Abstract
LetV = {v 1,⋯, v n } be a set ofn points on the real line (existing facilities). The problem considered is to locatep new point facilities,F 1,⋯, F p , inV while satisfying distance constraints between pairs of existing and new facilities and between pairs of new facilities. Fori = 1, ⋯, p, j = 1, ⋯, n, the cost of locatingF i at pointv j isc ij . The objective is to minimize the total cost of setting up the new facilities. We present anO(p 3 n 2 logn) algorithm to solve the model.
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References
D. Chhajed and T.J. Lowe, “m-Median andm-Center problems with mutual communication: solvable special cases,”Operations Research 40 (1992) S56-S66.
D. Chhajed and T.J. Lowe, “Solving structured multifacility location problems efficiently,”Transportation Science 28 (1994) 104–115.
R.L. Francis, T.J. Lowe and H.D. Ratliff, “Distance constraints for tree network multifacility location problems,”Operations Research 26 (1978) 570–596.
M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1979).
A. Goldberg and R. Tarjan, “A new approach to the maximum flow problem,”Journal of the ACM 35 (1988) 921–940.
A. Kolen, Location problems on trees and in the rectilinear plane, Mathematisch Centrum, Amsterdam (1982).
G.L. Nemhauser and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley, New York, 1988).
J.C. Picard, “Maximal closure of a graph and applications to combinatorial problems,”Management Science 22 (1976) 1268–1272.
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Tamir, A. A distance constrainedp-facility location problem on the real line. Mathematical Programming 66, 201–204 (1994). https://doi.org/10.1007/BF01581145
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DOI: https://doi.org/10.1007/BF01581145