Electronic Theses and Dissertation

Penelitian dalam tugas akhir ini mengkaji masalah kontrol optimal permasalahan pajak kendaraan bermotor yang mengacu pada penelitian Program Kreativitas Mahasiswa (PKM). Tujuan dari penelitian ini adalah mengembangkan model pajak kendaraan bermotor yang telah dilakukan pada penelitian PKM dengan penambahan variabel pemutihan pajak serta menemukan solusi optimal permasalahan pajak kendaraan bermotor dalam hal meminimumkan jumlah kendaraan yang menunggak pajak. Penyelesaian masalah dalam penelitian ini dilakukan dengan pendekatan analitik dan pendekatan numerik. Penyelesaian secara analitik menggunakan prinsip minimum Pontryagin yaitu dengan membentuk persamaan Hamiltonian sehingga diperoleh fungsi pengontrol. Selanjutnya hasil yang diperoleh dari pendekatan analitik diselesaikan melalui pendekatan numerik dengan menggunakan metode Runge-Kutta orde 4 serta disimulasikan menggunakan MATLAB R2017a. Berdasarkan hasil penelitian dapat disimpulkan bahwa solusi optimal pengontrolan permasalahan pajak kendaraan bermotor terjadi ketika semua jenis kontrol diterapkan pada model. Sistem yang diberikan kontrol sosialisasi, Early Warning System (EWS), dan tilang mampu memberikan hasil yang paling optimal sehingga jumlah kendaraan yang menunggak pajak yang tereduksi semakin banyak. Akibatnya jumlah kendaraan yang wajib pajak, jatuh tempo pajak, pemutihan pajak, dan lunas pajak meningkat.
Kata kunci: Pajak kendaraan bermotor, kontrol optimal, prinsip minimum Pontryagin, metode Runge-Kutta orde 4, MATLAB R2017a.

The research in this final project examines the problem of optimal control of motor vehicle tax problems which refers to the Student Creativity Program (PKM) research. The purpose of this study is to develop a motor vehicle tax model that has been carried out in the PKM research with the addition of a tax whitening variable and to find the optimal solution to the motor vehicle tax problem in terms of minimizing the number of vehicles that are tax arrears. Problem solving in this research is done by using analytical approach and numerical approach. Analytical solution using Pontryagin minimum principle namely by forming the Hamiltonian equation so that the controller function is obtained. Furthermore, the results obtained from the analytical approach were resolved through a numerical approach using the Runge-Kutta method of order 4 and simulated using MATLAB R2017a. Based on the results of the study, it can be concluded that the optimal solution for controlling motor vehicle tax problems occurs when socialization, EWS, and ticketing controls are carried out on the model. The system that is given socialization control, Early Warning System (EWS), and ticketing is able to provide the most optimal results so that the number of vehicles that are tax arrears is reduced more and more. As a result, the number of vehicles that are taxpayers, tax due, tax waivers, and paid off taxes increases. Keywords: Motor vehicle tax, optimal control, Pontryagin minimum principle, Runge-Kutta method of order 4, MATLAB R2017a.