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Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Use of Constraints in the Hierarchical Aggregation Procedure Intramax Abstract Background: Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past. Objectives: In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint. Methods/Approach: The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically. Results: The use of the contiguity constraint is important only at the beginning of the aggregation procedure; the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation. Conclusions: The original Intramax procedure (without the inclusion of any constraint) gives the most balanced and operative hierarchical sets of functional regions without any singletons or isolated regions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Business Systems Research Journal de Gruyter

Use of Constraints in the Hierarchical Aggregation Procedure Intramax

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1847-9375
eISSN
1847-9375
DOI
10.1515/bsrj-2016-0009
Publisher site
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Abstract

Abstract Background: Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past. Objectives: In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint. Methods/Approach: The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically. Results: The use of the contiguity constraint is important only at the beginning of the aggregation procedure; the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation. Conclusions: The original Intramax procedure (without the inclusion of any constraint) gives the most balanced and operative hierarchical sets of functional regions without any singletons or isolated regions.

Journal

Business Systems Research Journal – de Gruyter

Published: Sep 1, 2016

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