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# JURNAL: PENDEKATAN ALGORITMA GENETIKA DALAM MENYELESAIKAN PERMASALAHAN FUZZY LINEAR PROGRAMMING

### 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. Programming, Linear Programming, Two-Phase Simplex Method

### Pendahuluan

Sejauh ini, metode untuk mengkonversi fuzzy linear programming ke dalam matematika programming konvensional didominasi oleh penyelesaian masalah fuzzy linear programming. Penelitian tentang permasalahan fuzzy linear programming dimana koefisien fungsi kendala bersifat fuzzy sudah pernah dilakukan. Proses pendekatan yang dilakukan yaitu dengan mendefinisikan fungsi keanggotaan operasi aritmatika dan α-cut dalam proses perhitungannya.

Peneliti: S. Dewi Lestari dan Subanar