Domains of Structural Stability for Minimal-Cost Discrete Flows with Reference to the Hierarchical Central-Place Models

Bibliographic Data

ID5161747
AuthorsMichael Sonis (Bar-Ilan University, corresponding author)
Year1982
Volume14
Issue4
Pages455-469
Publication date1982-04-01
Open AccessYes
TypeARTICLE
VenueEnvironment and Planning A Economy and Space (JOURNAL)
Journal identifiersISSN: 0308-518X • E-ISSN: 1472-3409
PublisherSAGE Publications Inc (PUBLISHER)
DOI10.1068/a140455
OpenAlexW1971373786
LanguageEN
Citations received1
References cited6

The purpose of this paper is to construct the domains of structural stability for optimal discrete flows, to compare the discrete case with the case of the Beckmann model of continuous flows, and to find the structurally stable minimal-cost flows for the hierarchical central-place models. The mathematical basis for this construction is the sensitivity analysis of the linear programming problem instead of the generic theory of differential equations and the catastrophe theory in the continuous case. The domain of structural stability is the Cartesian product of the domain (cone) of the existence of flow with a preset topological structure and the domain (wedge) of optimality of the flow with the same structure. A detailed algorithm for the construction of these domains of structural stability is given. This algorithm leads to the vector generalization of method of potentials of Kantorovitch-Dantzig for the transportation problem and also gives a description of structural change for dynamic flows. As an application, the generalized (Christaller-Parr) hierarchical three-level central-place models are investigated, for which structurally stable optimal flows exist

Cartesian product · Discrete mathematics · Generalization · Geometry · Mathematical analysis · Mathematical optimization · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Computer Science · Mathematical Control Systems and Analysis · Mathematics · Modeling, Simulation, and Optimization · Applied Mathematics

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