The paper presents the problem of controlling the input and output material flows of an industrial enterprise, supplemented by the condition for the choice of sales prices and adjusted in terms of the number of products sold. This economic and mathematical model finds optimal solutions for the management problem at enterprises, namely, the problem of forming a production program according to the criterion of the maximum net profit at the end of the planning period. In the constraints of the model, both production components and constraints on resources and the logic of input and output material flows are systematically taken into account. The considered model and the given control problems are investigated using a unified approach that allows working with logical conditions of any complexity and setting the corresponding formal optimization problems. The results of testing the algorithm on test data close to industrial (real) dimensions are also given.

At present, any unified approach that would allow solving the problems of coordinated optimal control of input and output material flows and production has not been implemented in the theory and practice of managing technological and organizational systems. The works published in this area are often aimed at solving specific problems. When attempting a complex solution the declared systemicity is either indicated only in words, or is implemented heuristically by gluing the constituent components without discussing and analyzing the effectiveness and, moreover, proof. This article, based on the earlier works of the authors, develops an apparatus of coordinated optimal control of all logically related subsystems. A formal setting created for this purpose is a discrete optimization problem and it takes into account all the main factors of production and movement of material flows. A special algorithm for an approximate solution is constructed, which transfers the created problem from the category of NP-hard problems to the category of polynomially solvable ones. The formal setting contains logical conditions for choosing from a variety of parameters, including sources and directions of flows, conditions of supply, volumes and dynamics of production, and determination of optimal prices at the output. Thus, the restrictions systematically take into account both production components and restrictions on resources and the logic of movement of input and output material flows. A maximum net profit at the end of the planning period was used as a criterion for the effectiveness of all processes. The considered model and control problems are investigated using a unified approach that allows working with logical conditions of any complexity and setting appropriate formal optimization problems. The results of testing the algorithm on test data close to real dimensions are also given.

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The results of modelling the problem of supply management of an enterprise using discrete optimization tools are presented. The formulation of the optimization problem of supply management and the found method for its solution are presented. Since there may be cases when the number of variables in the problem is large enough, an algorithm was developed that uses the decomposition of the problem as a solution. A numerical example of the application of the decompositional algorithm for optimizing supplies and comparison of the results using the direct algorithm are given.

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