Abstract
Classical location theories and models were initially developed for the private sector, so that the related operational research literature has emphasized performance measures of efficiency and effectiveness. For public sector applications, measures of equity become important, yet such measures have received little formal treatment. This paper suggests a locational equity measure, the variance measure, and investigates its properties for tree networks. A fast algorithm (O(M)) to locate the minimum variance point on a tree network is developed, and some numerical results illustrate the variance optimal location.
Similar content being viewed by others
References
A.V. Aho, J.E. Hopcroft and J.D. Ullman,The Design and Analysis of Computer Algorithms (Addison-Wesley, 1976).
M. Avriel,Nonlinear Programming-Analysis and Methods (Prentice-Hall, 1976).
A.J. Goldman, Optimum location for centers in networks, Trans. Sci. 3(1969)352.
A.J. Goldman, Convex combination of points in tree networks, TIMS/ORSA Bulletin No. 9 (1980) TC 10.3 (abstract).
S.L. Hakimi, Optimum locations of switching centers and the absolute centers and medians of a graph, Oper. Res. 12(1964)450.
J. Halpern, Duality in the cent-dian of a graph, Oper. Res. 28(1980)722.
J. Halpern and O.Z. Maimon, Accord and conflict among several objectives in locational decisions on tree networks, in:Locational Analysis of Public Facilities, eds. J.F. Thisse and H.G. Zoller, Studies in Mathematical and Managerial Economics (North-Holland, Amsterdam, 1983) p. 301.
J. Halpern and O.Z. Maimon, Algorthim for them-center problems: A survey, Eur. J. Oper. Res. 10(1982)90.
G.Y. Handler, Medi-centers of a tree, Working paper 278/76, Tel-Aviv University, Israel (1976)
R.C. Larson and K. Stevenson, On insensitivities in urban redistricting and facility location, Oper. Res. 20(1972)595.
D.M. McAllister, Equity and efficiency in public facility location, Geographical Analysis 8(1976)47.
O.Z. Maimon, Equity measures in location decisions on trees, unpublished MSc Thesis, Technion, Israel (1980).
O.Z. Maimon, The Lorenz measure in locational decisions on trees, ISOLDE III Conf. Proc., Boston (1984).
E.S. Savas, On equity in providing public service, Management Science 24(1978)800.
Author information
Authors and Affiliations
Additional information
This work is dedicated to the memory of Professor Jonathan Halpern
Rights and permissions
About this article
Cite this article
Maimon, O. The variance equity measure in locational decision theory. Ann Oper Res 6, 147–160 (1986). https://doi.org/10.1007/BF02026822
Issue Date:
DOI: https://doi.org/10.1007/BF02026822