PENGEMBANGAN MODEL INTEGER LINIER PROGRAMMING PADA OPTIMASI PRODUKSI TAHU UMKM MENGGUNAKAN METODE BRANCH DAN BOUND DENGAN VALIDASI LINGO

Abstract

Production optimization is an important strategy for Micro, Small, and Medium Enterprises (MSMEs) to maximize profits under limited resources. Previous studies on tofu production optimization using the simplex method generated fractional solutions, making them less applicable in real production systems. Therefore, this study aims to determine the optimal production solution for tofu MSMEs using Integer Linear Programming with the Branch and Bound method and compare the results with the simplex method from previous research. This study used secondary data on the production of two types of tofu, namely white tofu and magel tofu. The problem was solved manually using the Branch and Bound method and validated using LINGO software. The results showed that the optimal integer solution was achieved by producing 14 buckets of white tofu and 6 buckets of magel tofu, resulting in a maximum profit of IDR 1,990,000. Meanwhile, the simplex method produced a higher profit of IDR 2,176,146, but the solution did not satisfy integer constraints. Validation using LINGO showed consistent results with manual calculations. Thus, the Branch and Bound method provides a more realistic solution for tofu production optimization in MSMEs.