# Location‐Allocation Systems: A Review

Location‐Allocation Systems: A Review âThe class of mathematical and geographical problems considered in this review is characterized by the following general structure: [Suppose that there are given (a) a set of n points distributed in the plane, (b) a numerical weight to be attached to each point, and (c) a set of m indivisible centroids without predetermined locations; then, the location-allocation problem, in its most general form, is to find locations for the m centroids and an allocation of each point, or fraction of a point, to some centroid so as to optimize an objective function3 The usual practical interpretation of this problem is to consider it as representative of a social or economic system which is identifiable as a set of flows between a number of central facilities and some set of geographically dispersed source or destination points. The problem is then simultaneously to locate the central facilities and to determine an assignment of flows, so that the total costs of operation of the system are the least possible. This sort of problem arises in a great variety of practical planning situations. It is strongly evident, for example, in the planning of geographical systems centered upon such phenomena as hospitals, schools, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geographical Analysis Wiley

# Location‐Allocation Systems: A Review

Geographical Analysis, Volume 2 (2) – Apr 1, 1970
25 pages

/lp/wiley/location-allocation-systems-a-review-oJH53cVoNU
Publisher
Wiley
1970 The Ohio State University
ISSN
0016-7363
eISSN
1538-4632
DOI
10.1111/j.1538-4632.1970.tb00149.x
Publisher site
See Article on Publisher Site

### Abstract

âThe class of mathematical and geographical problems considered in this review is characterized by the following general structure: [Suppose that there are given (a) a set of n points distributed in the plane, (b) a numerical weight to be attached to each point, and (c) a set of m indivisible centroids without predetermined locations; then, the location-allocation problem, in its most general form, is to find locations for the m centroids and an allocation of each point, or fraction of a point, to some centroid so as to optimize an objective function3 The usual practical interpretation of this problem is to consider it as representative of a social or economic system which is identifiable as a set of flows between a number of central facilities and some set of geographically dispersed source or destination points. The problem is then simultaneously to locate the central facilities and to determine an assignment of flows, so that the total costs of operation of the system are the least possible. This sort of problem arises in a great variety of practical planning situations. It is strongly evident, for example, in the planning of geographical systems centered upon such phenomena as hospitals, schools,

### Journal

Geographical AnalysisWiley

Published: Apr 1, 1970

### References

• An Activity Analysis Approach to Location Theory
Beckmann, Beckmann; Marschak, Marschak
• Solutions of Generalized Locational Equilibrium Models
Cooper, Cooper
• An Extension of the Generalized Weber Problem
Cooper, Cooper
• Backtrack Programming
Golomb, Golomb; Baumert, Baumert
• An Efficient Algorithm for the Numerical Solution of the Generalized Weber Problem in Spatial Economics
Kuhn, Kuhn; Kuenne, Kuenne
• On Approximation Methods for the Assignment Problem
Kurtzberg, Kurtzberg
• Locational Equilibria
Leamer, Leamer
• Toward a Theory of Urban Public Facility Location
Teitz, Teitz
• Industrial Development Planning Models with Economies of Scale and Indivisibilities
Vietorisz, Vietorisz

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