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Numerical study of models of optimal distribution of recreational resources

Numerical realization of the problems of optimal distribution of recreational resources adapted to the continuous non-linear multiproduct problem of optimal partitioning of sets, the solution of which can be interesting in the sense of the development of recreation and tourism, is carried out. The success of most management tasks depends on the best way to use resources. In general, this problem is reduced to the problems of optimal resource allocation. The tasks of this type include the tasks of optimal placement of tourist complexes on a given territory, which is attractive in the sense of the tourism industry. In this case, the models of functioning and development of tourist and recreational systems are considered that can be used for analysis and forecasting of the tourism industry, both at the regional and national and international levels. The problem of the optimal distribution of recreational resources in the conditions of the modern and perspective structure of recreational needs was investigated. A mathematical model of the problem is constructed, which is a nonlinear continuous multi-product problem of the optimal partition of a set into its disjoint subsets (among which there may be empty ones) with fixed coordinates of the centers of these subsets under constraints in the form of equalities and inequalities. An analytical solution of the problem is obtained, which includes parameters that are sought as the optimal solution of the auxiliary dual finite-dimensional optimization problem with a nonsmooth target functional. On the basis of the analytical solution of the problem studied, a theoretically grounded solution algorithm was developed. A numerical investigation of the problem is carried out. The presented research results can serve as a useful tool in the sense of effective optimal partitioning of the functioning zones of existing tourist and recreational facilities that are able to produce service complexes to meet the necessary needs of recreants from the service area in conditions of the optimal cost of recreational needs