<abstract xmlns="http://www.w3.org/1999/xhtml"><bold>Background:</bold> 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.<bold>Objectives:</bold> 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.<bold>Methods/Approach:</bold> 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.<bold>Results:</bold> 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.<bold>Conclusions:</bold> 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.</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.

Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Faculty of Civil and Geodetic Engineering, University of Ljubljana,

Business Systems Research Journal

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Use of Constraints in the Hierarchical Aggregation Procedure Intramax"}

Background: Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set...

Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Published Online: Oct 17, 2016

Page range: 5 - 22

Received: Feb 12, 2016

Accepted: Jul 10, 2016

DOI: https://doi.org/10.1515/bsrj-2016-0009

Keywords
hierarchical aggregation procedure, Intramax, constraint, functional regionalisation, functional region

© 2016 Samo Drobne et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Use of Constraints in the Hierarchical Aggregation Procedure Intramax

Published Online: Oct 17, 2016

Page range: 5 - 22

Received: Feb 12, 2016

Accepted: Jul 10, 2016

DOI: https://doi.org/10.1515/bsrj-2016-0009

Keywordshierarchical aggregation procedure, Intramax, constraint, functional regionalisation, functional region

© 2016 Samo Drobne et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
hierarchical aggregation procedure, Intramax, constraint, functional regionalisation, functional region