Pengoptimalan Masalah Nonlinier dalam Meminimumkan Biaya Produksi Menggunakan Separable Programming dan Algoritma Genetika

Abstract

This research aims to form a nonlinear model of the objective function in the case of minimizing production costs and the number of products that must be produced by Lanting Bumbu An-Nisa. The application of the separable programming method is carried out by transforming the nonlinear objective function and constraints to produce a linear objective function and constraints which are then solved by applying the genetic algorithm method. The application of this method produces a solution that producers must produce 250 packages of onion flavored lanting, 750 packages of cheese flavored lanting, 500 packages of sweet and spicy lanting and 500 packages of corn flavored lanting with a production cost of IDR 12,706,037.29. The nonlinear model formed in this problem was also solved directly using the genetic algorithm method which resulted in the solution that the total production of onion flavored lanting was 533 packages, 507 packages of cheese flavored lanting, 505 packages of sweet and spicy lanting and 455 packages of corn flavored lanting at a cost of the production that must be spent is IDR 11,213,943.55. The application of these two methods results in a difference in production costs of IDR 1,492,093.74. Based on these results, it shows that solving the nonlinear model directly using a genetic algorithm results in production costs that are 11.74% lower than the costs solved using separable programming.