Karush Kuhn-Tucker (KKT) Approach for Production Cost Optimization in Falish Kitchen MSMEs, Prabumulih

Abstract

In the production process of Micro, Small, and Medium Enterprises (MSMEs), there is often a lack of careful calculation regarding the optimal production quantity for each type of product, which can lead to cost inefficiencies and suboptimal resource utilization. This study aims to minimize production costs at Dapur Falish MSMEs by applying the Karush Kuhn-Tucker (KKT) method as an optimization approach. The optimization model incorporates various constraints, including limited production capacity, to determine the optimal production levels. This problem is modeled mathematically and then formulated in the form of a Lagrange function. Each equation produced is analyzed systematically to ensure that the solution obtained meets the optimal conditions based on KKT requirements. The results show that the minimum production cost for Dapur Falish is IDR 897,389.7 per month. These findings provide practical insights for MSME owners in improving cost efficiency and support more effective production planning by identifying optimal resource allocation under existing constraints.