Abstract
We consider the problem of locating a single facility on a network in the presence of r >= 2median‐type objectives, represented by r sets of edge weights (or lengths)corresponding toeach of the objectives. When r = 1, then one gets the classical 1‐median problem whereonly the vertices need to be considered for determining the optimal location (Hakimi [1]).The paper examines the case when r >= 2 and provides a method to determine the non‐dominatedset of points for locating the facility.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.L. Hakimi, Optimal locations switching centers and the absolute centers and medians of a graph, Operations Research 12(1964)450-459.
G. Handler and P. Mirchandani, Locations on Networks, MIT Press, 1979.
P. Harvinen, T. Rajala and K. Sinerva, A branch and bound algorithm for seeking the p-median, Operations Research 20(1972)173-178.
O. Kariv and S.L. Hakimi, Optimum distribution of switching centers in a communication network and some related graph-theoretic problems, Operations Research 13(1965)462-475.
O. Kariv and S.L. Hakimi, An algorithmic approach to network location problems. II: The p-medians, SIAM Journal of Applied Mathematics 37(1979)539-560.
P.B. Mirchandani and R.L. Francis, Discrete Location Theory, Wiley Interscience, 1990.
S.C. Narula, U.L. Ogbu and H.M. Samuelsson, An algorithm for the p-median problem, Operations Research 25(1977)709-712.
A. Oudjit, Mediam locations on deterministic and probabilistic multidimensional networks, Ph.D. Dissertation, Rensselaer Polytechnic Institute, Troy, NY, 1981.
S. Singer, Multi-centers and multimedians of a graph with an application to optimal warehouse location, Operations Research 16(1968) B-87-88.
Rights and permissions
About this article
Cite this article
Ramos, R., Ramos, M., Colebrook, M. et al. Locating a facility on a network with multiple median‐type objectives. Annals of Operations Research 86, 221–235 (1999). https://doi.org/10.1023/A:1018902701712
Issue Date:
DOI: https://doi.org/10.1023/A:1018902701712