Analisis Sensitivitas Model Linear Programming Untuk Optimalisasi Produksi Pia Cendana Menggunakan Metode Branch and Bound
DOI:
https://doi.org/10.55657/rmns.v4i2.273Keywords:
Production Optimization, Linear Programming, Branch and Bound Method, Sensitivity Analysis, Pia CendanaAbstract
This study aims to optimize the production of Pia Cendana enterprise using a linear programming model based on the Branch and Bound method. In order to achieve maximum profit, a mathematical formulation is constructed, including an objective function and constraint functions based on data regarding raw material composition, resource availability, production costs, and selling prices of each product variant. The Branch and Bound method was applied to obtain an optimal solution in the form of integers that are operationally valid. In addition, a sensitivity analysis was conducted to evaluate the impact of changes in coefficients within the objective function and constraints on the optimal solution. The findings show that the Pia Cendana enterprise can achieve an optimal profit of IDR 1,620,000 or 1.86 % per month. This amount is higher than the previous actual profit of only IDR 86,888,000, indicating a profit increase of IDR 88,508,000. The study indicates that this method improves resource efficiency and yields more profitable production. The optimal solution demonstrates that production can be increased while still considering capacity and raw material limitations. The sensitivity analysis also proves that the model is sufficiently stable against parameter variations. This study provides practical contributions to Pia Cendana enterprise in formulating more efficient and profitable production strategies.
Downloads
References
[1] G. E. W. Mosey, J. U. L. Mangobi, and M. G. Maukar, “Optimasi Matematis Keuntungan Home Industry Pia Ibu Sandra Di Tombatu Utara,” J. Lebesgue J. Ilm. Pendidik. Mat. Mat. dan Stat., vol. 4, no. 2, pp. 1001–1009, 2023, doi: 10.46306/lb.v4i2.376.
[2] E. Oyokunyi, O. E. Isaac, and B. Nkoi, “The Cost of Gas Production Optimization Using Linear Programing on Reverse Fishbone Diagram : A Case Study,” vol. 3, no. 3, pp. 96–104, 2021.
[3] H. Aminudin, Prinsip-prinsip riset operasi. Jakarta,Erlangga, 2005.
[4] A. Alyanisa, J. Nahar, and N. Anggriani, “Apparel Production Optimization Model with Branch and Bound Method (Case Study: Sawargi Jersey Confectionery, West Java),” Int. J. Quant. Res. Model., vol. 4, no. 1, pp. 57–64, 2023, doi: 10.46336/ijqrm.v4i1.412.
[5] N. K. Oladejo, A. Abolarinwa, S. O. Salawu, A. F. Lukman, and H. I. Bukari, “Optimization principle and its’ application in optimizing landmark university bakery production using linear programming,” Int. J. Civ. Eng. Technol., vol. 10, no. 2, pp. 183–190, 2019.
[6] G. B. Dantzig, “Linear programming,” vol. 50, no. 1, pp. 42–47, 2002.
[7] M. Ismail, N. Achmad, and S. L. Mahmud, “Analisis Sensitivitas dalam Optimasi Keuntungan Produksi Kue Ulang Tahun dengan Metode Branch and Bound,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 10, no. 2, pp. 282–291, 2022, doi: 10.34312/euler.v10i2.15307.
[8] D. N. Syafitri, K. Kamid, and N. Rarasati, “Pengoptimalan Jumlah Produksi Roti Menggunakan Metode Branch and Bound,” Imajiner J. Mat. dan Pendidik. Mat., vol. 3, no. 2, pp. 183–194, 2021, doi: 10.26877/imajiner.v3i2.8099.
[9] K. V. Adtria, K. Kamid, and N. Rarasati, “Analisis Sensitivitas Dalam Optimalisasi Jumlah Produksi Makaroni Iko Menggunakan Linear Programming,” Imajiner J. Mat. dan Pendidik. Mat., vol. 3, no. 2, pp. 174–182, 2021, doi: 10.26877/imajiner.v3i2.8098.
[10] Y. Wakiden, D. Wungguli, N. Achmad, and N. Abas, “Analisis Sensitivitas Model Linear Programming dalam Optimalisasi Penjualan Produk di Toko Anggrek Plastik,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 12, no. 1, pp. 82–89, 2024, doi: 10.37905/euler.v12i1.21625.
[11] S. M. Mohungo, L. Yahya, R. Resmawan, and D. Wungguli, "Penerapan Model Integer Linear Programming pada Penjadwalan Petugas Satuan Pengamanan,'' Euclid, vol. 8, no. 1, pp. 6-15, Jan. 2021.
[12] F. Khilaliyah Azzahrha, R. Puspa Sari, M. Dhika Rahma Fauzi, and S. Karawang, “String (Satuan Tulisan Riset dan Inovasi Teknologi) Optimalisasi Produksi Tahu Menggunakan Metode Branch and Bound dan Cutting Plane,” Satuan Tulisan Ris. dan Inov. Teknol., vol. 6, no. 2, pp. 175–184, 2021.
[13] A. Saryoko, “Metode Simpleks dalam Optimasi Hasil Produksi,” J. Informatics Educ. Prof., vol. 1, no. 1, pp. 27–36, 2016.
[14] G. Tarigan, “Penerapan Metode Branch and Bound Dalam Menentukan Jumlah Produksi Optimum P,” Saintia Mat., vol. 2, no. 2, pp. 137–145, 2014.
[15] R. Ahmad, M. R. Katili, S. L. Mahmud, D. Wungguli, and L. O. Nashar, “Analisis Sensitivitas Model Goal Programming Pada Optimasi Produksi Roti Menggunakan Metode Branch and Bound,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 11, no. 2, pp. 216–227, 2023, doi: 10.37905/euler.v11i2.22299.
[16] S. Siswanto and M. S. Erlangga, Operational research. Jakarta: Erlangga, 2007.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Novarianti Firdaus, Salmun K. Nasib, Djihad Wungguli
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
