This paper proposes an algorithm for optimizing the garbage collection route in a local community (or a separate settlement). The study was conducted for one garbage truck. To achieve the maximum efficiency of the algorithm, it has been assumed that the points of discharge of collected waste by a garbage truck could be arranged along the way between the proposed clusters of garbage collection points. The optimization of the built routes has been proven, taking into consideration the above assumptions. The study's results could be used to reduce the budget expenditures by territorial community authorities for the collection and disposal of waste. The reported solutions could significantly shorten the garbage collection time, which would improve the environmental and aesthetic situation within the study area. The use of a new algorithm makes it possible to display the results both in quantitative and qualitative forms. An improved k-means algorithm with a maximum cluster size was selected for clustering. Each cluster was built on the basis of the maximal value of garbage truck tonnage. That means that the size of the cluster would be determined by the value of the maximum amount of waste that can be removed by a garbage truck in one run. A task of the traveling salesman was applied to find the shortest path between representatives of one cluster (garbage collection points) calling at all its points and to establish the optimal path between all the clusters formed for a territorial community. The issue related to efficient waste disposal in local communities tends to aggravate rapidly while the task to optimize garbage collection and removal is becoming increasingly acute. This is because at present, along with the increase in the global population, all types of production are increasing their volumes, which, in turn, leads to an increase in the amount of waste, in particular, household.

The problems of development of united territorial communities, in particular unemployment and economic problems, are considered. Communities, in most cases, lack the resources to address economic and other issues. Therefore, it is necessary to create self-sufficient communities in which there are enough financial instruments for their own development. The mathematical model of the decision support system for the development of territorial communities using the agro-industrial sector was considered. An important step in building a mathematical model of the agro-industrial complex is to take into account the specifics of agriculture. The article considers a mathematical model of linear multifactor regression, which describes the relationship between the number of resources expended and the volume of output. Since the processes of economics and production processes of agriculture are complex, it is difficult to describe them using only linear deterministic models. It is common for task variables to take some discrete values or values from a certain interval. This situation makes the search difficult.

In this paper, the problems of development of associations of territorial communities in the tourism direction of economic development are considered. The object of research is the improvement of territorial communities on the example of Ukraine. One of the most problematic places is the lack of funds for the development of existing large tourist complexes and the creation of new ones. The study uses the idea that tourism development has a direct stimulating effect on the development of a number of important economic sectors. The use of a mathematical apparatus is also considered, which allows to analyze the main factors influencing the development of the tourism industry of territorial communities. A comprehensive solution of economic, social and environmental issues of sustainable tourism development is impossible without the development of mathematical models and supporting tools that allow predicting the main indicators of sustainable tourism development. The paper considers PLS-PM modeling using such internal consistency criteria as Cronbach’s Alpha coefficient, Dillon-Goldstein coefficient ρ, model reliability, mean variance. The purpose of the PLS-PM model is to obtain estimates of latent variables for further forecasting procedures for the development of the system. The processes taking place in the tourism industry are characterized by a complex interaction of economic, environmental and social factors. Their influence should be taken into account for the implementation of the sustainable tourism development strategy. The analysis of the model was also carried out with the help of a single coefficient of quality of the correspondence of the data model, which characterizes the quality of the internal and external models of the system. Thanks to the listed tools, the statement is formed that the regulation of key factors of the tourism sector of the economic sector can have a positive impact on the development of national culture and economy in the united territorial communities. The created mathematical model clearly forms the conclusion that the development of tourism in local communities can become the engine of their sustainable economic development, given the available regional conditions.

ity Local development of a certain area is formed under the influence of many criteria. The rapid pace of globalization of the world economy is one of the criteria that significantly affect the formation of new trends and patterns of local development. The manifestation of this criterion can be seen in the strengthening of the role of communities in the economic development of certain territories and countries. The Ukrainian state is already one of several countries whose societies have understood and accepted the importance of community interest in direct participation in local development. For key community representatives, the process of decentralization and changes in self-government processes will determine a fundamentally different level of responsibility for development. Consideration of such a concept of local community development will form the transformation of territorial communities from the object of government to the subject of government. And you will be able independently provide your own capacity. In general, local communities will be responsible for planning their development and economic well-being in the future. Given these perspectives, local authorities must have a good understanding of the specifics of modern development and have the necessary knowledge, information, skills, and experience to further ensure the competitiveness of their communities. The purpose of this study was to develop a system for choosing the best direction for the development of territorial communities, based on the resources belonging to these communities. This scientific work proposes to use the method of analysis of hierarchies to determine the direction of development of territorial communities, as this method allows to quantify the comparative importance of the criteria of the direction of development. The method of analysis of hierarchies involves pairwise comparisons of objects using subjective judgments, which are quantified on a certain scale. An important point in the comparison is the unbiased views of experts for the correct use of the method of analysis of hierarchies.

This article examines the problems of the development of united territorial communities, in particular, unemployment and economic problems. The object of the research is the improvement of territorial communities on the example of the Lviv region (Ukraine). One of the most problematic areas is the fact that communities, in most cases, do not have enough funds to solve economic and other problems. The study uses the idea of the need to create self-sufficient communities with a sufficient number of financial instruments for their own development. The mathematical model of the decision support system for the development of territorial communities using the agro-industrial sector is also considered. An important step in building a mathematical model of the agro-industrial complex is taking into account the specifics of agriculture. The paper considers a mathematical model of linear and multifactorial regression, which describes the relationship between the amount of resources expended and the volume of output. Since the processes in the economy and production processes in agriculture are complex, it is difficult to describe them using only linear deterministic models. A common case is when task variables take some discrete values or values from a specific one. This situation makes the search difficult. To build a mathematical model for the development of territorial communities and study the fact that the development of agro-industry will improve the overall economic situation of the territorial community, correlation and regression analysis, the Farrar-Glauber method and the method of least squares are used. Thanks to the listed instruments, the statement is formed that the regulation of key factors of economic indicators of the agricultural sector can positively affect the growth of the economic component of territorial communities. The created mathematical model clearly forms the conclusion that agriculture in local communities can become an economic engine of community development, taking into account regional conditions.