APPLICATION OF UNCERTAIN MAX PLUS LINEAR FOR SHIP SCHEDULE SAFETY ANALYSIS: A CASE STUDY OF KM. LAMBELU
Abstract
This study aims to analyze the safety of the KM. Lambelu passenger ship schedule on its Parepare-Balikpapan route using the uncertain Max-Plus Linear (uMPL) approach. The uMPL model is used to represent the dynamics by considering the uncertainty of travel times between ports. Forward reachability analysis is conducted to verify whether the ship scheduling system meets the established safety criteria. The analysis results show that the analysis indicates that the KM. Lambelu scheduling system has safety vulnerabilities. This finding indicates the presence of potential accident or incident risks and emphasizes the need for evaluation and improvement of scheduling system to ensure ship operation within safe limits. This study identifies potential problems and risks associated with these findings and provides recommendations for improving the ship schedule.
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References
H. N. F. Adhalia et al, “SIMULATING THE DEPARTURE OF EGON PASSENGER MOTORSHIP USING UNCERTAIN MAX PLUS LINEAR,” in Proceedings of The 5th International Conference on Statistics, Mathematics, Teaching and Research, Atlantis Press International BV, 2023, pp. 138–144. doi: https://doi.org/10.2991/978-94-6463-332-0_16.
N. F. Adhalia H, A. P. Pratama, R. A. Tungga, I. M. Hamdani, and A. Bin Akkas, “PEMODELAN RUTE PERJALANAN KAPAL MOTOR BUKIT SIGUNTANG MENGGUNAKAN PETRI NET,” vol. 8, no. 2, 2025, doi: https://doi.org/10.30605/proximal.v8i2.5925.
N. Adhalia et al, “DYNAMICAL AFFINE SYSTEM DESIGN FOR SCHEDULING KM: EGON PASSENGER SHIP,” in Proceedings of The 5th Borneo International Conference BICAME, Balikpapan: SciTePress, Jul. 2025, pp. 149–155. doi: https://doi.org/10.5220/0013408500004605.
Anonymous, “MENHUB: PENUMPANG KM LAMBELU YANG KANDAS HARUS DILAYANI SAMPAI TUJUAN,” DIREKTORAT JENDERAL PERHUBUNGAN LAUT KEMENTERIAN PERHUBUNGAN REPUBLIK INDONESIA. Accessed: Apr. 30, 2025. [Online]. Available: https://hubla.dephub.go.id/home/post/read/4667/menhub-penumpang-km-lambelu-yang-kandas-harus-dilayani-sampai-tujuan
Anonymous, “TABRAKAN DENGAN KM LAMBELU, KM JOURNEY TENGGELAM DI SELAT MADURA,” Kompas.com. Accessed: Apr. 30, 2025. [Online]. Available: https://lifestyle.kompas.com/read/2014/04/01/0832486/Tabrakan.dengan.KM.Lambelu.KM.Journey.Tenggelam.di.Selat.Madura#google_vignette
B. Heidergott, G. J. Olsder, and J. Van Der Woude, MAX PLUS AT WORK: MODELING AND ANALYSIS OF SYNCHRONIZED SYSTEMS: A COURSE ON MAX-PLUS ALGEBRA AND ITS APPLICATIONS. Princeton University Press, 2014. [Online]. Available: http://about.jstor.org/terms
A. Kurniawan and A. Suparwanto, “MAX-PLUS LINEAR EQUATION SYSTEM AND ITS APPLICATION ON RAILWAY NETWORK SYSTEM,” Jurnal Matematika Thales (JMT), vol. 02, no. 01, pp. 63–77, 2020, doi: https://doi.org/10.22146/jmt.55316.
K. Sagawa, N. Yoshimura, Y. Shimakawa, and H. Goto, “A RAILWAY TIMETABLE SCHEDULING MODEL BASED ON A MAX-PLUS-LINEAR SYSTEM,” in 2020 59th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), IEEE, Sep. 2020, pp. 1575–1580. doi: https://doi.org/10.23919/SICE48898.2020.9240433.
K. Sagawa, Y. Shimakawa, and H. Goto, “TWO-LEVEL PRIORITY SCHEDULING FRAMEWORK IN A MAX-PLUS LINEAR REPRESENTATION,” SICE Journal of Control, Measurement, and System Integration, vol. 14, no. 2, pp. 97–103, 2021, doi: https://doi.org/10.1080/18824889.2021.1894886.
G. Espindola-Winck, R. M. F. Cândido, L. Hardouin, and M. Lhommeau, “EFFICIENT STATE-ESTIMATION OF UNCERTAIN MAX-PLUS LINEAR SYSTEMS WITH HIGH OBSERVATION NOISE,” in IFAC-PapersOnLine, Elsevier B.V., 2022, pp. 228–235. doi: https://doi.org/10.1016/j.ifacol.2022.10.347.
X. David-Henriet, J. Raisch, L. Hardouin, and B. Cottenceau, “MODELING AND CONTROL FOR (MAX, +)-LINEAR SYSTEMS WITH SET-BASED CONSTRAINTS,” in 2015 IEEE International Conference on Automation Science and Engineering (CASE), IEEE, Aug. 2015, pp. 1369–1374. doi: https://doi.org/10.1109/CoASE.2015.7294289.
P. Segovia, M. Pesselse, T. Van Den Boom, and V. Reppa, “SCHEDULING INLAND WATERWAY TRANSPORT VESSELS AND LOCKS USING A SWITCHING MAX-PLUS-LINEAR SYSTEMS APPROACH,” IEEE Open Journal of Intelligent Transportation Systems, vol. 3, pp. 748–762, 2022, doi: https://doi.org/10.1109/OJITS.2022.3218334.
B. Kersbergen, J. Rudan, T. van den Boom, and B. De Schutter, “TOWARDS RAILWAY TRAFFIC MANAGEMENT USING SWITCHING MAX-PLUS-LINEAR SYSTEMS,” Discret Event Dyn Syst, vol. 26, no. 2, pp. 183–223, 2016, doi: https://doi.org/10.1007/s10626-014-0205-7.
H. Al Bermanei, J. M. Böling, and G. Högnäs, “MODELING AND SCHEDULING OF PRODUCTION SYSTEMS BY USING MAX-PLUS ALGEBRA,” Flex Serv Manuf J, vol. 36, no. 1, pp. 129–150, 2024, doi: https://doi.org/10.1007/s10696-023-09484-z.
V. Subramanian, F. Farhadi, and S. Soudjani, “REINFORCEMENT LEARNING FOR STOCHASTIC MAX-PLUS LINEAR SYSTEMS,” in 2023 62nd IEEE Conference on Decision and Control (CDC), IEEE, Dec. 2023, pp. 5631–5638. doi: https://doi.org/10.1109/CDC49753.2023.10384207.
C. Wang, Y. Tao, and H. Yan, “OPTIMAL INPUT DESIGN FOR UNCERTAIN MAX‐PLUS LINEAR SYSTEMS,” International Journal of Robust and Nonlinear Control, vol. 28, no. 16, pp. 4816–4830, Nov. 2018, doi: https://doi.org/10.1002/rnc.4285.
D. Adzkiya, B. De Schutter, and A. Abate, “FORWARD REACHABILITY COMPUTATION FOR AUTONOMOUS MAX-PLUS-LINEAR SYSTEMS,” in Tools and Algorithms for the Construction and Analysis of Systems, E. Ábrahám and K. Havelund, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 2014, pp. 248–262. doi: https://doi.org/10.1007/978-3-642-54862-8_17.
D. Adzkiya, B. De Schutter, and A. Abate, “COMPUTATIONAL TECHNIQUES FOR REACHABILITY ANALYSIS OF MAX-PLUS-LINEAR SYSTEMS,” Automatica, vol. 53, pp. 293–302, 2015, doi: https://doi.org/10.1016/j.automatica.2015.01.002.
R. M. F. Cândido, L. Hardouin, M. Lhommeau, and R. S. Mendes, “CONDITIONAL REACHABILITY OF UNCERTAIN MAX PLUS LINEAR SYSTEMS,” 2018. doi: https://doi.org/10.1016/j.automatica.2017.11.030.
R. M. F. Candido, L. Hardouin, M. Lhommeau, and R. S. Mendes, “AN ALGORITHM TO COMPUTE THE INVERSE IMAGE OF A POINT WITH RESPECT TO A NONDETERMINISTIC MAX PLUS LINEAR SYSTEM,” IEEE Trans Automat Contr, vol. 66, no. 4, pp. 1618–1629, Apr. 2021, doi: https://doi.org/10.1109/TAC.2020.2998726.
A. P. Pratama and N. F. Adhalia H, “ALJABAR MAX-PLUS: VERIFIKASI KEAMANAN SISTEM PENJADWALAN KEBERANGKATAN KERETA API,” Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika, vol. 6, no. 2, pp. 1–11, 2023, doi: https://doi.org/10.30605/proximal.v6i2.2447.
Subiono, ALJABAR MIN-MAX PLUS DAN TERAPANNYA. Surabaya, 2017. Accessed: Apr. 30, 2025. [Online]. Available: https://www.its.ac.id/matematika/wp-content/uploads/sites/42/2018/08/Buku-Min-Max-Plus-2015-Subiono.pdf
A. P. Pratama, S. Subchan, and D. Adzkiya, “SAFETY VERIFICATION OF UNCERTAIN MAX-PLUS-LINEAR SYSTEMS,” INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND APPLIED MATHEMATICS, vol. 4, no. 2, pp. 52–55, 2018, doi: https://doi.org/10.12962/j24775401.v4i2.3454.
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