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On the use of lexicographic min cost flows in evacuation modeling

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  • H. W. Hamacher
  • S. Tufekci

Abstract

Building evacuation problems can be represented as dynamic network‐flow problems [3]. The underlying network structure of a building evolves through time yielding a time‐expanded network (a dynamic network). Usually in such evacuation problems involving time, more than one objective function is appropriate. For example, minimizing the total evacuation time and evacuating a portion of the building as early as possible are two such objectives. In this article we show that lexicographical optimization is applicable in handling such multiple objectives. Minimizing the total evacuation time while avoiding cyclic movements in a building and “priority evacuation” are treated as lexicographical min cost flow problems.

Suggested Citation

  • H. W. Hamacher & S. Tufekci, 1987. "On the use of lexicographic min cost flows in evacuation modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 487-503, August.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:4:p:487-503
    DOI: 10.1002/1520-6750(198708)34:43.0.CO;2-9
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    References listed on IDEAS

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    1. John J. Jarvis & H. Donald Ratliff, 1982. "Note---Some Equivalent Objectives for Dynamic Network Flow Problems," Management Science, INFORMS, vol. 28(1), pages 106-109, January.
    2. L. G. Chalmet & R. L. Francis & P. B. Saunders, 1982. "Network Models for Building Evacuation," Management Science, INFORMS, vol. 28(1), pages 86-105, January.
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    Cited by:

    1. Douglas Bish & Esra Agca & Roger Glick, 2014. "Decision support for hospital evacuation and emergency response," Annals of Operations Research, Springer, vol. 221(1), pages 89-106, October.
    2. K L Poh & K W Choo & C G Wong, 2005. "A heuristic approach to the multi-period multi-commodity transportation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 708-718, June.
    3. H. Taubenböck & N. Goseberg & G. Lämmel & N. Setiadi & T. Schlurmann & K. Nagel & F. Siegert & J. Birkmann & K.-P. Traub & S. Dech & V. Keuck & F. Lehmann & G. Strunz & H. Klüpfel, 2013. "Risk reduction at the “Last-Mile”: an attempt to turn science into action by the example of Padang, Indonesia," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 65(1), pages 915-945, January.
    4. Altay, Nezih & Green III, Walter G., 2006. "OR/MS research in disaster operations management," European Journal of Operational Research, Elsevier, vol. 175(1), pages 475-493, November.
    5. Lovas, Gunnar G., 1995. "On performance measures for evacuation systems," European Journal of Operational Research, Elsevier, vol. 85(2), pages 352-367, September.
    6. Bish, Douglas R. & Sherali, Hanif D., 2013. "Aggregate-level demand management in evacuation planning," European Journal of Operational Research, Elsevier, vol. 224(1), pages 79-92.
    7. S Opasanon & E Miller-Hooks, 2009. "The Safest Escape problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1749-1758, December.
    8. Nadine Baumann & Martin Skutella, 2009. "Earliest Arrival Flows with Multiple Sources," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 499-512, May.

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