R. L.Church, M. P. Scaparra and R. S. Middleton, “Identifying Critical Infrastructure, the Median and Covering Facility Interdiction Problems,” Annals of the Association of American Geographers, Vol. 94, No. 3, 2004, pp. 491- 502. doi:10.1111/j.1467-8306.2004.00410.x

has been cited by the following article:

• TITLE: Reliability Analysis of Facility Systems Subject to Edge Failures: Based on the Uncapacitated Fixed-Charge Location Problem

  AUTHORS: Zongtian Wei, Huayong Xiao

  KEYWORDS: Facility System, Reliability, Edge Failure, Uncapacitated Fixed-Charge Location Problem

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.1 No.3, October 17, 2011

  ABSTRACT: A facility system can be modeled by a connected graph in which the vertices represent entities such as suppliers, distribution centers or customers and the edges represent facilities such as the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. Such failures may be caused by various natural disasters or terrorist attacks. In this paper, we consider facility systems’ reliability analysis based on the classical uncapacitated fixed-charge location problem when subject to edge failures. For an existing facility system, we formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.