constructing maximal dynamic flows from static flows,, Operations Research, 6 (1958), 419. doi: 10.1287/opre.6.3.419. [29] F. R. Ford and D. R. Fulkerson, Flows in Networks,, Princeton University Press, (1962). [30] D. Gale, Transient flows in networks,, Michigan Mathematical Journal, 6 (1959), 59. doi: 10.1307/mmj/1028998140. [31] G. M. Gallo, M. Grigoriadis and R. E. Tarjan, A Fast parametric maximum flow algorithm and applications,, SIAM Journal of Computing, 18 (1989), 30. doi: 10.1137/0218003. [32] B. George, S. Kim and S. Shekhar, Spatio-temporal network databases and routing algorithms: A summary of results,, in Proceedings of the 11th International Symposium on Spatial and Temporal Databases (SSTD), 4605 (2007), 460. doi: 10.1007/978-3-540-73540-3_26. [33] B. George and S. Shekhar, Time-aggregated Graphs for Modeling Spatio-temporal Networks- An Extended Abstract,, in Proceedings of the Workshop at International Conference on Conceptual Modeling, (2006). [34] M. Grötschel, L. Lovász and A. Schrijver, Geometric Algorithms and Combinatorial Optimization,, Springer Verlag Berlin, (1988). doi: 10.1007/978-3-642-97881-4. [35] B. Hajek and R. G. Ogier, Optimal dynamic routing in communication networks with continuous traffic,, Networks, 14 (1984), 457. doi: 10.1002/net.3230140308. [36] J. Halpern, A generalized dynamic flows problem,, Networks, 9 (1979), 133. doi: 10.1002/net.3230090204. [37] H. W. Hamacher, Min Cost and Time Minimizing Dynamic Flows,, Technical Report 83-16, (1983), 83. [38] H. W. Hamacher, S. Heller and B. Rupp, Flow location (FlowLoc) problems: dynamic network flows and location models for evacuation planning,, Annals of Operations Research, 207 (2013), 161. doi: 10.1007/s10479-011-0953-9. [39] H. W. Hamacher, S. Heller and S. Ruzika, A Sandwich Approach for Evacuation Time Bounds,, in PED 2010 Conference Proceedings, (2010). [40] H. W. Hamacher and S. A. Tjandra, Mathematical Modeling of Evacuation Problems: A State of the Art,, in Pedestrain and Evacuation Dynamics, (2002), 227. [41] H. W. Hamacher and S. Tufecki, On the use of lexicographic min-cost flows in evacuation modeling,, Naval Research Logistics, 34 (1987), 487. doi: 10.1002/1520-6750(198708)34:4<487::AID-NAV3220340404>3.0.CO;2-9. [42] G. Hamza-Lup, K. A. Hua, M. Le and R. 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