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Analisis Kinerja Sistem

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

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  1. Analisis Kinerja Sistem Teori Antrian - Aurelio Rahmadian -

  2. Sifat Antrian • Pelanggantidakmenunggubilaada pelayananyangmenganggur • Pelangganharusmenunggubilapelayanansedangdipakaipelangganlain • Pelangganakansegeramemasukipelayananbilaadapelangganyangmeninggalkanpelayanan

  3. 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

  4. Cost Trade-off

  5. 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.

  6. Elemen Antrian • Komponen dalam antrian: • Customer • Server • Faktor yang perlu diperhatikan: • Queue Discipline • Nature of calling population • Arrival rate • Service rate

  7. 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

  8. Rumus Umum

  9. Notasi Kendall A/S/m/B/K/SD 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)

  10. M/M/1 Ambil :

  11. Contoh 1

  12. Contoh 1 Antri Layanan 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

  13. M/M/S

  14. M/M/S

  15. Contoh 2

  16. Contoh 2 Antri Layanan  = 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

  17. 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

  18. 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.

  19. Keputusan Manajerial Operating Characteristics for Each Alternative System Cost trade-offs for service levels

  20. 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.

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