Modifikasi Metode Big-M dan Analisis Sensitivitasnya untuk Optimasi Produksi Usaha Kecil Menengah

Abstract

UKM (Small and Medium Enterprises) X is a business that produces various types of peanut brittle. Rempeyek is suitable as a snack and is popular with children and adults. The production process of UKM X is related to the quantity of demand and availability of raw materials. Therefore, optimal production planning is needed for UKM X to meet customer demand and obtain maximum profits. The problem of production is modeled into linear programming with the method used, namely, the method of Big M. The Big-M method is used because, on the function of the barrier on the production target, there is an equation , so artificial variables must be added to its solution. In this study, a modification of the Big-M method is made, and at the completion stage, it uses iteration with the determinant algorithm of the order of two matrices. The calculation results obtained the maximum profit of UKM X in a week of Rs5.455.775 by producing 56 kg of peanuts, 20 kg of seeds, 16 kg of spinach, 23 kg of tempe, and 60 kg of shrimp to meet customer requirements and utilize the availability of raw materials. Subsequently, sensitivity analysis is performed on the target function coefficient and the right street constants of the barrier to determine how the change affects the optimal solution. The results show that the solution remains optimal when profits are in the interval obtained, but the maximum profit value changes with constant production. Based on the calculation results, raw material supplies remain optimal when the change value is within the interval obtained.