PENDEKATAN ALGORITMA GENETIKA DALAM MENYELESAIKAN PERMASALAHAN FUZZY LINEAR PROGRAMMING

https://doi.org/10.22146/ijccs.5211

Siska Dewi Lestari(1*), Subanar Subanar(2)

(1) 
(2) 
(*) Corresponding Author

Abstract


Fuzzy linear programming is one of the linear programming developments which able to accommodate uncertainty in the real world. Genetic algorithm approach in solving linear programming problems with fuzzy constraints has been introduced by Lin (2008) by providing a case which consists of two decision variables and three constraint functions. Other linear programming problem arise with the presence of some coefficients which are fuzzy in linear programming problems, such as the coefficient of the objective function, the coefficient of constraint functions, and right-hand side coefficients constraint functions. In this study, the problem studied is to explain the genetic algorithm approach to solve linear programming problems where the objective function coefficients and right-hand sides are fuzzy constraint functions.

PT Dakota Furniture study case provides a linear programming formulation with a given objective function coefficients and right-hand side coefficients are fuzzy constraint functions. This study describes the use of genetic algorithm approach to solve the problem of linear programming of PT Dakota to maximize the mean income. The genetic algorithm approach is done by simulate every fuzzy number and each fuzzy numbers by distributing them on certain partition points. Then genetic algorithm is used to evaluate the value for each partition point. As a result, the Final Value represents the coefficient of fuzzy number.  Fitness function is done by calculating the value of the objective function of linear programming problems. Empirical results indicated that the genetic algorithm approach can provide a very good solution by giving some limitations on each fuzzy coefficient.

Genetic algorithm approach can be extended not only to resolve the case of PT Dakota Furniture, but can also be used to solve other linear programming case with some coefficients in the objective function and constraint functions are fuzzy.

Keywords : Genetic Algorithm, Fuzzy Linear Programming, Linear Programming, Two-Phase Simplex Method



Keywords


Genetic Algorithm, Fuzzy Linear Programming, Linear Programming, Two-Phase Simplex Method

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References

[1] Kumar, V.S.S., Awad S. Hanna dan P. Natarajan, 2003, Application of Fuzzy Linear Programming in Construction Projects, International Journal of IT in Architecture, Engineering and Construction, Volume I / Issue 4/ December 2003.

[2] Susanto, S., Dedy S., Hari A. dan YMK Aritonang, 2006, Pemodelan Pemprograman Linear dengan Koefisien Fungsi Objektif Berbentuk Bilangan Kabur Segitiga dan Kendalanya Kabur Beserta Usulan Solusinya, Jurnal Teknik Industri Vol. 8, No. 1 Juni 2006: 14-27. Universitas Katolik Parahyangan, Bandung.

[3] Lin, Feng-Tse, 2008, A Genetic Algorithm for Linear Programming With Fuzzy Constraints, Journal of Information Science and Engineering 24, 801-817, Chinese Culture University, Taipei, Taiwan.

[4] Winston, Wayne L., 2004, Operation Research Applications and Algorithm, Thomson Brooks/Cole, Canada.

[5] Wang, Li-Xin, 1996, A Course in Fuzzy Systems and Control, Prentice-Hall International, Inc., United States of America.

[6] Gen, M. dan R. Cheng, 1997, Genetic Algorithms and Engineering Design, John Wiley & Sons, Inc., United States of America.

[7] Haupt, L.R., and Haupt, E.S., 2004, Practical Genetic Algorithm, John Willey and Son, United States of America.



DOI: https://doi.org/10.22146/ijccs.5211

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