Optimal Locations on a Network

Richard E. Wendell · Arthur P. Hurter

46 citations0/0 files storedTransportation Science

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Facility Location and Emergency Management Complexity and Algorithms in Graphs Vehicle Routing Optimization Methods

Abstract

The paper considers the location of centers (e.g., plants, warehouses) on a network. Necessary conditions and sufficient conditions for optimal solutions to occur at nodes in the network are determined. The conditions include consideration of capacity constraints and the possibility that not all shipments are made via the “shortest route.” The cost functions may differ from arc to arc. A proof is given for the sufficiency of node locations in situations of multistage processing when transport costs are concave over each arc. Three sets of conditions under which it is necessary for an optimal solution to occur at a node are investigated. One set of conditions involves a production function characterization of the centers being located.

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References

1964Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph 1958Location and the Theory of Production 1970An Analysis of Private and Public Sector Location Models 1973Location Theory, Dominance, and Convexity 1964Investment and Production.1972Optimum Locations of Centers in Networks 1967An Extended Theorem for Location on a Network

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2008Asymmetric distances, semidirected networks and majority in Fermat–Weber problems 1982The median problem with congestion 1982Location theory and transportation costs 1977Multiplant Location for Profit Maximisation 1987Single Facility Location on Networks 1985Production and location on a network under demand uncertainty 1977A Survey of Recent Results for a Class of Facilities Location Problems 2007

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