MATHEMATICAL MODEL OF THE PROBLEM OF OPTIMAL LOCATION OF PRODUCTIVE FORCES TAKING INTO ACCOUNT THE MINIMUM DAMAGE TO THE ENVIRONMENT

Abstract

The work analyses the latest research and publications on the quality management of the natural environment. It reveals the previously unresolved problems and tasks of forecasting for the future. The task of optimal distribution of productive forces from the standpoint of minimization of costs for the environment under the normal operation of the object proposed. A mathematical model of this problem formed with a fractional-linear objective function, which is the ratio of total costs of the industrial sector of the region to the total income was created. It is explaining in detail and the formulas for calculation of each component of the function of the total costs of the industrial sector of the region are given. In particular, there are presented comparisons for costs in the sphere of supply; costs for production; costs in the sphere of distribution, costs for production system management. The function of total costs includes environmental costs, which form at the expense of current and capital environmental costs. Environmental and economic costs, as a constituent part of the total costs function, in the production sphere for a particular industrial unit, includes the following components: possible unrealized profit due to unplanned reduction in the volume of production; additional costs; costs associated with loss compensation and costs of various types of material resources. The mathematical model includes a combinatorial condition on the number of manufactured products of a particular type on a particular industrial facility, when the values of the variables are selected by the combinatorial multiplicity of dimensions. The model also contains line limitations on the total quantity of a particular type of production. Additional conditions are imposed on the coefficients that determine the share of material resources in the total material flow of transport and storage enterprises. The model of the problem is selecting the area for the construction of industrial facilities to minimize losses to the natural environment at the level of the region, which takes into account the social and economic needs of its population and environmental safety, can be used in the planning and design.