Facility location for large-scale emergencies.

*(English)*Zbl 1209.90236Summary: In the \(p\)-center problem, it is assumed that the facility located at a node responds to demands originating from the node. This assumption is suitable for emergency and health care services. However, it is not valid for large-scale emergencies where most of facilities in a whole city may become functionless. Consequently, residents in some areas cannot rely on their nearest facilities. These observations lead to the development of a variation of the \(p\)-center problem with an additional assumption that the facility at a node fails to respond to demands from the node. We use dynamic programming approach for the location on a path network and further develop an efficient algorithm for optimal locations on a general network.

##### MSC:

90B85 | Continuous location |

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##### References:

[1] | Caprara, A., Fischetti, M., & Toth, P. (2000). Algorithms for the set covering problem. Annals of Operations Research, 98, 353–371. · Zbl 0974.90006 |

[2] | Chalmet, L., Leiserson, T., & Saunders, P. (1982). Network model for building evacuation. Management Science, 28, 86–105. |

[3] | Daskin, M. (2000). A new approach to solving the vertex P-center problem to optimality: algorithm and computational results. Communications of the Operations Research Society of Japan, 45(9), 428–436. |

[4] | Francis, R., & Chalmet, L. (1984). A negative exponential solution to an evacuation problem (Research Report No. 84-86). National Bureau of Standards, Center for Fire Research. |

[5] | Gary, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: W.H. Freeman. · Zbl 0411.68039 |

[6] | Handler, G. (1990). p-center problems. In P. B. Mirchandani & R. L. Francis (Eds.), Discrete Location Theory (pp. 305–347). New York: Wiley. · Zbl 0731.90049 |

[7] | Hoppe, B., & Tardos, E. (1994). Polynomial time algorithms for some evacuation problems. In Proceedings of the 5th annual ACM-SIAM symposium on discrete algorithms (pp. 433–441). · Zbl 0867.90048 |

[8] | Ilhan, T., Ozsoy, F., & Pinar, M. (2002). An efficient exact algorithm for the vertex p-center problem and computational experiments for different set covering subproblems (Technical report). Available at http://www.optimization-online.org/DB_HTML/2002/12/588.html . |

[9] | Jia, H., Ordonez, F., & Dessouky, M. (2007a). A modeling framework for facility location of medical services for large-scale emergencies. IIE Transactions, 39(1), 41–55. |

[10] | Jia, H., Ordonez, F., & Dessouky, M. (2007b). Solution approaches for facility location of medical supplies for large-scale emergencies. Computers & Industrial Engineering, 52, 257–276. |

[11] | Kariv, O., & Hakimi, S. (1979). An algorithmic approach to network location problems. I: the P-centers. SIAM Journal on Applied Mathematics, 37, 513–538. · Zbl 0432.90074 |

[12] | Lu, Q., Huang, Y., & Shekhar, S. (2003). Evacuation planning: a capacity constrained routing approach. In Proceedings of the first NSF/NIJ symposium on intelligence and security informatics (pp. 111–125), June 2003. |

[13] | Lu, Q., George, B., & Shekhar, S. (2006). Capacity constrained routing algorithms for evacuation route planning (Technical Report). Department of Computer Science and Engineering, University of Minnesota, May 2006. |

[14] | MacReady, N. (2008). After the storm. Neurology Lancet, 7(9), 772–773. |

[15] | Tansel, B., Francis, R., & Lowe, T. (1983). Location on networks: a survey. Part I: The p-center an p-median problems. Management Science, 29, 482–497. · Zbl 0513.90022 |

[16] | Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emergency service facilities. Operations Research, 19, 1363–1373. · Zbl 0224.90048 |

[17] | USGS (U.S. Geological Survey) (2008). Magnitude 7.9–Eastern Sichuan, China. http://earthquake.usgs.gov/eqcenter/eqinthenews/2008/us2008ryan/#details . |

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