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Construction of a Non-negative Solution of the Leontief-Ford Model
Science Journal of Circuits, Systems and Signal Processing
Volume 8, Issue 1, June 2019, Pages: 19-23
Received: Jun. 26, 2019; Accepted: Jul. 24, 2019; Published: Aug. 8, 2019
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Fatima Ashakova, Department of Сomputer Science and Mathematics, U. D. Aliev Karachay-Cherkess State University, Karachayevsk, Russia
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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.
Leontief-Ford Model, Non-negative Solution, Regularization Method, Iteration Method
To cite this article
Fatima Ashakova, Construction of a Non-negative Solution of the Leontief-Ford Model, Science Journal of Circuits, Systems and Signal Processing. Vol. 8, No. 1, 2019, pp. 19-23. doi: 10.11648/j.cssp.20190801.13
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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