Cherevatenko A. Information technology for territorial service market segmentation on the basis of models and methods of multiplex-partitioning of sets

The research object is the process of territorial service market segmentation of an arbitrary region. The research subject is models, methods and information technology of territorial segmentation and determination of service areas for existing or new service centers in a given territory. Research methods: methods of system analysis, mathematical modeling, infinite-dimensional mathematical programming, non-differentiable optimization, methods for solving continuous linear problems of optimal sets partition, duality theory, theory of algorithms and principles of object-oriented programming. The mathematical models of continuous problems of optimal multiplex-partitioning of sets , which describe the process of region segmentation according to the territorial criterion taking into account the capacities of service centers and allow determining the real service areas of existing enterprises, quantitatively substantiate and support decisions about choosing locations for new enterprises, have been built and implemented for the first time. The continuous OSP problems are generalized for the case of subsets overlapping for the first time, ; the obtained problems in various formulations constituted a new class of partition problems, namely, continuous problems of optimal multiplex-partitioning of sets. The solution methods for problems of optimal multiplex-partitioning of sets are theoretically substantiated and developed for the first time that allow implementation of territorial segmentation with multiple service areas overlapping, with the possibility of better (in some sense) placement of service centers considering their limited capacities. A new approach to the construction of higher-order Voronoi diagrams and their various generalizations based on the formulation and solution of continuous linear problems of optimal multiplex-partitioning of sets in the corresponding statements is proposed, which, in contrast to existing methods and approaches, allows immediate construction of a Voronoi diagram of k -th order without preliminary construction of all diagrams up to the (k-1) -th order, secondly, take into account the “power” of generator points and their optimal placement. The developed information technology was used during development and implementation of the “Program for the Innovative Development of the Dnipropetrovsk Region until 2020” by the Pridneprovsk Scientific Center of the National Academy of Sciences of Ukraine and the Ministry of Education and Science of Ukraine when forming recommendations on determining service areas for the departments of labor and social protection of the population of the Dnipro and Dnipropetrovsk region. The work results are used to determine the functional efficiency of mining and metallurgy enterprises at the stages of structural elements interaction, and are introduced into the educational process of the System Analysis and Control Department of NTU "DP". The introduction of materials is confirmed by relevant acts.