Simplex vs. Revised Simplex for Budget Allocation in Madrasah Teacher and Staff Development Programs under MoRA Kudus, Indonesia - Dina Fakhriyana; Mia Ning Anggreini (UIN Sumatera Utara, 2026)
This study compared the Simplex and Revised Simplex Methods for allocating the 2025 budget for the madrasah teacher and staff development programs under the Madrasah Education Division of the Ministry of Religious Affairs (MoRA) in Kudus, Indonesia. A quantitative case study design was employed to formulate a weighted linear programming model that identifies the most beneficial combination of programs under fixed budget constraints, with an emphasis on procedural comparison rather than policy impact. Both methods converged to the same optimal solution after four iterations, indicating equivalent computational performance for the small-scale model. The optimal allocation resulted in implementable program frequencies and achieved a maximum total weighted benefit of 129,133.6, primarily by prioritizing cost-free, high-benefit training programs while maintaining compliance with budget limits. Methodologically, the study demonstrates a transferable and reproducible linear programming framework that contributes to applied mathematics by illustrating how Simplex-based techniques can be adapted as transparent decision-support tools for small-scale public-sector budgeting problems. Although the Revised Simplex Method offers theoretical advantages for larger models, empirical differences in this case were minimal due to the model’s scale. The study was limited to a single fiscal year and did not include sensitivity analysis, which should be addressed in future research.