Modeling the dynamics of product output by a manufacturing enterprise due to the digital transformation of its workforce

摘要

The published article proposes a mathematical model of the dynamics of product output by a manufacturing enterprise, whose labor resources are being replaced by digital technologies and robotics. The development of the model is based on the application of a dynamic two-factor production function of the enterprise. The structure of this function includes a variable from zero to one dimensionless logistic function of digitalization and two Cobb-Douglas functions. The first Cobb-Douglas function refers to the period of operation of the enterprise before the start of digitalization, and it uses capital and human labor resources as production factors. The second function of Cobb-Douglas corresponds to the period of operation of the enterprise, in which its digitalization is fully completed and capital is used as production factors, and human labor resources are completely replaced by digital technologies and robotics. Models of the dynamic development of an enterprise, the production of which is restoring its capacity due to the introduction of its own internal investments, are presented in the form of systems of differential equations for production factors. Stationary solutions of these systems of equations correspond to the equilibrium states of the operation of enterprises and represent the limiting values of the factors of production. It is shown that the models of output by an enterprise corresponding to the absence of digital transformation and complete digitalization of production represent the lower and upper boundaries of all possible options for displacing human labor resources.