Development of an algorithm for the optimal distribution of mutual indebtedness in the economic system using the transportation problem

Optimization of financial and material flows requires the analysis of many factors and large amounts of information, which is impossible without the information technology use. The presence of counter financial flows is possible, both between economic entities, for example, budgetary institutions and unitary enterprises, non-state sector enterprises and state institutions of federal subordination. The current level of information technologies makes it possible to create a database containing information on the receivables and payables of budget institutions and their counterparties for a certain time point. Creation and maintenance of such a base in the current state of the information-analytical center of the region is necessary for optimizing financial flows. When collecting information for the database creation, it should be taken into account that the most important information is about the mutual debts within the considered group of subjects of economic relations. In the article, we consider the question of for which values of the coefficients the problem reduces to a transportation problem. The outlined approach to optimization of financial and commodity flows in integrated structures by solving the problem of counter flows repayment as a problem of linear programming of the transport class has a number of advantages. The next problem of the algorithm development for calculating the net result for solving practical problems is the large dimension of the mutual debts matrix. As the experience of works on repayment of non-payments in the Sverdlovsk region has shown, the matrix of mutual indebtedness is characterized by a large dimension and high discharge. To solve the problem of the return of mutual debts, we have developed an algorithm that, after a finite number of steps, solves the problem and leads to the state of minimally possible mutual debts, and, the higher the discharge of the matrix is, the less number of algorithm steps are required to get the optimal distribution of mutual debts. One of the advantages of the presented algorithm is that it is focused on a step-by-step compliance with the rules for conducting financial transactions. The algorithm for solving the problem of counter financial flows repayment allows us to find the optimal distribution of mutual indebtedness for a finite number of steps and has following main advantages: first, step-by-step compliance with the rules for conducting financial transactions; second, taking into acc