Duality and Distance Constraints for the Nonlinear p -Center Problem and Covering Problem on a Tree Network

B. C. Tansel, R. L. Francis, T. J. Lowe and M. L. Chen
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B. C. Tansel: Georgia Institute of Technology, Atlanta, Georgia
R. L. Francis: The University of Florida, Gainesville, Florida
T. J. Lowe: Purdue University, West Lafayette, Indiana
M. L. Chen: The University of Florida, Gainesville, Florida

Operations Research, 1982, vol. 30, issue 4, 725-744

Abstract: The problem of locating a fixed number, p , of facilities (centers) on a network, where there are constraints on the center locations and where the centers provide a service to customers (demand points) located at vertices of the network is addressed. The cost or “loss” of servicing a given demand point is a nonlinear function of the distance between the demand point and the closest center. We consider the case where the network has special structure (a tree network), i.e., there is a unique shortest path between any two points on the network. We also provide and interpret a dual to this problem and give polynomially bounded procedures for solving both problems. The primal location problem is solved with the aid of a related problem for which we also give a dual.

Keywords: 185 p-center location problem; 490 tree network; 651 duality for the nonlinear p-center problem (search for similar items in EconPapers)
Date: 1982
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