Models and algorithms of the consistent financial distribution in the implementation of projects of the association of business entities

Introduction. A characteristic feature of the development of modern economic systems is active association, integration of enterprises into larger economic entities. A distinctive feature of such associations is the multidirectional interests of its members. The development of innovative mechanisms for financial management of an integrated structure, allowing to take into account the conflicting interests of the enterprises of the association, is an urgent task. Aim. To develop mathematical models and algorithms to improve the efficiency of financial management of the association of business entities by forming an optimal package of projects and coordinated distribution of profits from its implementation between enterprises. Materials and methods. The proposed approach is based on the use of systems analysis methods, optimization methods, decision theory and game theory. The paper discusses the mechanism for the coordinated distribution of funds of the enterprises of the association in the implementation of projects, which consists of two enlarged stages. At the first stage, an optimal package of merger projects is formed. Each enterprise of the association offers its own variants of projects, from which a package of projects is formed. The constructed model of the formation of a package of projects that ensures the amalgamation of obtaining the greatest profit is a knapsack problem and is solved by the branch and bound method. At the second stage, the distribution of profits from the implementation of projects between the enterprises of the association is carried out. To find the distribution of profits, ensuring the coordination of the economic interests of the enterprises of the association, it is proposed to use the methods and principles of the theory of cooperative games. The paper shows that the described problem can be formally represented as a game in the form of a characteristic function. It is proposed to choose a certain element of the C-core as an agreed profit distribution. The formation of this element is carried out on the basis of an optimization model, the function of the goal and the system of restrictions of which takes into account quantitative indicators of the activity of enterprises' participation in the implementation of merger projects. Results. A mechanism has been developed for the coordinated distribution of financial resources of the enterprises of the association during the implementation of projects, based on mathematical models and methods. A feature of the mechanism is the application of the game principle when distributing the profit of projects. Practical calculations are carried out to substantiate the advantages of the presented approach in comparison with the known methods. Conclusion. The coordinated distribution of finances proposed in the work reasonably ensures the benefit of each enterprise from the joint implementation of projects and stimulates the management of enterprises to search for highly effective projects.