Max-plus algebra modeling for outpatient service queues in Yogyakarta private hospitals
DOI:
https://doi.org/10.30606/absis.v8i1.2785Keywords:
Aljabar Max-Plus, Antrian, Rawat Jalan, Max-Plus algebra, Petri net, outpatient queue, simulation, mathematical modelingAbstract
This study aims to model the outpatient service queue system in a private hospital in Yogyakarta using the Max-Plus algebra approach and to represent the model using a Petri net. The research was motivated by the complexity and inefficiency observed in outpatient queues, which often lead to long and unpredictable waiting times. Data were collected through direct observation of the outpatient process on the fourth floor of a private hospital. The sequence of services was first illustrated using a flowchart to map each stage experienced by patients. The time data for each process were then used to construct a Max-Plus algebra matrix, providing a mathematical model of the system. This model was further expressed in the form of a Petri net to illustrate the discrete and sequential nature of the service flow. The simulation was performed using Scilab software to analyze the system's dynamics. Results from the simulation revealed that the service system is non-periodic, indicated by the absence of an eigenvalue. This suggests that the total service time may increase as the number of patients grows. The findings provide insight into the structure of the outpatient queue system and offer a mathematical framework for future system analysis or optimization.
Downloads
References
Alamsyah, A., & Sari, R. F. (2023). Optimisasi Multi-Objektif Pada Pelayanan Kesehatan Di Ruang Rawat Inap Rumah Sakit . Jurnal Absis: Jurnal Pendidikan Matematika Dan Matematika, 6(1), 826–838. https://doi.org/10.30606/absis.v6i1.2200
Hardiyanti, S. A., Yuniwati, I., & Yustita, A. D. (2017). Bentuk Petri Net dan model aljabar Max-Plus pada sistem pelayanan pasien rawat jalan Rumah Sakit Al Huda Genteng, Banyuwangi. Jurnal UJMC, 3(2), 1–8.
Hariputra, R. P., Defit, S., & Sumijan. (2022). Analisis sistem antrian dalam meningkatkan efektivitas pelayanan menggunakan metode accidental sampling. Jurnal Sistem Informasi dan Teknologi, 4(2), 70–75. https://doi.org/10.37034/jsisfotek.v4i2.127
Kementerian Kesehatan Republik Indonesia. (2020). Peraturan Menteri Kesehatan Republik Indonesia Nomor 3 Tahun 2020 tentang Klasifikasi dan Perizinan Rumah Sakit.
Nawar, W., Rahakbauw, D. L., & Patty, D. (2023). Penjadwalan waktu proses produksi tahu menggunakan pendekatan aljabar Max-Plus (Studi kasus: Pabrik Sumber Rizki). Tensor, 4(2), 73–82. https://doi.org/10.30598/tensorvol4iss2pp73-82
Maure, O. P., Ningsi, G. P., & Nay, F. A. (2021). Pemodelan sistem antrian pasien rawat jalan menggunakan Petri Net dan aljabar Max-Plus: Studi kasus RSU di Yogyakarta. Leibniz: Jurnal Matematika, 1(2), 1–11. https://doi.org/10.59632/leibniz.v1i2.101
Rudhito, M. A. (2016). Aljabar Max-Plus dan Penerapannya. Sanata Dharma University Press.
Saumi, F., Amalia, R., Amelia, & Nurviana. (2021). Analisis Sistem Antrian Pada Pelayanan Poli Jantung RSUD Kota Langsa. Jurnal Absis: Jurnal Pendidikan Matematika Dan Matematika, 3(2), 297–308. https://doi.org/10.30606/absis.v3i2.668
Subiono. (2015). Aljabar Min-Max Plus dan terapannya.
Tutupary, F. S., & Lesnussa, Y. A. (2013). Aplikasi Petri Net pada sistem pelayanan pasien rawat jalan peserta Askes di Rumah Sakit Umum Daerah Dr. Haulussy Ambon. Gamatika, 3(2), 147–154.
Yahya, L., Nurwan, N., & Resmawan, R. (2022). Menentukan waktu optimal untuk pembuatan kerajinan sulaman Karawo menggunakan aljabar Max-Plus. Vygotsky, 4(1), 23. https://doi.org/10.30736/voj.v4i1.442
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Helena Noventyas Pradnyamita Budiarta, Brigitta Kierra Purwa Adhiananta, Marcellinus Andy Rudhito
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
