Abstract
This paper addresses the problem of locating a service facility on an undirected network having unreliable edges so that some equitable performance level of network service to the demand nodes is provided, termed as thereliable 1-center problem. Equivalently, a point is sought on a network that maximizes service availability to the most critical demand node, i.e., the node associated with the least service availability. Two sub-problems of thereliable 1-center problem are considered based on the form of the objective function: (a) thereli-minmax problem in which the maximum expected number of unsuccessful responses to demand requests over all nodes is minimized, and (b) thereli-maxmin problem in which the minimum expected number of successful responses to demand requests over all nodes is maximized. The objective functions of these two sub-problems are based on the calculation of 2-terminal reliabilities, which is#P-Complete for general networks. By modeling the operational probability of the edges as an exponential function of the physical distance, we present linear time algorithms that solve both sub-problems when applied on weighted or unweighted tree networks.
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Santiváñez, J., Melachrinoudis, E. Location of a reliable center on a tree network. Oper Res Int J 7, 419–445 (2007). https://doi.org/10.1007/BF03024856
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DOI: https://doi.org/10.1007/BF03024856