ANALISIS PERBANDINGAN METODE FUZZY SIMPLEKS DAN KUMAR DALAM OPTIMASI PRODUKSI FULLY FUZZY LINEAR PROGRAMMING
DOI:
https://doi.org/10.23969/jp.v11i03.57441Keywords:
Fully Fuzzy Linear Programming, Fuzzy simplex, Kumar method, Trapezoidal Fuzzy Numbers, Production optimizationAbstract
This study presents a comparative analysis of the fuzzy simplex method and Kumar’s method in solving production optimization problems based on Fully Fuzzy Linear Programming (FFLP). Since production systems often involve uncertainty in costs, resource availability, and market demand, all model parameters are represented using Trapezoidal Fuzzy Numbers. A quantitative comparative approach was employed using simulation data with two decision variables. The optimization model was solved using both methods, with Kumar’s method utilizing the Liou–Wang ranking function. The results show that the two methods produce the same optimal decision variable values, fuzzy profit values, and number of iterations required to achieve optimality. However, Kumar’s method offers a simpler computational procedure through ranking-based pivot selection, while the fuzzy simplex method better preserves fuzzy information during the iterative process. These findings indicate that both methods are effective for solving FFLP-based production optimization problems, with differences primarily in their computational mechanisms and operational complexity.
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Arana-Jiménez, M. (2022). On Generating Fuzzy Pareto Solutions in Fully Fuzzy Multiobjective Linear Programming via a Compromise Method. RAIRO-Operations Research, 56(6), 4035–4045. https://doi.org/10.1051/ro/2022196
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Arana-Jiménez, M. (2022). On Generating Fuzzy Pareto Solutions in Fully Fuzzy Multiobjective Linear Programming via a Compromise Method. RAIRO-Operations Research, 56(6), 4035–4045. https://doi.org/10.1051/ro/2022196
Behera, D., Peters, K., Edalatpanah, S. A., & Qiu, D. (2020). New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty. Journal of Information and Optimization Sciences, 25(24). https://doi.org/10.1080/02522667.2020.1758369
Bhowmick, A., Chakraverty, S., & Chatterjee, S. (2024). Parametric Optimization for Fully Fuzzy Linear Programming Problems with Triangular Fuzzy Numbers. Mathematics, 12(3051), 1–18.
Das, K. (2024). On Fully Fuzzy Linear Programming Problems. International Journal of Science and Social Science Research [IJSSSR], 2(3), 72–76.
Fathy, E., Ammar, E., & Helmy, M. A. (2023). Three Different Optimization Techniques for Solving the Fully Rough Interval Multi-Level Linear Programming Problem. Journal of Intelligent & Fuzzy Systems, 45(2). https://doi.org/10.3233/JIFS-230057
Figueroa-García, J. C., Hernández, G., & Franco, C. (2022). A review on history , trends and perspectives of fuzzy linear programming. Operations Research Perspectives, 9, 100247.
Ghanbari, R., Nezam, K. G., Mahdavi-Amiri, N., & Baets, B. De. (2019). Fuzzy linear programming problems : models and solutions. Soft Computing, 2(2012). https://doi.org/10.1007/s00500-019-04519-w
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