Program Multiobjektif Fuzzy Probabilistik dan aplikasinya untuk Model Inventory

ERTININGSIH, Dwi, Dr. Widodo, MS

2007 | Tesis | S2 Matematika

Dalam tesis ini dibahas penerapan pemrograman fuzzy untuk menyelesaikan masalah program multiobjektif probabilistik. Setelah mengkonversi dari masalah program probabilistik ke masalah deterministik (linear/ nonlinear), program fuzzy diterapkan menggunakan fungsi keanggotaan linear/ nonlinear untuk menemukan solusi komprominya. Diasumsikan koefisien variabel keputusan dalam fungsi tujuan dan kendala, termasuk parameter RHS (Right Hand Side), sebagai variabel random normal. Model inventory dalam program nonlinear fuzzy probabilistik dirumuskan dengan kendala biaya investasi dan kendala tempat. Biaya inventory, suatu parameter keputusan yang digunakan dalam fungsi objektif dan kendala, permintaan dan biaya investasi merupakan variabel random, dimana permintaan sebagai fungsi harga. Selain itu, ketidakpastian (impreciseness) juga berlaku pada tersedianya tempat penyimpanan dan total biaya rata-rata. Dengan asumsi variabel random di atas independen dan berdistribusi normal, model diformulasikan sebagai masalah program nonlinear probabilistik dan masalah program fuzzy probabilistik. Selanjutnya kedua masalah tersebut diselesaikan dengan metode pemrograman nonlinear fuzzy.

This thesis presents an application of fuzzy programming approach to the multiobjective probabilistic linear or nonlinear programming problem. After converting the proposed probabilistic programming problem into a deterministic problem, fuzzy programming approach using linear or nonlinear membership function is applied to find the compromise solution. For the multiobjective linear fuzzy probabilistic programming problem assume the coefficients of the decision variables in the objective functions and in the constraints and the right-hand-side parameters in the constraints as normal random variables. The inventory models in the fuzzy probabilistic nonlinear programming problem are formulated under investment and floor space constraints. For the models, inventory costs, one decision parameter involved in the objective function and goal on one of the constraints, goal on other constraint alongwith the objective goal are assumed to be random variables, which demand is a function of cost price. In the probabilistic problem, impreciseness is also introduced in the available storage area and permissible total average cost. Assuming random variables to be independent and to follow normal distribution, the models hva been formulated as probabilistic nonlinear and fuzzy probabilistic programming problems. Thus, both the problems are solved by fuzzy nonlinear programming method.

Kata Kunci : Program Fuzzy Probabilistik, Model Inventory, Fuzzy probabilistic programming, Linear and nonlinear membership function, Inventory model, Chance constrained programming.