استخدام طريقتي روسل التقريبية الضبابية والتوزيع المعدل الضبابي لحل مشكلة النقل في البيئة الضبابية

Muna Shaker Salman

doi:10.51173/jt.v5i4.1035

Authors

Muna Shaker Salman Technical Institute / Alsuwayra, Middle Technical University, Baghdad, Iraq

DOI:

https://doi.org/10.51173/jt.v5i4.1035

Keywords:

Fuzzy Transportation Problem (FTP), Fuzzy Russell’s Approximation Method (FRAM), Fuzzy Modified Distribution Method (FMDM), Ranking Function (RF), Triangular Fuzzy Numbers (TFN)

Abstract

The transportation problem is one of the applications of linear programming problems. The traditional transportation problem assumes that the decision maker is sure of the transportation costs, supply, and demand for the product, but there are many cases in which the decision maker is not able to accurately determine the objective function data and/or constraints, so the fuzzy theory was used so that the decision-maker can determine that data. In this study, fuzzy Russell’s approximation method (FRAM) was developed to solve the fuzzy transport problem (FTP) when all the transport, supply, and demand cost parameters of the product are fuzzy numbers to get an initial basic feasible solution (IBFS). The fuzzy modify distribution method (FMDM) was also developed to test the fuzzy optimum solution from the accepted IBFS. The proposed methods are efficient, subtle, and easy to apply. To clarify the mechanism of action of these methods, an example was taken from real life and the problem of fuzzy transportation was solved in it.

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References

Hillier, F.S. and Liberman, G.J. Introduction to Operations Research. 7th Edn, McGraw-Hill Company, New York, USA, 2001.

Khalaf, W.S. Operations Research for Decision Support, Dar Ghaida for Publishing and Distribution. Amman. Jordan, 2022.

Bellman, R. E., & Zadeh, L. A., Decision-making in a fuzzy environment. Management science, 17(4), B-141, 1970, https://doi.org/10.1287/mnsc.17.4.B141.

Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28, 1978, https://doi.org/10.1016/0165-0114(78)90029-5.

Zimmermann, H. J., Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55, 1978, https://doi.org/10.1016/0165-0114(78)90031-3.

O. Eigeartaigh, M. A fuzzy transportation algorithm. Fuzzy Sets Syst., 8, 235-243, 1982.

Dubois, D., & Prade, H., Additions of interactive fuzzy numbers. IEEE Transactions on Automatic Control, 26(4), 926-936, 1981, https://doi.org/10.1109/TAC.1981.1102744.‏

Chanas, S., Kolodziejczyk, W. and Machaj, Anna, A fuzzy approach to the transportation problem. Fuzzy sets and Systems, 13(3), 211-221, 1984.‏

Lai, Y.J. and Hwang, C.L. Fuzzy Mathematical Programming: Methods and Applications. Springer-Verlag, Berlin, Germany, Pages: 301,1992.

Chanas, S., & Kuchta, D., A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy sets and systems, 82(3), 299-305, 1996.‏

Chanas, S., & Kuchta, D., Fuzzy integer transportation problem. Fuzzy sets and systems, 98(3), 291-298, 1998, https://doi.org/10.1016/S0165-0114(96)00380-6.‏

Liu, S. T., & Kao, C., Solving fuzzy transportation problems based on extension principle. European Journal of operational research, 153(3), 661-674, 2004, https://doi.org/10.1016/S0377-2217(02)00731-2.

Kumar, A., & Kaur, A., Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems. Fuzzy Information and Engineering, 3(1), 81-99, 2011, https://doi.org/10.1007/s12543-011-0068-7.‏

Kumar, B. R., & Murugesan, S., On fuzzy transportation problem using triangular fuzzy numbers with modified revised simplex method. International Journal of Engineering Science and Technology, 4(1), 285-294, 2012.

Narayanamoorthy, S., Saranya, S., & Maheswari, S., A method for solving fuzzy transportation problem (ftp) using fuzzy russell's method. International Journal of Intelligent Systems and Applications, 5(2), 71, 2013.‏

Hedid, M., & Zitouni, R., Solving the four index fully fuzzy transportation problem. Croatian Operational Research Review, 11(2), 199-215, 2020, https://hrcak.srce.hr/248145.‏

Krishnaveni, G., & Ganesan, K., An effective approach for the solution of fully fuzzy transportation problems. In IOP Conference Series: Materials Science and Engineering (Vol. 1130, No. 1, p. 012065). IOP Publishing, 2021, DOI 10.1088/1757-899X/1130/1/012065.‏

Ramesh a, R. and Suganya, R. Solving Russell’s Approximation method using best candidate method. International Journal of Mechanical Engineering, Vol. 7, No. 4, 2022.

Dubois, D.J. Fuzzy sets and systems: theory and applications. Academic press, 1980.‏

Pardalos, P. M., Aydogan, E. K., Gurbuz, F., Demirtas, O., & Bakirli, B. B., Fuzzy combinatorial optimization problems. Handbook of combinatorial optimization. Springer, New York, 1357-1413, 2013.

Khalaf, W. S., Solving the fuzzy project scheduling problem based on a ranking function. Australian Journal of Basic and Applied Sciences, 7(8), 806-811, 2013.

Kaufmann, A. and Gupta, M.M. Introduction to Fuzzy Arithmetic: Theory and Applications, New York, strand Reinhold, 1985.

Maleki, H. R., Ranking functions and their applications to fuzzy linear programming. Far East Journal of Mathematical Sciences, 4(3), 283-302, 2002.

Russell, E. J., Letters to the Editor—Extension of Dantzig's Algorithm to Finding an Initial Near-Optimal Basis for the Transportation Problem. Operations Research, 17(1), 187-191, 1969.

Zadeh, L.A. Fuzzy sets. Info. Contr., 8: 338-353, 1965.

Zimmermann, H. J., Fuzzy set theory—and its applications. Springer Science & Business Media, 2011.

WANG, S., A Manufacturer Stackelberg Game in Price Competition Supply Chain under a Fuzzy Decision Environment. IAENG International Journal of Applied Mathematics, 47(1), 2017.

Khalaf, W. S., A Fuzzy Dynamic Programming for the Optimal Allocation of Health Centers in some Villages around Baghdad. Baghdad Science Journal, 19(3), 0593-0593, 2022.

Khalaf, W. S., Khalaf, B. A., & Abid, N. O., A plan for transportation and distribution the products based on multi-objective travelling salesman problem in fuzzy environmental. Periodicals of Engineering and Natural Sciences, 9(4), 5-22, 2021, http://dx.doi.org/10.21533/pen.v9i4.2253.

A.M. Al-Mubarqa, “The use of hierarchical analysis and fuzzy goal programming in decision making with practical application” Master’s thesis / University of Baghdad, College of Administration and Economics. Iraq.

Herlina, L., & Anggraeni, E. (2019, December). Fuzzy inference system for evaluating supplier in shrimp agroindustry. In IOP Conference Series: Materials Science and Engineering (Vol. 673, No. 1, p. 012083). IOP Publishing, 2019, DOI 10.1088/1757-899X/673/1/012083.