1
Faculty of Science, Damascus University, Damascus, Syria
(maissam.jdid66@damascusuniversity.edu.sy)
2
University of New MexicoŘ Mathematics, Physics and Natural Sciences Division 705 Gurley Ave., Gallup, NM 87301, USA
( smarand@unm.edu)
Abstract :
Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort.
Keywords :
Linear programming; neutrosophic logic; neutrosophic simplex algorithm; modified neutrosophic simplex algorithm.
References :
[1] Alali. Ibrahim Muhammad, Operations Research. Tishreen University Publications, 2004. (Arabic version).
[2] Bugaha J.S, Mualla.W, Nayfeh.M, Murad. H, and other ,Operations Research Translator into Arabic, The Arab Center for Arabization, Translation, Authoring and Publishing, Damascus,1998. (Arabic version).
[3] Al Hamid .M, Mathematical programming, Aleppo University, Syria, 2010. (Arabic version).
[4] Maissam Jdid, Operations Research, Faculty of Informatics Engineering, Al-Sham Private University Publications, 2021. (Arabic version).
[5] David.G. Luenbrgrr.YinyuYe, Linear and Nonlinear Programming, Springer Science + Business Media-2015.
[6] Florentin Smarandache, Maissam Jdid, On Overview of Neutrosophic and Plithogenic Theories and Applications, Prospects for Applied Mathematics and Data Analysis (PAMDA), Vol .2, No.1, 2023.
[7] Smarandache, F., Introduction to Neutrosophic statistics, Sitech & Education Publishing, 2014.
[8] Smarandache, F., Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics University of New Mexico, Gallup, NM 87301, USA,2002.
[9] Smarandache, F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, Rehoboth, NM, 1999.
[10] Maissam Jdid, The Use of Neutrosophic linear Programming Method in the Field of Education, Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education, Chapter 15, IGI-Global,2023
[11] Maissam Jdid, Studying Transport Models with the Shortest Time According to the Neutrosophic Logic, Journal Neutrosophic Sets and Systems, NSS Vol. 58, 2023.
[12] Maissam Jdid, Florentin Smarandache, Optimal Neutrosophic Assignment and the Hungarian Method, Neutrosophic Sets and Systems, NSS, Vol.57,2023
[13] Maissam Jdid, Florentin Smarandache, Lagrange Multipliers and Neutrosophic Nonlinear Programming Problems Constrained by Equality Constraints, Journal of Neutrosophic Systems with Applications, Vol. 6, 2023
[14] Maissam Jdid, Florentin Smarandache, The Use of Neutrosophic Methods of Operation Research in the Management of Corporate Work, Journal of Neutrosophic Systems with Applications, Vol. 3, 2023
[15] Maissam Jdid, Said Broumi, Neutrosophic Rejection and Acceptance Method for the Generation of Random Variables, Neutrosophic Sets and Systems, NSS, Vol.56,2023
[16] Maissam Jdid, Khalifa Alshaqsi, Optimal Value of the Service Rate in the Unlimited Model , Journal of Neutrosophic and Fuzzy Systems (JNFS), Vo .6, No .1, 2023
[17] Maissam Jdid- Hla Hasan, The state of Risk and Optimum Decision According to Neutrosophic Rules, International Journal of Neutrosophic Science (IJNS), Vol. 20, No.1,2023
[18] Maissam Jdid, Important Neutrosophic Economic Indicators of the Static Model of Inventory Management without Deficit, Journal of Neutrosophic and Fuzzy Systems (JNFS), Vo .5, No .1, 2023
[19] Maissam Jdid, Florentin Smarandache, The Graphical Method for Finding the Optimal Solution for Neutrosophic linear Models and Taking Advantage of Non-Negativity Constraints to Find the Optimal Solution for Some Neutrosophic linear Models in Which the Number of Unknowns is More than Three, Journal Neutrosophic Sets and Systems, NSS Vol.58,2023
[20] Maissam Jdid, Huda E Khalid, Mysterious Neutrosophic Linear Models, International Journal of Neutrosophic Science, Vol.18, No. 2, 2022
[21] Maissam Jdid, AA Salama, Huda E Khalid, Neutrosophic Handling of the Simplex Direct Algorithm to Define the Optimal Solution in Linear Programming ,International Journal of Neutrosophic Science, Vol.18,No. 1, 2022
| Style | # |
|---|---|
| MLA | Maissam Jdid, Florentin Smarandache. "Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models." International Journal of Neutrosophic Science, Vol. 23, No. 1, 2024 ,PP. 117-124 (Doi : https://doi.org/10.54216/IJNS.230110) |
| APA | Maissam Jdid, Florentin Smarandache. (2024). Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 117-124 (Doi : https://doi.org/10.54216/IJNS.230110) |
| Chicago | Maissam Jdid, Florentin Smarandache. "Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models." Journal of International Journal of Neutrosophic Science, 23 no. 1 (2024): 117-124 (Doi : https://doi.org/10.54216/IJNS.230110) |
| Harvard | Maissam Jdid, Florentin Smarandache. (2024). Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 117-124 (Doi : https://doi.org/10.54216/IJNS.230110) |
| Vancouver | Maissam Jdid, Florentin Smarandache. Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 1 ): 117-124 (Doi : https://doi.org/10.54216/IJNS.230110) |
| IEEE | Maissam Jdid, Florentin Smarandache, Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 1 , (2024) : 117-124 (Doi : https://doi.org/10.54216/IJNS.230110) |