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All Journal Prosiding Seminar Nasional MIPA Jurnal Pendidikan Matematika RAFA EDU-MAT: Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Zero : Jurnal Sains, Matematika, dan Terapan Square : Journal of Mathematics and Mathematics Education Jurnal Pendidikan Matematika Unpatti
Dewa Putu Wiadnyana Putra
Universitas Sanata Dharma
Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Designing an Optimal Route Network for the Synchronized Trans Gadjah Mada Electric Bus (TGMEB) using Max-Plus Algebra Pranatta, Franciscus Budi; Rudhito, Marcellinus Andy; Putra, Dewa Putu Wiadnyana
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i2.25392

Abstract

We develop an optimal route network and synchronized timetable for the Trans Gadjah Mada Electric Bus (TGMEB), designed to cover the entire campus with 4 buses and 28 stops. Using literature review, field observation, and online mapping, we create three network candidates-one-, two-, and three-terminal-and model each as a max-plus linear discrete-event system. Service period and periodic departures are derived from eigenvalue-eigenvector analysis and implemented in Scilab 5.5.2 with a max-plus toolbox. The two-terminal layout performs best: its average inter-stop travel time is 32% faster than the other alternatives while keeping departures synchronized and coverage intact. The results confirm that jointly selecting the network architecture and its timetable yields superior campus operations. This is the first campus-scale study that co-designs a multi-terminal electric-bus route network and synchronized timetable via max-plus algebra, optimizing departure throughput and average inter-stop travel time. Unfortunately, this design has not been tested on the field.
Synchonized DAMRI Public Tourist Transportation Route Design using Max-Plus Algebra Yonantha, Krisma; Putra, Dewa Putu Wiadnyana; Rudhito, Marcellinus Andy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 1 (2026): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i1.33242

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.
Co-Authors Ayuningtyas, Lusia Diva Eko Budi Santoso Gede Suweken Herwidasari, Maria Priska Marcellinus Andy Rudhito Nugraha, Adhi Surya Pranatta, Franciscus Budi Pratiwi, Ni Putu Ayu Dias Ruditho, Marcellinus Andy Septicitaningtyas, Damiana Dewi Susanto, Anindito Wisnu Yonantha, Krisma Yovela, Christabel Yulia, Vista Putri