Model Aljabar Max-Plus pada Sistem Distribusi Produk Bakery dengan Representasi Petri Net

Penulis

  • Siti Nurlaila Mustapa Universitas Negeri Gorontalo
  • Nurwan Nurwan Universitas Negeri Gorontalo, Gorontalo-Indonesia
  • La Ode Nashar Universitas Negeri Gorontalo, Gorontalo-Indonesia

DOI:

https://doi.org/10.47662/farabi.v9i1.1397

Kata Kunci:

Aljabar Max-Plus, Petri Net, Pemodelan Waktu Distribusi, Distribusi Produk Bakery, Analisis Bottleneck

Abstrak

Distribution efficiency is a critical aspect of bakery product distribution systems, as delivery delays affect product freshness, operational costs, and service reliability to customers. This study aims to develop a mathematical model to analyze product distribution time at UD. Win Win Bakery by integrating Petri Nets and Max-Plus Algebra. Petri Nets are used to represent the sequential, event-based distribution process, including vehicle preparation, goods loading, distribution travel, goods unloading, and the return trip to the factory. The Petri Net structure is then transformed into a Max-Plus Algebra model and matrix to calculate the total distribution time for each team. Data were collected through observations and interviews regarding distribution schedules, routes, number of vehicles, loading time, unloading time, and travel duration. The results show significant variations in distribution times among the nine delivery teams. The longest durations were found on the Toboli–Parigi, Ampibabo, and Kotamobagu routes, indicating workload imbalance and potential bottlenecks in the distribution system. The main contribution of this study lies in the application of Max-Plus Algebra supported by Petri Nets as a structured framework to identify time inefficiencies in regional-scale distribution. The implications of this study suggest that Max-Plus Algebra can be effectively used in discrete event-based distribution systems and supports route evaluation, workload balancing, and operational decision-making in perishable product logistics.

Referensi

Adhalia, N. F. H., Pratama, A. P., Tungga, R. A., Hamdani, I. M., & Akkas, A. Bin. (2025). Pemodelan rute perjalanan kapal motor Bukit Siguntang menggunakan Petri Net. Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 8(2), 685–692.

Bhardwaj, M., & Agrawal, R. (2020). Operational efficiency of perishable product supply chain using Petri Net technique. Proceedings of the International Conference on Industrial Engineering and Operations Management, 2126–2133. Dubai, UAE.

Clarisa, Rahma, F. L., Nur, F., Hasibuan, K., Khodijah, N., & Maysarah, S. (2021). Analisis Kemampuan Berpikir Kritis Mahasiswa Pendidikan Matematika Dalam Memecahkan Masalah Struktur Aljabar Ring Materi Daerah Integral Dan Field. FARABI: Jurnal Matematika Dan Pendidikan Matematika, 4(1), 52–60. https://doi.org/https://doi.org/10.47662/farabi.v4i1.93

Doberhol, J., Suroto, & Guswanto, B. H. (2024). Penyelesaian Sistem Persamaan Linier Atas Aljabar Max-Plus Dan Aplikasinya Menggunakan Visual Studio. Jurnal Ilmiah Matematika Dan Pendidikan Matematika (JMP), 16(2), 185–200.

Khairina, I. N., A’yun, Q. Q., & Sandariria, H. (2025). Aplikasi Aljabar Max-Plus dan Petri Net dalam penentuan waktu optimal produksi tempe di Pabrik Tempe Asli HB Samarinda. Journal of Mathematics Education and Science, 8(1), 38–49.

Khotimah, S. H., A’yun, Q. Q., & Wasono. (2024). Pemodelan Sistem Antrean Pelayanan Pembayaran Pajak Kendaraan Bermotor Menggunakan Petri Net dan Aljabar Max-Plus di Samsat MT Haryono Samarinda. Journal of Mathematics Education and Science, 7(1), 65–75. https://doi.org/https://doi.org/10.32665/james.v7il.1935

Kismanti, S. T., & Indriyani, D. (2021). Penerapan aljabar pada sistem produksi. Jurnal Borneo Saintek, 4(1), 37–42.

Mustofani, D., Farida, U., & Ariadhita, B. Y. (2022). Model matematika perencanaan dan pengadaan obat di instalasi farmasi rumah sakit dengan menggunakan aljabar Max Plus. Unisda Journal of Mathematics and Computer Science (UJMC), 8(2), 15–20.

Nabilasalva, A., & Nurdiani, T. W. (2024). Pentingnya layanan logistik dari produsen ke konsumen yang dilaksanakan oleh PT. Sinarmas Distribusi Nusantara dalam pemasaran produk. Jurnal Pengabdian Masyarakat, 1(1), 303–306.

Putri, D. P. A., & Sukardi, A. (2023). Analisis Pengaruh Distribusi dan Harga Terhadap Peningkatan Penjualan Produk. MENAWAN: Jurnal Riset Dan Publikasi Ilmu Ekonomi, 1(6), 42–50.

Rauf, M. D. A., Nurwan, Yahya, L., & Nuha, A. R. (2021). Model penjadwalan proyek pembangunan perumahan Menggunakan Petri Net dan aljabar Max-Plus. Jurnal Edukasi Dan Sains Matematika (JES-MAT), 7(1), 31–42.

Sakta, R. R., Yanita, & Helmi, M. R. (2022). Aljabar Max-Plus serta aplikasinya pada sistem antrian. Jurnal Matematika UNAND, 11(4), 271–283.

Sholehurrohman, R., Ilman, I. S., Hermanto, B., & Muhaqiqin. (2024). Sistem distribusi sederhana penjualan kopi Lampung menggunakan aljabar Max-Plus. Ilmu Komputer Unila, 12(1), 19–28.

Simanjuntak, S. N., Sahputra, N., & Firah, A. (2024). Pengaruh persediaan barang dan saluran distribusi terhadap volume penjualan pada PT. Everbright di Medan. Jurnal Ilmiah Manajemen Dan Bisnis, 18(2), 414–425.

Subiono. (2015). Aljabar min-max plus dan terapannya. Surabaya: Institut Teknologi Sepuluh November.

Unduhan

Diterbitkan

2026-06-24

Cara Mengutip

Mustapa, S. N., Nurwan, N., & Nashar, L. O. (2026). Model Aljabar Max-Plus pada Sistem Distribusi Produk Bakery dengan Representasi Petri Net. FARABI: Jurnal Matematika Dan Pendidikan Matematika , 9(1), 01–14. https://doi.org/10.47662/farabi.v9i1.1397

Terbitan

Vol 9 No 1 (2026): FARABI: Jurnal Matematika dan Pendidikan Matematika

Bagian

Articles

Lisensi

Hak Cipta (c) 2026 Siti Nurlaila Mustapa, Nurwan Nurwan, La Ode Nashar

Creative Commons License

Artikel ini berlisensiCreative Commons Attribution-ShareAlike 4.0 International License.