The paper gives a brief description of the Leontief mathematical model of inter-branch balance. It is noted that the main difficulty in constructing the input-output model is related to the estimation of the components of the direct cost matrix. Its traditional point specification is usually associated with very time-consuming research and, as a rule, leads to the need for multi-step refinements of these components. It is much more realistic and practical instead to set the lower and upper bounds of this matrix A, as it is customary in interval mathematics. This assumes the absence of any consideration specifying the true location of the components within or on the boundaries of the corresponding intervals. With such setting of the direct cost matrix, the input-output model takes the form of the interval system of linear algebraic equations (ISLAE) with interval uncertainty on the left side. The set of its solutions in the form of systems of linear inequalities and one nonlinear condition, which can be eliminated by the introduction of Boolean variables, is described.

input-output model, interval mathematics, interval input-output model, Boolean variables, linear Boolean programming problem.

Received: September 6, 2022;  Accepted: October 15, 2022; Published: November 4, 2022

How to cite this article: S. I. Noskov and A. S. Vergasov, The interval model of input-output balance, Advances and Applications in Discrete Mathematics 35 (2022), 11-16. http://dx.doi.org/10.17654/0974165822047

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