The least element property of center location on tree networks with applications to distance and precedence constrained problems

The least element property of center location on tree networks with applications to distance and precedence constrained problems

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Article ID: iaor19951895
Country: Netherlands
Volume: 62
Issue: 3
Start Page Number: 475
End Page Number: 496
Publication Date: Dec 1993
Journal: Mathematical Programming (Series A)
Authors:
Keywords: location
Abstract:

In the classical p-center location model on a network there is a set of customers, and the primary objective is to select p service centers that will minimize the maximum distance of a customer to a closest center. Suppose that the p centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective ‘as close as possible’ to the central depot. The paper considers tree networks and two p-center models. It shows that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property the paper proves that there is a p-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of the p centers from the existing central depot. Restricting the location models to a rooted path network (real line) it proves that the above results hold for the respective classical p-median problems as well.

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