ABSTRACT
The continuous problems of the optimal multiplex-partitioning of sets (OMPS) for the fixed centers or those to be located with a variety of the partitioning quality criteria are formulated. The practical application of these problems in economics, as well as in the image analysis and segmentation, are presented. In particular, the problems of multiplex-partitioning are presented as mathematical models of problems for service centers’ location within a limited area simultaneously with partitioning of this area into regions that cover customers with the same set of k nearest centers. As this takes place, the formation of partitioning-location quality criterion to specify the located centers, along with a type of provided services, is considered. By means of the presented models for the OMPS problems the competition between service centers, determined real activity sphere of each center according to its capacities, etc can be studied.
