### Abstract

This paper develops a location-allocation model of Losch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. Consumer behavior postulates concerning the "nearest center hypothesis' and the "indifference principle' are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions. -from Author

Original language | English (US) |
---|---|

Pages (from-to) | 316-337 |

Number of pages | 22 |

Journal | Geographical Analysis |

Volume | 21 |

Issue number | 4 |

State | Published - 1989 |

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### ASJC Scopus subject areas

- Geography, Planning and Development

### Cite this

**A location-allocation model of Losch's central place theory : testing on a uniform lattice network.** / Kuby, Michael.

Research output: Contribution to journal › Article

*Geographical Analysis*, vol. 21, no. 4, pp. 316-337.

}

TY - JOUR

T1 - A location-allocation model of Losch's central place theory

T2 - testing on a uniform lattice network

AU - Kuby, Michael

PY - 1989

Y1 - 1989

N2 - This paper develops a location-allocation model of Losch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. Consumer behavior postulates concerning the "nearest center hypothesis' and the "indifference principle' are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions. -from Author

AB - This paper develops a location-allocation model of Losch's central place theory that maximizes the number of firms that can coexist in the market, subject to range, threshold, hierarchy, and other constraints. Consumer behavior postulates concerning the "nearest center hypothesis' and the "indifference principle' are formulated as nonlinear constraints but not used during solution. Methods are developed for simulating the continuous, infinite plain with a discrete, bounded network by use of an outer overflow network and a symmetrical market area constraint. The model is tested by applying it to a uniform lattice network and comparing the results to the expected pattern of nested hexagons. Solutions consistent with the k = 3, 4, and 7 patterns are generated by changing threshold values. The long-run purpose of developing and validating a location-allocation model of a location theory is to use it to relax the theory's restrictive assumptions and to apply the theory to nonuniform regions. -from Author

UR - http://www.scopus.com/inward/record.url?scp=0024799437&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024799437&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0024799437

VL - 21

SP - 316

EP - 337

JO - Geographical Analysis

JF - Geographical Analysis

SN - 0016-7363

IS - 4

ER -