Penjadwalan Kereta Bandara dan Commuter Line Yogyakarta Menggunakan Aljabar Max-Plus

Trains serve as a crucial mode of public transportation, significantly impacting people's mobility. Residents of Solo and Yogyakarta have experienced firsthand the benefits of trains for traveling between cities, whether using commuter or airport trains. However, the schedules for the YIA airport train, Adi-Soemarmo airport train, and Yogyakarta Commuter Line are not currently coordinated, as they are planned based solely on passenger demand. Synchronizing the departure times of these three train types is essential to ensure that trains are available when passengers need to transfer between different routes. This study aims to develop a network model for the departure schedules of the Yogyakarta Commuter Line, Yogyakarta International Airport (YIA) airport train, and Adi-Soemarmo airport train. It uses max-plus algebra to analyze the scheduling, culminating in the determination of eigenvalues and eigenvectors. The research employs literature review and Software Scilab. The findings revealed a maximum eigenvalue of (A) = 136 and an eigenvector in the form of a 16 1 real number matrix. Based on this maximum eigenvalue, a synchronized train schedule was created, with departures every 2 hours and 16 minutes, or 136 minutes.