Volume 18 , Issue 1 , PP: 30-41, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Maissam Jdid 1 * , A. A. Salama 2 , Huda E. Khalid 3
Doi: https://doi.org/10.54216/IJNS.180104
Mathematical programming can express competency concepts in a well-defined mathematical model for a particular situation or system, and the ability to derive computational methods to solve this mathematical model, it is also a mathematical tool that allows us to model, analyze and solve a wide range of problems concerned with allocating rare resources of labor, materials, machinery, and capitals. Consequently, using them in the best attainable way to minimize costs or maximize profits. In such issues, the linear programming is one of the most widely used types of mathematical programming because it is a method that helps to make good decisions and decide the best program for independent activities, considering the available sources. It does not take in consideration the continuous and rapid changes and the state of instability in data. So, this manuscript studies one of the methods to solve linear models, which is the simplex method using the neutrosophic theory that covers all the data in analysing, whether specific or not, determined or not, having consistency or not, as well as it deeming all occurring changes. However, the optimal solution is related to the variables in the objective function, which in turn are affected by the fixed quantities that express the available possibilities. This article presents a study to solve the linear model using the simplex method in which the variables and their coefficients are indeterminate values, and we will explain the effected of the indeterminate values on the optimal solution of the mathematical model. The product mixture problem has been presented as case study to demonstrate the efficiency of the proposed method.
Simplex Algorithm , Operations Research , Mathematical Programming , Linear Programming , Neutrosophic Logic , Products Mixture Model
[1] Wael Khansa- Ola Abu Amsha . Operations Research (1), Faculty of Informatics Engineering -
Damascus University Publications, 2005.
[2] Maissam Jdid, Operations Research, Faculty of Informatics Engineering, Al-Sham Private
University Publications, 2021.
[3] Alali. Ibrahim Muhammad, Operations Research. Tishreen University Publications, 2004.
(Arabic version).
[4] Al Hamid, Mohammed Dabbas, Mathematical programming, Aleppo University, Syria, 2010,
(Arabic version).
[5] DavidG. Luenbrgrr.YinyuYe, Linear and Nonlinear Programming, Springer Science + Business
Media-2015.
[6] Zadeh, L. A., Fuzzy Sets. Inform. Control 8 (1965).
[7] Smarandache, F., Introduction to Neutrosophic statistics, Sitech & Education Publishing, 2014.
[8] Atanassov, K., Intuitionistic fuzzy sets. In V. Sgurev, ed., ITKRS Session, Sofia, June 1983,
Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984.
[9] 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.
[10] Smarandache, F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic
Set, Neutrosophic Probability. American Research Press, Rehoboth, NM, 1999.
[11] Smarandache, F., Neutrosophic set a generalization of the intuitionistic fuzzy sets. Inter. J. Pure
Appl. Math., 24, 287 – 297, 2005.
[12] Salama, A. A., Smarandache, F., & Kroumov, V., Neutrosophic crisp Sets & Neutrosophic crisp
Topological Spaces. Sets and Systems, 2(1), 25-30, 2014.
[13] Smarandache, F. & Pramanik, S. (Eds). (2016). New trends in neutrosophic theory and
applications. Brussels: Pons Editions.
[14] Alhabib, R., The Neutrosophic Time Series, the Study of Its Linear Model, and test Significance
of Its Coefficients. Albaath University Journal, Vol.42, 2020, (Arabic version).
[15] Alhabib, R., Ranna, M., Farah, H. & Salama, A. A., Neutrosophic Exponential Distribution.
Albaath University Journal, Vol.40, 2018, (Arabic version).
[16] Alhabib, R., Ranna, M., Farah, H. and Salama, A. A, studying the random variables according to
Neutrosophic logic. Albaath- University Journal, Vol (39), 2017, (Arabic version).
[17] Alhabib, R., Ranna, M., Farah, H. & Salama, A. A., Neutrosophic decision-making &
neutrosophic decision tree. Albaath- University Journal, Vol (04), 2018, (Arabic version).
[18] Alhabib, R., Ranna, M., Farah, H. & Salama, A. A., Studying the Hypergeometric probability
distribution according to neutrosophic logic. Albaath- University Journal, Vol (04), 2018,
(Arabic version).
[19] Salama, A. A., Smarandache, F., Neutrosophic Crisp Set Theory, Educational. Education
Publishing 1313 Chesapeake, Avenue, Columbus, Ohio 43212, (2015).
[20] Salama, A. A., & Smarandache, F. Neutrosophic crisp probability theory & decision making
process, Critical Review: A Publication of Society for Mathematics of Uncertainty, vol. 12, p.
34-48, 2016.
[21] Alhabib, R., Ranna, M., Farah, H. & A. A Salama, Foundation of Neutrosophic Crisp Probability
Theory, Neutrosophic Operational Research, Volume III, Edited by Florentin Smarandache,
Mohamed Abdel-Basset and Dr. Victor Chang (Editors), pp.49-60, 2017.
[22] Alhabib, R., Ranna, M., Farah, H., & Salama, A. A., Some Neutrosophic Probability
Distributions. Neutrosophic Sets and Systems, 22, 30-38, 2018.
[23] Aslam, M., Khan, N., & Khan, M.A., Monitoring the Variability in the Process Using the
Neutrosophic Statistical Interval Method, Symmetry, 10 (11), 562, 2018.
[24] Aslam, M., Khan, N. and AL-Marshadi, A. H., Design of Variable Sampling Plan for Pareto
Distribution Using Neutrosophic Statistical Interval Method, Symmetry, 11 (1), 80, 2019.
[25] F. Smarandache, H. E. Khalid, A. K. Essa, M. Ali, “The Concept of Neutrosophic Less Than or
Equal To: A New Insight in Unconstrained Geometric Programming”, Critical Review, Volume
XII, 2016, pp. 72-80.
[26] F. Smarandache, H. E. Khalid, A. K. Essa, “Neutrosophic Logic: The Revolutionary Logic in
Science and Philosophy”, Proceedings of the National Symposium, EuropaNova, Brussels, 2018.
[27] H. E. Khalid, “An Original Notion to Find Maximal Solution in the Fuzzy Neutrosophic Relation
Equations (FNRE) with Geometric Programming (GP)”, Neutrosophic Sets and Systems, vol. 7,
2015, pp. 3-7.
[28] H. E. Khalid, “The Novel Attempt for Finding Minimum Solution in Fuzzy Neutrosophic
Relational Geometric Programming (FNRGP) with (max, min) Composition”, Neutrosophic Sets
and Systems, vol. 11, 2016, pp. 107-111.
[29] H. E. Khalid, F. Smarandache, A. K. Essa, (2018). The Basic Notions for (over, off, under)
Neutrosophic Geometric Programming Problems. Neutrosophic Sets and Systems, 22, 50-62.
[30] H. E. Khalid, (2020). Geometric Programming Dealt with a Neutrosophic Relational Equations
Under the Operation. Neutrosophic Sets in Decision Analysis and Operations
Research, chapter four. IGI Global Publishing House.
[31] H. E. Khalid, “Neutrosophic Geometric Programming (NGP) with (max-product) Operator, An
Innovative Model”, Neutrosophic Sets and Systems, vol. 32, 2020.
[32] H. E. Khalid, F. Smarandache, A. K. Essa, (2016). A Neutrosophic Binomial Factorial Theorem
with their Refrains. Neutrosophic Sets and Systems, 14, 50-62.
[33] H. E. Khalid, A. K. Essa, (2021). The Duality Approach of the Neutrosophic Linear
Programming. Neutrosophic Sets and Systems, 46, 9-23.
