Mathematical model of transition of a production enterprise to a circular economy

Abstract

In the published article, a mathematical model of an enterprise is proposed, the production activity of which is described by two production functions. The main production function converts resources into the products of an enterprise, the additional production function turns resources into its waste, which are usually included in costs. Enterprises of a waste-free circular economy organize their own production so that the waste of an enterprise becomes new production factors and is completely converted into additional useful products. The process of transition in time of an enterprise of an ordinary economy to an enterprise of a waste-free circular economy is described using a special dimensionless transformation function, which varies from zero to one. Two variants of the peculiarities of changes in the economic indicators of an enterprise that arise during the transition to waste-free production are considered. In the first case, a one-factor manufacturing enterprise was investigated, which in its production activity uses only one resource, which integrates the volumes of factors of production consisting of fixed capital, production assets involved in the production of labor resources, used in the production of materials, applied technologies, of various kinds innovation. In the second case, a two-factor manufacturing enterprise has been investigated, which in its production activity uses two resources, the first of which is fixed capital and production assets, the second production factor includes labor resources involved in production. Regularities have been established for changes in the time of production, waste, profits and costs of an enterprise when introducing waste-free technologies for the case of one-factor production. Anumerical analysis of the obtained economic and mathematical model shows that the maximum value of the enterprise's profit changes over time and corresponds to the level of the introduced circular technologies.