Simulation of interaction of production systems of industrial enterprises and business groups

The article considers the system of industrial enterprises constituting a business group, jointly producing some final product, supplying it with their private products. Since, in general, the capacities of enterprises are different, their products are not produced in proportional volumes, which simultaneously leads to both overstocking and the formation of a shortage of individual components of the final product. This leads to a decrease in the overall efficiency of the business group and to the instability of its individual enterprises. In the study, the task has been set to develop a mathematical model and a mechanism for a coordinated and fairly evaluated activity of enterprises using the basic concepts of the theory of active systems. The proposed model design is based on the requirements: private products must be supplied by enterprises in the required proportions, and penalties for failure to complete tasks must be characterized by a single penalty coefficient. In particular, in the development of well-known approaches to reconcile the conflicting interests of two different economic entities, it is proposed: – to clarify the area of agreed decisions by expanding it, taking into account not only the possibility of exceeding the optimal task for the enterprise, but also its underestimation; – to form a criterion for assigning penalty coefficients, as the equality of the lower value of the region of feasible solutions of a stronger enterprise and the upper value of the region of feasible solutions of a weaker enterprise. The solution of the problem is generalized to the case of an arbitrary number of enterprises. A general algorithm for solving the problem has been developed, including determining two critical enterprises, calculating the allowable (agreed) volume of product output for them, calculating the corresponding penalty coefficient and the values of output of individual products for each enterprise. An illustrative example has been given.