**MODELING BUS SCHEDULING IN BANDUNG CITY USING MAX-PLUS ALGEBRA***Iwan Sugiarto (a*), Ferry Jaya Permana (a**), Andry Yosep (a)*

a) Department of Mathematics, Parahyangan Catholic University

*iwans[at]unpar.ac.id; iwan301[at]gmail.com

**ferryjp[at]unpar.ac.id

**Abstract**

Problems in the network (graph theory) which are mainly related to synchronization problems can be modeled and solved using max-plus algebra. The problem above is that using ordinary mathematics in the form of non-linear mathematical models, using max-plus algebra can be a linear model in its operation. Problems that can be modeled and solved using Max-Plus Algebra, including the problem of scheduling public transportation. Congestion is now a common thing in big cities . One of the main factors causing traffic congestion is the lack of use of public transportation, one of which is the DAMRI bus. Referring to developed countries, such as Japan, the timely departure of public transportation is quite crucial in an effort to foster public interest in using public transportation rather than private vehicles. In this research, a DAMRI bus scheduling model will be developed in Bandung using Max-Plus Algebra. In the assessment, selected two DAMRI bus route in the city of Bandung, namely Dipatiukur - Leuwi Panjang and Ledeng - Leuwi Panjang. Both routes are transformed into a directed graph and then modeled for scheduling with Max-Plus Algebra. After being modeled, the eigenvalues and eigenvectors of the system will be determined. The eigenvalue represents the period (in minutes) of departure at each stop point or stop and the eigenvector represents the initial time of departure of the DAMRI bus in the city of Bandung. Determination of eigenvalues and eigenvectors using the application Scilab 5.3.3 and Max-Plus Toolbox Algebra. The results show the performance of the bus departure scheduling system, which means that every 3,7492308 minutes departs at each stop / stop. As for the bus departure schedule, if the DAMRI bus operation starts at 05.00, the result that departs first is the departure from the Pasir Kaliki stop point to Hasan Sadikin Hospital stop, followed by bus departures at other stops. With the bus departure scheduling system at each bus stop or terminal, it is expected that the Bandung City Transportation Department will pay attention to the DAMRI bus departure scheduling system so that there is no late departure at each stop.

**Keywords:** max-plus algebra, scheduling, eigenvalue and vector

**Topic:** Mathematics