Profit Optimization for MSMEs in the Patchwork Fabric Industry Using Linear Programming and Simulated Annealing

Afnaria Afnaria (Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Islam Sumatera Utara, Medan)
Rina Filia Sari (Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Sumatera Utara, Medan)
Isnaini Halimah Rambe (Department of Mathematics Education, Faculty of Teacher Training and Education, Universitas Islam Sumatera Utara, Medan)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

Maximizing profitability is a key objective for Micro, Small, and Medium Enterprises (MSMEs), particularly those in the patchwork fabric industry. This study develops a multi-constraint Linear Programming (LP) model integrated with Simulated Annealing (SA) to determine the optimal production plan that maximizes profits while considering resource constraints. The LP model provides an optimal solution by selecting the most profitable product mix, whereas the SA heuristic explores a broader solution space to find alternative production plans. The results indicate that the LP model achieves a maximum profit of 16,640,000, primarily by selecting Tote bag as the most profitable product, while the SA approach distributes production across multiple products, resulting in a lower total profit of 7,739,000. Sensitivity analysis of the LP model highlights high reduced costs for non-selected products, making their inclusion in the production plan economically unfeasible. The findings suggest that LP is superior for-profit maximization, while SA provides alternative solutions for production diversification. Future research should explore hybrid approaches that integrate LP’s precision with SA’s flexibility to optimize MSME production strategies under uncertain demand conditions.