ON THE METHODS OF INVESTIGATING THE TRAJECTORIES OF THE MOTION OF OBJECTS OF LABOR IN THE PHASE SPACE OF STATES
A model of an economic-production system with a flow-based method for organizing production is considered. The space of states of the subject of labor is introduced. The state of a particular subject of labor is determined by a point in the state space. The state of the economic-production system is determined through the aggregation of the states of a large number of the subjects of labor that are in the process of production. The paper assumes that if the state of each individual subject of labor is known, then the state of the parameters of the economic-production system is known. Using the variational and differential principles, Lagrange's function of the economicproduction system is recorded. The equation for the normative technological trajectory of the movement of a subject of labor along a technological route is defined in the state space. When the subject of labor moves along a technological trajectory from one technological operation to another technological operation, technological resources are transferred to the subject of the labor as a result action of technological equipment. The Lagrange function of the economic-production system with a flow-based method of organizing production is recorded. The Lagrange function is constructed using the variational and differential principle. Methodological differences are shown when using the variational and differential approach to construct the Lagrange function of economic-production systems. It is shown that the Lagrange function, taking into account production and technical and socio-economic constraints, determines the subjective function of the economic-production system. The integrals of the movement of subjects of labor in the state space are defined, which can be used to model economic-production systems with a flow-based method of organizing production. It is shown that the integrals of motion are conservation laws that characterize the process of processing subjects of labor along the technological route.
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