Article1986

Solving Nonlinear Single-Facility Network Location Problems

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Facility Location and Emergency Management Complexity and Algorithms in Graphs Optimization and Mathematical Programming

Abstract

We present a general approach to solving nonlinear single-facility network location problems. We assume that cost is any convex function of distances, and solve this class of problem by solving convex subproblems on “treelike segments” into which the network is decomposed. We show that only a fraction of treelike segments generally need be examined, and that our method results in a reasonably efficient general-purpose algorithm. The algorithm is particularly effective on real-world (as opposed to random) networks, and when the cost function is nondecreasing and “semiseparable,” as are many popular cost functions. Finally, we describe theoretical complexity bounds and computational experience.

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References

1964Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph 1971Optimal Center Location in Simple Networks 1979Location on Networks: Theory and Algorithms 1978Locating an Obnoxious Facility on a Network 1973Minimax Location of a Facility in an Undirected Tree Graph 1976THE LOCATION OF A CENTER‐MEDIAN CONVEX COMBINATION ON AN UNDIRECTED TREE*1978Finding Minimal Center-Median Convex Combination (Cent-Dian) of a Graph 1976Convex Location Problems on Tree Networks

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1989An Overview of Representative Problems in Location Research 2002Solving Rectilinear Planar Location Problems with Barriers by a Polynomial Partitioning 1998An Axiomatic Characterization of a Class of Locations in Tree Networks 2011Discrete Center Problems 1985Location problems 1998A spanning tree approach to the absolute p-center problem

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