Synchonized DAMRI Public Tourist Transportation Route Design using Max-Plus Algebra

Krisma Yonantha; Dewa Putu Wiadnyana Putra; Marcellinus Andy Rudhito

doi:10.31764/jtam.v10i1.33242

Synchonized DAMRI Public Tourist Transportation Route Design using Max-Plus Algebra

Krisma Yonantha, Dewa Putu Wiadnyana Putra, Marcellinus Andy Rudhito

Abstract

The transportation system is a crucial infrastructure for supporting connectivity between each National Strategic Tourist Area (NSTA) tourist destination of Yogyakarta. Management of transportation network and scheduling departure of transportation services are not yet optimal. This study aims to design a synchronized DPTT route and schedule that covers the entire service area using max-plus algebra. This type of study is applied research. The scheduling problem will focus on determining the number of fleets serving all routes with departure periods below 60 minutes. This research was conducted through literature review, field observations and online maps using Google Maps, and computation using the Scilab program. The results show that time travel between 8 tourist destinations are organized into a strongly connected directed graph with 20 routes. Departures are modeled as a linear discrete-event system over max-plus algebra. Computation in Scilab produce a baseline departure period of 90 minutes. We evaluate by adding 2, 8, 10, or 12 of buses by reinforcing the longest route. The simulation shows that the addition of 10 and 12 buses in certain section can reduce the departure period to 56 and 48 minutes respectively. The results demonstrate that targeted fleet additions and network reconnection, guided by max-plus synchronization, can substantially improve service regularity and passenger connectivity.

Keywords

Route Design; Transportation; Synchonized; Max-Plus Algebra.

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References

Al Bermanei, H., Böling, J. M., & Högnäs, G. (2024). Modeling and scheduling of production systems by using max-plus algebra. Flexible Services and Manufacturing Journal, 36(1), 129–150. https://doi.org/10.1007/s10696-023-09484-z

Baccelli, F. (François). (1992). Synchronization and linearity : an algebra for discrete event systems. Wiley.

Dirza, R., Marquez-Ruiz, A., Özkan, L., & Mendez-Blanco, C. S. (2019). Integration of Max-Plus-Linear Scheduling and Control. In Computer Aided Chemical Engineering (Vol. 46, pp. 1279–1284). https://doi.org/10.1016/B978-0-12-818634-3.50214-9

Eramo, V. (2023). A max plus algebra based scheduling algorithm for supporting time triggered services in ethernet networks. Computer Communications, 198(1), 85–97. https://doi.org/10.1016/j.comcom.2022.11.014

Fiardi, A., Sulfi, D., Fuady, I., Suradika, A., & Andriansyah, A. (2025). Journal of Social and Policy Issues Quality of Intermodal Public Transportation Services as a Tool of Economic Efficiency in East Lombok Regency. JOURNAL OF SOCIAL AND POLICY ISSUES, 5(2). https://doi.org/10.58835/jspi.v5i2.434

Gonçalves, V. (2019). On Max-plus linear dynamical system theory: The observation problem. Automatica, 107(1), 103–111. https://doi.org/10.1016/j.automatica.2019.05.026

Gonçalves, M. V. (2021). Scheduling tank trucks at a fuel distribution terminal using max-plus model-based predictive control. Journal of Process Control, 103(1), 8–18. https://doi.org/10.1016/j.jprocont.2021.05.005

Heidergott, B. (2000). A characterisation of (max, +)-linear queueing systems. Queueing Systems, 35(1), 237–262. https://doi.org/https://doi.org/10.1023/A:1019102429650

Heidergott, B., Olsder, G. J., & Woude, J. van der. (2006). Max Plus at Work. Princeton University Press. http://about.jstor.org/terms

Hoekstra, M. (2020). Control of Delay Propagation in Railway Networks Using Max-Plus Algebra. TU Delft. https://resolver.tudelft.nl/uuid:b5816386-0ed9-4760-a6de-f0db0c3a5226

Joelianto, E. (2020). Design and simulation of traffic light control system at two intersections using max-plus model predictive control. International Journal of Artificial Intelligence, 18(1), 97–116. https://api.semanticscholar.org/CorpusID:229599953

Krivulin, N. K. (1995). A Max-Algebra Approach to Modeling and Simulation of Tandem Queueing Systems. In Mathl. Comput. Modelling (Vol. 22, Issue 3).

Kudryashova, A. Y., Frisk, V. V, Semyonova, T. I., & Shakin, V. N. (2020). Study of Effectiveness of Scilab Software Means for Solving Optimization Problems. 1(1), 1–5. https://doi.org/10.1109/WECONF48837.2020.9131166

Markkassery, S. (2024). Eigenvalues of Time-invariant Max-Min-Plus-Scaling Discrete-Event Systems. 2024 European Control Conference, ECC 2024, 2017–2022. https://doi.org/10.23919/ECC64448.2024.10591257

Martinez, C. (2022). Systems synchronization in Max-Plus algebra: a controlled invariance perspective. IFAC-PapersOnLine, 55(40), 1–6. https://doi.org/10.1016/j.ifacol.2023.01.039

Ministry of Public Works and Public Housing. (2024). Rencana Pengembangan Infrastruktur Wilayah 2025-2034 D.I. Yogyakarta. https://bpiw.pu.go.id/produk/rencana-pengembangan-infrastruktur-wilayah/rencana-pengembangan-infrastruktur-wilayah-2025-2034-provinsi-daerah-istimewa-yogyakarta

Mrugalski, M. (2023). Identification and health-aware economic control of production systems: A fuzzy logic max plus algebraic approach. Engineering Applications of Artificial Intelligence, 120(1), 105802–105802. https://doi.org/10.1016/j.engappai.2022.105802

Muhamad, M., Baiquni, M., & Wiryanto, W. (2024). Sustainable Tourism Ecosystem in Strategic National Tourism Area (KSPN) Borobudur Yogyakarta and Prambanan (BYP). Indonesian Journal of Geography, 56(3), 515–524. https://doi.org/10.22146/ijg.96409

Nagar, S. (2017). Introduction to Scilab. In Introduction to Scilab (pp. 1–14). Apress. https://doi.org/10.1007/978-1-4842-3192-0_1

Putra, Y., Sujayanto, P., Handayani, S., & Sugiharti, E. (2025). Impact Of Land Transportation Development On Tourist Interest In Revisiting Borobudur Temple. Issue 5. Ser, 27, 1–12. https://doi.org/10.9790/487X-2705080112

Riess, H. (2023). Max-Plus Synchronization in Decentralized Trading Systems. Proceedings of the IEEE Conference on Decision and Control, 221–227. https://doi.org/10.1109/CDC49753.2023.10383918

Rudhito, M. A. (2016). Alajabar Max-Plus dan Penerapannya. Sanata Dharma University Press.

Sagawa, K. (2020). A Railway Timetable Scheduling Model based on a Max-Plus-Linear System. 2020 59th Annual Conference of the Society of Instrument and Control Engineers of Japan, SICE 2020, 1575–1580.

Schutter, B. De. (2020). Analysis and control of max-plus linear discrete-event systems: An introduction. Discrete Event Dynamic Systems: Theory and Applications, 30(1), 25–54. https://doi.org/10.1007/s10626-019-00294-w

Sinaga, S. Y., & Kusumawardahni, A. (2024). Strategic Planning In Tourism Development in Simalungun Regency, Lake Toba. The 3rd International Conference On Economics, Business, and Management Research, 472–486. https://e-conf.usd.ac.id/index.php/icebmr/

Subiono. (2015a). Aljabar Min-Max Plus dan Terapannya. Jurusan Matematika ITS.

Subiono. (2015b). Aljabar Min-Max Plus dan Terapannya. Jurusan Matematika Institut Teknologi Sepuluh Nopember.

Umer, M., Hayat, U., Abbas, F., Agarwal, A., & Kitanov, P. (2020). An Efficient Algorithm for Eigenvalue Problem of Latin Squares in a Bipartite Min-Max-Plus System. Symmetry, 12(2), 311. https://doi.org/10.3390/sym12020311

Wahyudi, S., Mardiyono, M., Suaidi, I., & Apridana, F. H. (2023). Tourism Development in National Tourism Strategic Areas: Prospects and Local Community Participation. Journal of Environmental Management and Tourism, 14(8), 3078. https://doi.org/10.14505/jemt.v14.8(72).09

Watanabe, S. (2020). A walk on max-plus algebra. Linear Algebra and Its Applications, 598(1), 29–48. https://doi.org/10.1016/j.laa.2020.03.025

Widiarsih, D., Murialti, N., Darwin, R., Hadi, M. F., & Hidayat, M. (2018). Strategic Development of National Tourism Strategic Area (NTSA) Pulau Rupat. Prosiding CELSciTech, 3, 42-48.

Žužek, T. (2019). A Max-Plus algebra approach for generating a non-delay schedule. Croatian Operational Research Review, 10(1), 35–44. https://doi.org/10.17535/crorr.2019.0004

DOI: https://doi.org/10.31764/jtam.v10i1.33242