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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'doi:10.4236/ojdm.2011.13019 fatcat:utwsszueojcypiyzcwqtjnmuly