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Analisis Kinerja Sistem. Teori Antrian. - Aurelio Rahmadian -. Sifat Antrian. Pelanggan t idak m enunggu b ila a da p elayanan y ang m enganggur Pelanggan h arus m enunggu b ila p elayanan s edang d ipakai p elanggan l ain

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Analisis kinerja sistem

Analisis Kinerja Sistem

Teori Antrian

- Aurelio Rahmadian -

Sifat antrian
Sifat Antrian

  • Pelanggantidakmenunggubilaada pelayananyangmenganggur

  • Pelangganharusmenunggubilapelayanansedangdipakaipelangganlain

  • Pelangganakansegeramemasukipelayananbilaadapelangganyangmeninggalkanpelayanan

Analisa antrian
Analisa Antrian

  • Jumlah waktu yang digunakan untuk berada dalam antrian oleh orang, produk, dll.

  • Menyediakan layanan yang cepat merupakan aspek penting dari kualitas pelayanan

  • Dasar analisa antrian adalah trade-off dari cost yang dibutuhkan untuk meningkatkan pelayanan dan cost yang berhubungan dengan menunggunya customer

  • Analisa antrian merupakan bentuk probabilistik dari analisa

  • Hasil analisa merupakan karakteristik operasi

  • Hasil analisa digunakan oleh manajer operasi antrian untuk mengambil keputusan

Elemen antrian
Elemen Antrian

  • Waiting lines form because people or things arrive at a service faster than they can be served.

  • Most operations have sufficient server capacity to handle customers in the long run.

  • Customers however, do not arrive at a constant rate nor are they served in an equal amount of time.

  • Waiting lines are continually increasing and decreasing in length.and approach an average rate of customer arrivals and an average service time, in the long run.

  • Decisions concerning the management of waiting lines are based on these averages for customer arrivals and service times.

  • They are used in formulas to compute operating characteristics of the system which in turn form the basis of decision making.

Elemen antrian1
Elemen Antrian

  • Komponen dalam antrian:

    • Customer

    • Server

  • Faktor yang perlu diperhatikan:

    • Queue Discipline

    • Nature of calling population

    • Arrival rate

    • Service rate

Elemen antrian2
Elemen Antrian

  • Queue discipline

    Urutan bagaimana customer yang menunggu dilayani

  • Calling population

    Sumber dari customer (finite atau infinite)

  • Arrival rate

    Frekuensi customer datang pada antrian, mengacu pada distribusi probabilitas

  • Service rate

    Rata-rata customer yang dapat dilayani dalam selang waktu tertentu

Notasi kendall
Notasi Kendall


Dimana :

  • A adalah distribusi waktu interarrival

  • S adalah distribusi waktu layanan.

  • m adalah jumlah server

  • B adalah jumlah buffer (sistem kapasitas)

  • K adalah besar populasi

  • SD adalah tertib layanan (service discipline)

M m 1

Ambil :

Contoh 11
Contoh 1



Lq = Rata-rata Pelanggan dalam Antrian

Ws = Rata-rata Waktu

tunggu dalam Sistem

Ls = Rata-rata Pelanggan dalam Sistem

Wq = Rata-rata Waktu tunggu dalam Antrian

Contoh 21
Contoh 2



 = 4 / jam

Lq = Rata-rata Pelanggan dalam Antrian

Ws = Rata-rata Waktu

tunggu dalam Sistem

Ls = Rata-rata Pelanggan dalam Sistem

Wq = Rata-rata Waktu tunggu dalam Antrian

Keputusan manajerial
Keputusan Manajerial

- Manager wishes to test several alternatives for reducing customer waiting time:

1. Addition of another employee to pack up purchases

2. Addition of another checkout counter.

- Alternative 1: Addition of an employee (raises service rate from  = 30 to  = 40 customers per hour)

Cost $150 per week, avoids loss of $75 per week for each minute of reduced customer waiting time.

System operating characteristics with new parameters:

Po = .40 probability of no customers in the system

L = 1.5 customers on the average in the queuing system

Lq = 0.90 customer on the average in the waiting line

W = 0.063 hour (3.75 minutes) average time in the system per customer

Wq = 0.038 hour ( 2.25 minutes) average time in the waiting line per customer

U = .60 probability that server is busy and customer must wait, .40 probability server available

Average customer waiting time reduxed from 8 to 2.25 minutes worth $431.25 per week.

Net savings = $431.25 - 150 = $281.25 per week

Keputusan manajerial1
Keputusan Manajerial

- Alternative 2: Addition of a new checkout counter ($6,000 plus $200 per week for additional cashier)

 =24/2 = 12 customers per hour per checkout counter.

 = 30 customers per hour at each counter

System operating cartelistic with new parameters:

Po = .60 probability of no customers in the system

L = 0.67 customer in the queuing system

Lq = 0.27 customer in the waiting line

W = 0.055 hour (3.33 minutes) per customer in the system

Wq = 0.022 hour (1.33 minutes) per customer in the waiting line

U = .40 probability that a customer must wait

I = .60 probability that server is idle and customer can be served.

Savings from reduced waiting time worth $500 per week - $200 = $300 net savings per week.

After $6,000 recovered, alternative 2 would provide $300 -281.25 = $18.75 more savings per week.

Keputusan manajerial2
Keputusan Manajerial

Operating Characteristics for Each Alternative System

Cost trade-offs for service levels

Waiting line psychology
Waiting Line Psychology

  • Waits with unoccupied time seem longer

  • Pre-process waits are longer than process

  • Anxiety makes waits seem longer

  • Uncertainty makes waits seem longer

  • Unexplained waits seem longer

  • Unfair waits seem longer than fair waits

  • Valuable service waits seem shorter

  • Solo waits seem longer than group waits

Maister, The Psychology of Waiting Lines,

teaching note, HBS 9-684-064.