A Linear Programming Approach for Optimizing the Number of Machines to Minimize Total Production Costs

Abstract

Production capacity planning plays an important role in manufacturing systems because it affects a company’s ability to meet market demand while maintaining operational efficiency and cost effectiveness. Many small and medium-sized enterprises (UMKM) face difficulties in determining the optimal number of production machines, which often results in either insufficient production capacity or excessive investment costs. This study aims to develop a Linear Programming model to determine the optimal number of production machines required to minimize total production costs while satisfying production capacity requirements. The study was conducted at a snack food manufacturing UMKM in West Java, Indonesia. Data related to machine capacity, production demand, operating time, and production costs were collected through field observations, interviews, and company records. The optimization model was formulated by considering machine capacity, available production time, labor availability, and demand constraints and was solved using Microsoft Excel Solver. The results show that the optimal solution requires the addition of five units of Machine 1 and ten units of Machine 2 during the 2027–2029 planning horizon, while no additional Machine 3 is required. The proposed machine configuration achieves a minimum total production cost of Rp479,284,521,556 while meeting projected production demand. These findings demonstrate that Linear Programming can serve as an effective decision-support tool for production capacity planning and machine investment allocation. Future research should incorporate demand uncertainty and machine reliability factors to improve the robustness of optimization results.