Systematic Literature Review: Implementasi Metode Big M dalam Mengoptimalkan berbagai Kasus Program Linier

Abstract

Linear programming is a crucial operations research method for optimization problems in various fields like manufacturing and logistics, but it is often hindered by the absence of a basic feasible solution due to artificial variables. The Big M method addresses this by adding artificial variables and a large penalty, allowing the discovery of a valid initial solution without altering the constraint structure. This research employs a Systematic Literature Review (SLR) to examine the implementation of the Big M method in Indonesia from 2015-2025, analyzing journals and proceedings related to linear programming optimization. The review findings indicate that this method is highly effective and flexible for diverse cases such as production, animal feed, and scheduling, capable of handling artificial constraints and optimizing profit or cost. Although efficient, the Big M method has drawbacks, including computational complexity and dependence on the precise selection of the M value, which can affect result accuracy. Overall, the Big M Method remains relevant and important for real-world optimization problems requiring systematic constraint handling.