Electronic Theses and Dissertation

Pada instansi penyedia layanan keuangan seperti Bank, antrian merupakan keadaan di mana nasabah yang membutuhkan pelayanan harus menunggu untuk mendapatkan pelayanan. Antrian terjadi karena tingginya kedatangan nasabah melebihi kapasitas pelayanan. Teori antrian adalah teori yang berkaitan dengan studi matematis dari antrian-antrian atau garis tunggu nasabah. Tujuan penelitian ini memperoleh model antrian yang optimal pada suatu Bank menggunakan distribusi kedatangan dan waktu pelayanan. Sistem antrian dikatakan optimal ketika nilai kuantitas steady state kurang dari 1 atau nilai rho kurang dari 1 yang artinya laju kedatangan tidak lebih besar dari laju pelayanan dan jumlah server pelayanan. Berdasarkan analisa yang dilakukan, model antrian pada Bank X yang diperoleh yaitu(M/M/5):(FCFS/∞/∞) yang berarti kedatangan nasabah berdistribusi Poisson dan waktu pelayanan pelayanan nasabah berdistribusi Eksponensial. Jumlah server pelayanan pada Bank X sebanyak 5 server, dengan disiplin antrian first come first served yang artinya nasabah yang datang pertama mendapatkan pelayanan terlebih dahulu. Kapasitas sistem antrian dan sumber populasi yang dimiliki tidak terbatas. Rata-rata laju kedatangan yang diperoleh sebesar 0,3246 nasabah per menit dengan rata-rata laju pelayanan sebesar 0,2839 nasabah per menit. Nilai rata-rata steady state yang diperoleh yaitu 0,2348, yang artinya rho kurang dari 1 maka sistem antrian pada Bank X sudah optimal sehingga tidak dilakukan penambahan server. Telah diperoleh pula ukuran-ukuran kefektifan pada model antrian berupa peluang rata-rata teller sedang tidak melayani nasabah sebesar 34,08% dari keseluruhan pelayanan. Rata-rata jumlah nasabah dalam antrian sebanyak 1 nasabah dengan rata-rata waktu nasabah harus menunggu dalam antrian adalah 0,0310 menit dan rata-rata waktu yang dihabiskan nasabah dalam sistem adalah 3,6520 menit dengan rata-rata jumlah nasabah yang menunggu dalam sistem adalah 1 nasabah. Pada sistem antrian Bank X, diperoleh minimum server supaya sistem antrian tetap optimal adalah saat jumlah servernya 3 dan diperoleh model antriannya yaitu (M/M/3):(FCFS/∞/∞).

Kata kunci : Antrian, Bank, Distribusi Kedatangan, Distribusi Waktu Pelayanan.

In financial service providers such as banks, queuing is a situation where customers who need services have to wait to get service. Queues occur because the high number of customer arrivals exceeds the service capacity. Queuing theory is a theory related to the mathematical study of customer queues or waiting lines. The purpose of this study is to obtain an optimal queuing model at a bank using the arrival distribution and service time. The queuing system can be described as optimal when the steady state quantity value is less than 1 or the rho value is less than 1, which means the arrival rate is not greater than the service rate and the number of service servers. Based on the analysis, the queuing model at the Bank X obtained is (M/M/5):(FCFS/∞/∞) which means that customer arrivals have a Poisson distribution and customer time service has an exponential distribution. The number of service servers at the Bank X are 5 servers, with a first-come-first-served queue discipline, which means that the customer who arrive earliest get served or treated before the people who arrive later. The capacity of the queuing system and population resources are unlimited. The average arrival rate obtained is 0.3246 customers per minute with the average service rate is 0.2839 customers per minute. The average steady-state value obtained is 0,2348, which means that rho is less than 1, so the queuing system at Bank X is optimal, so there is no additional server. Measures of effectiveness in the queuing model have also been obtained the average chance that the teller is not serving customers at 34.08% of the total service. The average number of customers in the queue is 1 customer with the average time of a customer must wait in the queue is 0,0310 minutes and the average time a customer spends in the system is 3,6520 minutes with the average number of customers waiting in the system is 1 customer. In the Bank X's queuing system, the minimum server obtained so that the queuing system remains optimal is when the number of servers are 3 and the queuing model is (M/M/3):(FCFS/∞/∞). Keywords: Queue, Bank, Arrival Distribution, Service Time Distribution.