Abstract
Typical formulations of thep-median problem on a network assume discrete nodal demands. However, for many problems, demands are better represented by continuous functions along the links, in addition to nodal demands. For such problems, optimal server locations need not occur at nodes, so that algorithms of the kind developed for the discrete demand case can not be used. In this paper we show how the 2-median of a tree network with continuous link demands can be found using an algorithm based on sequential location and allocation. We show that the algorithm will converge to a local minimum and then present a procedure for finding the global minimum solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T.M. Cavalier and H.D. Sherali, Network location problems with continuous link demands: p-medians on a chain, 2-medians on a tree, and 1-medians on isolated cycle graphs, Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University (1983).
S.S. Chiu, The minisum location problem on an undirected network with continuous link demands, Engineering-Economic Systems Department, Stanford University (1982).
S.S. Chiu, O. Berman and R.C. Larson, Locating a mobile server queueing facility on a tree network, Operations Research Center, MIT, Paper no. OR117–82 (1982).
L.L. Cooper, Heuristic methods for location-allocation problems, SIAM Review 6, 1(1964)37.
L.L. Cooper, Location-allocation problems, Oper. Res. 11(1963)331.
L.L. Cooper, Solutions of generalized locational equilibrium models, J. Regional Science 7(1967)1.
S. Eilon, C.D.T. Watson-Gandy and N. Christofides,Distribution Management: Mathematical Modelling and Practical Analyses (Griffin Publ. Co., London, 1971).
B.L. Golden and F.B. Alt, Interval estimation of a global optimum for large combinatorial problems, Naval Research Logistics Quarterly 26, 1(1979)69.
B.L. Golden, Point estimation of a global optimum for large combinatorial problems, Communications in Statistics B7(1978)361.
A.J. Goldman, Optimal center location in simple networks, Transportation Science 5(1971)212.
S.L. Hakimi, Optimal locations of switching centers and the absolute centers and medians of a graph, Oper. Res. 12(1964)450.
P. Jarvinen, J. Rajala and H. Sinervo, A branch and bound algorithm for seeking thep-median, Oper. Res. 20(1972)173.
O. Kariv and S.L. Hakimi, An algorithmic approach to network location problems, part 2: Thep-medians, SIAM J. Appl. Math. 34(1979)539.
R.E. Kuenne and R.M. Soland, Exact and approximate solutions to the multisource Weber problem, Mathematical Programming 22(1972)193.
R.C. Larson and G. Sadiq, Facility locations with the Manhattan metric in the presence of barriers to travel, Oper. Res. 31(1983)652.
F.E. Maranzana, On the location of supply points to minimize transport costs, Operational Research Quarterly 15(1964)261.
D.W. Matula and R. Kolde, Efficient multi-median location in acyclic networks, ORSA/TIMS Bulletin, No. 2 (1976).
P.B. Mirchandani and A. Oudjit, Localizing 2-medians on probabilistic and deterministic tree networks, Networks 10(1980)329.
A.J. Scott, Location-allocation systems: A review, Geographical Analysis 2(1970)95.
D.R. Shier and P.M. Dearing, Optimal locations for a class of nonlinear problems on a network, Oper. Res. 31(1983)292.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brandeau, M.L., Chiu, S.S. & Batta, R. Locating the two-median of a tree network with continuous link demands. Ann Oper Res 6, 223–253 (1986). https://doi.org/10.1007/BF02024584
Issue Date:
DOI: https://doi.org/10.1007/BF02024584