MASALAH NILAI EIGEN ATAS ALJABAR MAX-PLUS PADA SISTEM PRODUKSI BULU MATA

  • Nadya Novika Universitas Jenderal Soedirman
  • Suroto Suroto Universitas Jenderal Soedirman
  • Bambang Hendriya Guswanto Universitas Jenderal Soedirman
Keywords: Eigen, max-plus, periodic, discrete event system

Abstract

A discrete event system is a system whose behavior is determined by events and their events change at discrete times. The eyelash production system at PT Bio Takara Purwokerto is a discrete event system problem and can be expresses in a max-plus linear problem. By using the power algorithm, it is determined eigen values ​​and eigen vectors over max-plus algebra which will be used as production time periodization. The results obtained that the periodic time for the eyelash production system at PT Bio Takara Purwokerto is 78.488 minutes. Based on this periodic time, we can then obtain the time each processing unit starts working to produce eyelashes.

References

Amaliyah, D. N., Sasana, H., & Prakoso, J. A. (2021). Teknikal Efisiensi Produksi Bulu Mata dan Rambut Palsu di Kabupaten Purbalingga: Stocastic Frontier Analysis. DINAMIC : Directory Journal of Economic, 3(3), 741–753.
Cassandras, C. G., & Lafortune, S. (Eds.). (2008). Introduction to Discrete Event Systems. Springer US. https://doi.org/10.1007/978-0-387-68612-7
Darwin, M., & Widaningrum, A. (2018). Kebijakan Ramah Perempuan dan Anak dalam Merespons Antagonisme Industri Rambut dan Bulu Mata Palsu di Kabupaten Purbalingga. Palastren, 11(1), 25–50.
Goto, H. (2014). Introduction to max-plus algebra. Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC ’14, 21–22. https://doi.org/10.1145/2608628.2627496
Hasanah, U., & Putrawangsa, S. (2015). Penggunaan Aljabar Max-Plus dalam Pembentukan Model Matematis pada Sistem Penjadwalan Praktikum Laboratorium. Beta, 8(1), 66–78.
Komenda, J., Lahaye, S., Boimond, J.-L., & van den Boom, T. (2018). Max-Plus Algebra in the History of Discrete Event Systems. Annual Reviews in Control, 45, 240–249. https://doi.org/10.1016/j.arcontrol.2018.04.004
Mayola, C. A., Megasari, D. S., Dwiyanti, S., & Lutfiati, D. (2021). Strategi Pemasaran Marketing Mix Produk Bulu Mata Palsu Ellashes.Pro. e-Jurnal, 10(3), 83–95.
Musthofa, M., & Binatari, N. (2013). Sifat-Sifat Nilai Eigen dan Vektor Eigen Matriks atas Aljabar Max-Plus. Jurnal Sains Dasar, 2(1), 25–31.
Nasrulyati, T. S. (2017). Aljabar Max-Plus dan Aplikasinya: Model Sistem Produksi Sederhana. Majalah Ilmiah Matematika dan Statistika, 17(1), 1–6.
Nugroho, A. J. (2021). Rancangan Sistem Manajemen Keselamatan dan Kesehatan Kerja Berdasarkan Metode Swift (Studi Kasus: Perusahan Bulu Mata). Jurnal DISPROTEK, 12(1), 25–33.
Permana, A., Siswanto, S., & Pangadi, P. (2020). Eigen Problem Over Max-Plus Algebra on Determination of the T3 Brand Shuttlecock Production Schedule. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 4(1), 23–30. https://doi.org/10.25217/numerical.v4i1.702
Pramesthi, S. R. P. W. (2017). Terapan Aljabar Max-Plus pada Sistem Proses Produksi Gelas. Jurnal Widyaloka, 4(2), 223–239.
Puadah, E. S. (2020). Perencanaan Penjadwalan Produksi Tahu Bulat dengan Menggunakan Metode Material Requirement Planning (MRP) pada IKM Windo Jaya di Tasikmalaya. Jurnal Mahasiswa Industri Galuh, 1(1), 69–75.
Purwati, E., & Fitriana, A. (2023). Pengaruh Kompensasi dan Motivasi Terhadap Kinerja Karyawan Bagian Pasang Bulu Mata (Studi Kasus Perusahaan Bulu Mata PT Hyup Sung Indonesia di Purbalingga). 14(1).
Putri, R. K. (2016). Penentuan Jalur Terpendek Menggunakan Aljabar Min-Plus. Studi Kasus: Distribusi Kentang Jalur Pangalengan, Bandung - Jakarta. Wahana, 66(1), 7–15. https://doi.org/10.36456/wahana.v66i1.477
Schutter, B. D., & Boom, T. V. D. (2008). Max-plus Algebra and Max-Plus Linear Discrete Event Systems: An Introduction. 2008 9th International Workshop on Discrete Event Systems, 36–42. https://doi.org/10.1109/WODES.2008.4605919
Stacia, V., & Gunanto, E. Y. A. (2014). Profil Industri Bulu Mata dan Rambut Palsu di Kabupaten Purbalingga. Diponegoro Journal of Economics, 3(1), 1–10.
Subiono, S. (2009). Aljabar Maxplus dan Aplikasinya: Model Sistem Antrian. Limits: Journal of Mathematics and Its Applications, 6(1), 49–59. https://doi.org/10.12962/j1829605X.v6i1.1431
Tunisa, K., Wijayanti, K., & Veronica, R. B. (2016). Nilai Eigen dan Vektor Eigen Matriks atas Aljabar Max-Plus. UNNES Journal of Mathematics, 6(2), 189–197.
Wibowo, A., Wijayanti, K., & Veronica, R. B. (2018). Penerapan Aljabar Max-Plus pada Pengaturan Sistem Antrian Traffic Light. UNNES Journal of Mathematics, 7(2), 192–205.
Published
2023-10-10
Abstract viewed = 251 times
PDF downloaded = 163 times