Simulasi Perencanaan Produksi dengan Adanya Ketidakpastian pada Penambahan Bahan Baku Menggunakan Model Fuzzy Multi-Objective Linear Programming

Abstract

Production planning is a complex planning process carried out by companies to ensure that the production of goods or services can run efficiently and effectively. This research considers two objective functions and acknowledges the presence of uncertainty in the constraint functions, therefore the method used in this study is fuzzy multi-objective linear programming. The objectives that PTX Company aims to achieve are to maximize profit and minimize production costs. The first step is finding the solution from the linear programming model without tolerance (t = 0), with results of Z1 and Z2 equal to 1.457.300 and 537.700. Then, the solution to the linear programming model with tolerance (t = 1) with results for Z1 and Z2 equal to 1.537.800 and 567,200. The application of the fuzzy multi-objective linear programming model to the problem at PTX Company after using membership functions results is λ = 0.5, obtained using the LINDO application. After obtaining the value of λ, the additional raw materials to be added are as follows: 125 grams of flour, 85 grams of margarine, 82.5 grams of sugar, 97.5 grams of eggs, 35 grams of toppings, 22.5 grams of evaporated milk, and 12.5 grams of cream cheese. The total production for each type of cake after adding these raw materials for muffin (x1) is 110 pieces, cupcake (x2) is 50 pieces, brownies (x3) is 135 pieces, cream puff (x4) is 155 pieces, cheese tart (x5) is 128 pieces, and egg tart (x6) is 50 pieces. After substitute the quantities of each products to the maximum profit equation (Z1) and minimum product cost equation (Z2), PTX Company achieves a profit of Rp 1,493,450 for a day and production costs of Rp 550,550 for a day.