In continuous location theory , facilities to be optimally located are generally represented by points, and the customers or markets that they serve are also geometrical points in space. The objective is to find the optimal site of one or more facilities with respect to a specified performance measure such as the sum of transportation costs. This is one of the oldest formal optimization problems in mathematics and has a long and interesting history ([11], [9, Sect. 1.3], [4], [6]). Many variants of the problem exist. A very basic version of the location problem is to minimize:
where x = (x 1, x 2) is the unknown facility location in R 2, w i is a positive weight representing transportation cost per unit distance for customer i, and d(x − a i ) is the distance from the facility location x to the demand location a i = (a i1, a i2) of demand point i. The most common distance measure is Euclidean or straight-line distance and in this case, the most common solution procedure is some form...
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brimberg, J., and Mehrez, A.: ‘Multi-facility location using a maximin criterion and rectangular distances’, Location Sci.2 (1994), 11–19.
Brimberg, J., and Wesolowsky, G.O.: ‘A note on facility location with closest rectangular distances’, McMaster Univ., Canada (1998), submitted for publication.
Buchanan, D.J., and Wesolowsky, G.O.: ‘Locating a noxious facility with respect to several polygonal regions using asymmetric distances’, IIE Trans.25, no. 1 (1993), 77–88.
Drezner, Z. (ed.):Facility location: A survey of applications and methods, Springer, 1995.
Drezner, Z., and Wesolowsky, G.O.: ‘The location of an obnoxious facility with rectangular distances’, J. Reg. Sci.23 (1983), 241–248.
Francis, R.L., McGinnis Jr., L.F., and White, J.A.:Facility layout and location: An analytical approach, Internat. Ser. Industr. and Systems Engin., second ed., Prentice-Hall, 1992.
Hamacher, H.W., and Nickel, S.: ‘Restricted planar location problems and applications’, Naval Res. Logist.42 (1995), 967–992.
Juel, H., and Love, R.F.: ‘An efficient computational procedure for solving multi-facility rectilinear facilities location problems’, Oper. Res. Quart.26 (1976), 697–703.
Love, R.F., Morris, J.G., and Wesolowsky, G.O.:Facilities location: Models and methods, North-Holland, 1988.
Morris, J.G.: ‘Convergence of the Weiszfeld algorithm for Weber problems using a generalized distance function’, Oper. Res.29 (1981), 37–48.
Wesolowsky, G.O.: ‘The Weber problem: Its history and perspectives’, Location Sci.1, no. 1 (1993), 5–23.
Wesolowsky, G.O., and Love, R.F.: ‘Location of facilities with rectangular distances among point and area destinations’, Naval Res. Logist. Quart.18, no. 1 (1971), 83–90.
Wesolowsky, G.O., and Love, R.F.: ‘A nonlinear approximation method for solving a generalized rectangular distance Weber problem’, Managem. Sci.18 (1972), 656–663.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this entry
Cite this entry
Wesolowsky, G.O., Brimberg, J. (2001). Optimizing Facility Location with Rectilinear Distances . In: Floudas, C.A., Pardalos, P.M. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-306-48332-7_372
Download citation
DOI: https://doi.org/10.1007/0-306-48332-7_372
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-6932-5
Online ISBN: 978-0-306-48332-5
eBook Packages: Springer Book Archive