Construction of a Non-negative Solution of the Leontief-Ford Model

Fatima Ashakova

doi:doi:10.11648/j.cssp.20190801.13

| Peer-Reviewed

Construction of a Non-negative Solution of the Leontief-Ford Model

Fatima Ashakova

Published in Science Journal of Circuits, Systems and Signal Processing (Volume 8, Issue 1)

Received: 26 June 2019 Accepted: 24 July 2019 Published: 8 August 2019

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The article deals with the Leontief-Ford model, which is allowed to take into account the costs that necessary for the elimination of industrial waste. We consider its non-negative solution for those cases when the errors of the initial data have little influence on the result of the solution and for those cases when the errors of the initial data significantly affect the result of the solution. In the first case, it is called correctly delivered, and in the second incorrectly delivered. We use the iteration method to find a nonnegative solution to a correctly posed model, and also we use the regularization method to find a nonnegative solution to an ill-posed model. The developed technique is brought to a practical algorithm, which is implemented in the program "LF_2", it allows you to find a solution to the model, regardless of whether the model is correctly supplied or incorrectly supplied. An example of its application is given, where we enter the initial data of a poorly conditioned balance model into the program and obtain its non-negative solution. The results of this work may be interesting for specialists in economics and mathematical methods and models, as well as economic entities. It is known from practice that in the development of balance models of economic entities there are models with a bad number of conditionality. The application of the developed software product and methods described in this paper will allow economic entities to make quality and quick management decisions on the volume of product output of each sector of the economy, taking into account the costs necessary for the elimination of industrial waste, regardless of the conditionality and dimension of their balance models.

Published in	Science Journal of Circuits, Systems and Signal Processing (Volume 8, Issue 1)
DOI	10.11648/j.cssp.20190801.13
Page(s)	19-23
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Leontief-Ford Model, Non-negative Solution, Regularization Method, Iteration Method

References

[1]	Potravny I., Gusev A., Stoykov V. and Gassiy V. (2017) Modification of the Leontief-Ford Input-Output Model for the Green Economy Goals and Environment Protection. Journal of Geoscience and Environment Protection, 5, pp. 15-23.
[2]	Gazvan R. K., Marakhovsky A. S., Kiselyova T. V. (2017) Dual model of interindustry balance. Economy vector, no. 5 (11), pp. 20.
[3]	Gulay T. A., Kopylova E. P., Surmacheva A. V. (2013) The general case of model of Leontyev – Ford. Modern high technologies, no. 6, pp. 66-67.
[4]	Marakhovsky A. S. (2007) Leontiev-Ford Dynamic model with a constant level of external pollution / A. S. Marakhovsky, E. L. Toroptsev // Information systems, technologies and production management models. International scientific conf, Stavropol: SSAU, pp. 83-87.
[5]	Askhakova F. H. (2016) Methods of numerical solution of the model Leontiev-Ford. World science: Problems and innovatios: collection of articles of the V International scientific-practical conference, Penza: ICNS "Science and Education", pp. 18-20.
[6]	Leontief W., Ford D. (1972) Economics and mathematical methods, Moscow: Nauka, 242 p.
[7]	Semenchin E. A., Askhakova F. H. (2006) Method of constructing numerical methods of solving the balance model of Leontief-Ford // Progressive technologies in learning and production: Materials of IV all-Russian conference, Kamyshin. 18-20 October 2006: 4 vol. 3, Volgograd, pp. 45-48.
[8]	Gantmacher F. R. (1966) Matrix Theory, Moscow: Science, 576 p.
[9]	Numerical methods /H. S. Bakhvalov. N. P. Zhidkov, G. N. Kobelkov (2007) 5 ed., Мoscow: Binom. Knowledge laboratory, 636 p.
[10]	Fedoseev V. V., Garmash A. N., Dayitbegov D. M. ets. (2002) Economics mathematical methods and applied models: Studies. manual for schools, Moscow: UNITY, 391 p.
[11]	Amosov A. A., Dubinsky Yu. A., Kopchenova N. V. (1994) Computational methods for engineers: Proc. benefit, Мoscow: Higher. SHK, 544 p.
[12]	Tovstik T. M., Volosenko K. S. (2015) Monte Carlo Algorithm for solving systems of linear algebraic equations by Seidel method. In the collection: Actual problems of computational and applied mathematics proceedings of the International conference devoted to the 90th anniversary of academician G. I. Marchuk, pp. 771-776.
[13]	Semenchin E. A., Askhakova F. H. (2006) Method of constructing a non-negative solution in the model of Leontief-Ford. -In sat.: Abstracts VII all-Russian Symposium on applied and industrial mathematics, Yoshkar-Ola, pp. 347-348.
[14]	Tikhonov A. N., Arsenin V. Ya. (1986) Methods of solving ill-posed problems. Textbook for universities. Ed. 3rd., corrected, Мoscow: Science. Main edition of physics and mathematics literature, 288 p.
[15]	Sumin M. I. (2016) Tikhonov regularization Method for solving operator equations of the first kind: Educational and methodical manual. Nizhny Novgorod: Nizhny Novgorod State University, 56 p.
[16]	Verzhbitsky V. M. (2002) Fundamentals of numerical methods: Textbook for universities, Мoscow: Higher school, 840 p.
[17]	Askhakova F. H. (2008) Analysis of balance models of economic actors, the Karachay-Cherkess Republic, using the method of regularization. News of the Russian state pedagogical University named after A. I. Herzen, no. 36, SPb., pp. 15-17.

Cite This Article

Plain Text BibTeX RIS

APA Style

Fatima Ashakova. (2019). Construction of a Non-negative Solution of the Leontief-Ford Model. Science Journal of Circuits, Systems and Signal Processing, 8(1), 19-23. https://doi.org/10.11648/j.cssp.20190801.13

Copy | Download

ACS Style

Fatima Ashakova. Construction of a Non-negative Solution of the Leontief-Ford Model. Sci. J. Circuits Syst. Signal Process. 2019, 8(1), 19-23. doi: 10.11648/j.cssp.20190801.13

Copy | Download

AMA Style

Fatima Ashakova. Construction of a Non-negative Solution of the Leontief-Ford Model. Sci J Circuits Syst Signal Process. 2019;8(1):19-23. doi: 10.11648/j.cssp.20190801.13

Copy | Download

@article{10.11648/j.cssp.20190801.13,
  author = {Fatima Ashakova},
  title = {Construction of a Non-negative Solution of the Leontief-Ford Model},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {8},
  number = {1},
  pages = {19-23},
  doi = {10.11648/j.cssp.20190801.13},
  url = {https://doi.org/10.11648/j.cssp.20190801.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20190801.13},
  abstract = {The article deals with the Leontief-Ford model, which is allowed to take into account the costs that necessary for the elimination of industrial waste. We consider its non-negative solution for those cases when the errors of the initial data have little influence on the result of the solution and for those cases when the errors of the initial data significantly affect the result of the solution. In the first case, it is called correctly delivered, and in the second incorrectly delivered. We use the iteration method to find a nonnegative solution to a correctly posed model, and also we use the regularization method to find a nonnegative solution to an ill-posed model. The developed technique is brought to a practical algorithm, which is implemented in the program "LF_2", it allows you to find a solution to the model, regardless of whether the model is correctly supplied or incorrectly supplied. An example of its application is given, where we enter the initial data of a poorly conditioned balance model into the program and obtain its non-negative solution. The results of this work may be interesting for specialists in economics and mathematical methods and models, as well as economic entities. It is known from practice that in the development of balance models of economic entities there are models with a bad number of conditionality. The application of the developed software product and methods described in this paper will allow economic entities to make quality and quick management decisions on the volume of product output of each sector of the economy, taking into account the costs necessary for the elimination of industrial waste, regardless of the conditionality and dimension of their balance models.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Construction of a Non-negative Solution of the Leontief-Ford Model
AU  - Fatima Ashakova
Y1  - 2019/08/08
PY  - 2019
N1  - https://doi.org/10.11648/j.cssp.20190801.13
DO  - 10.11648/j.cssp.20190801.13
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 19
EP  - 23
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20190801.13
AB  - The article deals with the Leontief-Ford model, which is allowed to take into account the costs that necessary for the elimination of industrial waste. We consider its non-negative solution for those cases when the errors of the initial data have little influence on the result of the solution and for those cases when the errors of the initial data significantly affect the result of the solution. In the first case, it is called correctly delivered, and in the second incorrectly delivered. We use the iteration method to find a nonnegative solution to a correctly posed model, and also we use the regularization method to find a nonnegative solution to an ill-posed model. The developed technique is brought to a practical algorithm, which is implemented in the program "LF_2", it allows you to find a solution to the model, regardless of whether the model is correctly supplied or incorrectly supplied. An example of its application is given, where we enter the initial data of a poorly conditioned balance model into the program and obtain its non-negative solution. The results of this work may be interesting for specialists in economics and mathematical methods and models, as well as economic entities. It is known from practice that in the development of balance models of economic entities there are models with a bad number of conditionality. The application of the developed software product and methods described in this paper will allow economic entities to make quality and quick management decisions on the volume of product output of each sector of the economy, taking into account the costs necessary for the elimination of industrial waste, regardless of the conditionality and dimension of their balance models.
VL  - 8
IS  - 1
ER  -

Copy | Download

Author Information

Fatima Ashakova

Department of Сomputer Science and Mathematics, U. D. Aliev Karachay-Cherkess State University, Karachayevsk, Russia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Fatima Ashakova. (2019). Construction of a Non-negative Solution of the Leontief-Ford Model. Science Journal of Circuits, Systems and Signal Processing, 8(1), 19-23. https://doi.org/10.11648/j.cssp.20190801.13

Copy | Download

ACS Style

Fatima Ashakova. Construction of a Non-negative Solution of the Leontief-Ford Model. Sci. J. Circuits Syst. Signal Process. 2019, 8(1), 19-23. doi: 10.11648/j.cssp.20190801.13

Copy | Download

AMA Style

Fatima Ashakova. Construction of a Non-negative Solution of the Leontief-Ford Model. Sci J Circuits Syst Signal Process. 2019;8(1):19-23. doi: 10.11648/j.cssp.20190801.13

Copy | Download

@article{10.11648/j.cssp.20190801.13,
  author = {Fatima Ashakova},
  title = {Construction of a Non-negative Solution of the Leontief-Ford Model},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {8},
  number = {1},
  pages = {19-23},
  doi = {10.11648/j.cssp.20190801.13},
  url = {https://doi.org/10.11648/j.cssp.20190801.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20190801.13},
  abstract = {The article deals with the Leontief-Ford model, which is allowed to take into account the costs that necessary for the elimination of industrial waste. We consider its non-negative solution for those cases when the errors of the initial data have little influence on the result of the solution and for those cases when the errors of the initial data significantly affect the result of the solution. In the first case, it is called correctly delivered, and in the second incorrectly delivered. We use the iteration method to find a nonnegative solution to a correctly posed model, and also we use the regularization method to find a nonnegative solution to an ill-posed model. The developed technique is brought to a practical algorithm, which is implemented in the program "LF_2", it allows you to find a solution to the model, regardless of whether the model is correctly supplied or incorrectly supplied. An example of its application is given, where we enter the initial data of a poorly conditioned balance model into the program and obtain its non-negative solution. The results of this work may be interesting for specialists in economics and mathematical methods and models, as well as economic entities. It is known from practice that in the development of balance models of economic entities there are models with a bad number of conditionality. The application of the developed software product and methods described in this paper will allow economic entities to make quality and quick management decisions on the volume of product output of each sector of the economy, taking into account the costs necessary for the elimination of industrial waste, regardless of the conditionality and dimension of their balance models.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Construction of a Non-negative Solution of the Leontief-Ford Model
AU  - Fatima Ashakova
Y1  - 2019/08/08
PY  - 2019
N1  - https://doi.org/10.11648/j.cssp.20190801.13
DO  - 10.11648/j.cssp.20190801.13
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 19
EP  - 23
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20190801.13
AB  - The article deals with the Leontief-Ford model, which is allowed to take into account the costs that necessary for the elimination of industrial waste. We consider its non-negative solution for those cases when the errors of the initial data have little influence on the result of the solution and for those cases when the errors of the initial data significantly affect the result of the solution. In the first case, it is called correctly delivered, and in the second incorrectly delivered. We use the iteration method to find a nonnegative solution to a correctly posed model, and also we use the regularization method to find a nonnegative solution to an ill-posed model. The developed technique is brought to a practical algorithm, which is implemented in the program "LF_2", it allows you to find a solution to the model, regardless of whether the model is correctly supplied or incorrectly supplied. An example of its application is given, where we enter the initial data of a poorly conditioned balance model into the program and obtain its non-negative solution. The results of this work may be interesting for specialists in economics and mathematical methods and models, as well as economic entities. It is known from practice that in the development of balance models of economic entities there are models with a bad number of conditionality. The application of the developed software product and methods described in this paper will allow economic entities to make quality and quick management decisions on the volume of product output of each sector of the economy, taking into account the costs necessary for the elimination of industrial waste, regardless of the conditionality and dimension of their balance models.
VL  - 8
IS  - 1
ER  -

Copy | Download