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THE INTERVAL MODEL OF INPUT-OUTPUT BALANCE
Keywords:
input-output model, interval mathematics, interval input-output model, Boolean variables, linear Boolean programming problem.DOI:
https://doi.org/10.17654/0974165822047Abstract
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.
Received: September 6, 2022
Accepted: October 15, 2022
References
V. A. Ilyin, T. V. Uskova, E. V. Lukin and S. A. Kozhevnikov, Analysis and modeling of economy on the basis of inter-branch balance, Vologda, FGBUN VolSC RAS, 2017, 158 pp.
V. P. Peresada, Managing the dynamics of economic development on the basis of the inter-sectoral balance, Lap Lambert Academic Publishing, 2017, 208 pp.
D. V. Shapot and V. A. Malakhov, Experience in the development of the methodology and development of management models of inter-branch balance, Moscow, MEI, 2018, 176 pp.
A. G. Granberg, V. D. Marshak, L. V. Melnikova, V. I. Suslov, N. I. Suslov and S. A. Suspitsyn, Methodological bases of system modeling of socio-economic development of Siberia, Siberia in the first decades of the XXI century/ed. by V. V. Kuleshov, IEOPP SB RAS, Novosibirsk, 2008.
A. S. Popkov, Identification of dynamic model of inter-branch balance for Russian economy and optimal allocation of investments on its basis, Management Processes and Stability 2(18) (2015), 696-701.
G. Alefeld and J. Herzberger, Introduction to Interval Computing, Moscow, Mir, 1987, 356 pp.
A. V. Lakeyev and S. I. Noskov, A description of the set of solutions of a linear equation with interval defined operator and right-hand side, Russian Acad. Sci. Dokl. Math. 3(47) (1993), 518-523.
A. V. Lakeyev and S. I. Noskov, On the set of solutions of the linear equation with the intervally given operator and the right-had side, Sib. Math. J. 5(35) (1994), 1074-1084.
V. Kreinovich, A. V. Lakeyev and S. I. Noskov, Optimal solution of interval linear systems is intractable (NP-hard), Interval Computations 1 (1993), 6-14.
S. I. Noskov, Object Modeling Technology with Unstable Operation and Data Uncertainty Irkutsk, Oblinformpechat, Russia, 1996.
S. I. Noskov, Point characterization of solution sets of an interval system of linear algebraic equations, Information Technology and Mathematical Modeling in the Management of Complex Systems 1 (2018), 8-13.
S. I. Noskov and A. V. Lakeev, MS-solutions and quasi-solutions of interval system of linear algebraic equations, Bulletin of St. Petersburg University, Applied Mathematics, Informatics, Control Processes 3(17) (2021), 262-276.
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