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- 1. PROJECT ON “APPLICATION OF QUEUE MODEL TO ENHANCE BANK SERVICE IN WAITING LINES” PROJECT SUPERVISOR: KAZI ARIF-UZ-ZAMAN ASSISTANT PROFESSOR DEPT. OF INDUSTRIAL ENGINEERING AND MANAGEMENT KUET. ASSIGNED BY: MD. RAHAMAT ULLAH, 0911004 S.M. ISHTIAQ PARTHO, 0911025 DEPT. OF INDUSTRIAL ENGINEERING AND MANAGEMENT KUET.
- 2. WHAT IS THE • Queue - a line of people QUEUING THEORY? or vehicles waiting for something. • Queuing Theory- Mathematical study of waiting lines, using models to show results, and show opportunities within arrival, service, and departure processes.
- 3. PROJECT GOAL In this paper, queue theory is applied to enhance the service of a bank in lines. For this, firstly a queue model (M/M/C): (GD/∞/∞) is selected to find out efficiency of the servers.
- 4. KEY WORDS Queuing model, optimal number of server, service rate, first come first serve, (M/M/C): (GD/∞/∞) model.
- 5. OBJECTIVES OF THE PROJECT • Finding out the efficiency of the servers. • Signifying the number of service facilities. • When customers can typically be expected to arrive. • The amount of time customers has to spend to get the desired service. • The length of the queue (Waiting line). • How much time the customers have to wait before the service starts. • Human psychology (frustration, balking, impatience). • the optimal number of counter is calculated to improve the operational efficiency.
- 6. SIGNIFICANCE OF QUEUING MODELS • Queuing Models Calculate the best number of servers to minimize costs. • Queue lengths and waiting times can be predicted. • Improve Customer Service, continuously. • When a system gets congested, the service delay in the system increases. • A good understanding of the relationship between congestion and delay is essential for designing effective congestion control for queuing system. • Queuing Theory provides all the tools needed for this analysis.
- 7. TERMINOLOGY AND NOTATIONS • M=Number of servers • Pn= probability of exactly “n” customers in the system. • N= number of customers in the system. • Ls= expected number of customers in the system • Lq= expected number of customers in the queue. • Ws= waiting time of customers in the system • Wq= waiting time of customers in the queue. • λn= The mean arrival rate of new customers are in systems. • µn= The mean service rate for overall systems when “n” customers are in systems. • The mean arrival rate is constant for all n, this is denoted by λ and the mean service rate per busy server is constant for all n≥1, is denoted by µ. And when n ≥M that is all z servers are busy, µ=sµ. Under this condition, • The expected inter-arrival time is 1/λ • The expected service time is 1/µ. • The utilization factor for the service facility is ρ= λ/Mµ.
- 8. METHODOLOGY AND PROPOSED • Formula 1 [Adding another MODEL server to the system during busy days (Comparative analysis of adding an extra counter)] • Formula 2 [Improving the service rate by serving the customer quick (increase service rate)]
- 9. FORMULA 1 [ADDING ANOTHER SERVER TO THE SYSTEM DURING BUSY DAYS (INCREASE SERVER)] PROPOSED MODEL: (M/M/C): (GD/∞/∞) MODEL: •
- 10. •
- 11. Case study of a local bank [Service time per day is 10:00 to 1:00 and 3:00-4:00.total 240 minutes.] Bank data of customer count for one month Week No. Sunday Monday Tuesday Week 1 140 114 132 Wednesda Thursday y 146 156 Week 2 120 123 199 145 150 Week 3 199 171 159 120 130 Week 4 150 180 149 107 110 Total 609 588 639 518 546 Average 152.25 147 159.75 129.5 136.5
- 12. Bank data of customer count for one month Average number of customer 160 140 120 100 80 152.25 147 159.75 129.5 136.5 60 40 20 0 Sunday Monday Tuesday Day of the week Wednesday Thursday
- 13. Graphical representation of effect of adding an extra counter for Sunday number of counter vs waiting time of customers in minute Waiting time of customers, ws 30 25 20 15 26.58 10 9.5 5 3.27 1.75 4 5 0 2 3 number of server, s
- 14. Graphical representation of effect of adding an extra counter for Monday number of counter vs waiting time of customers in minute waiting time of customers 16 14 12 10 8 15.123 6 4 5.624 2 2.356 1.448 4 5 0 2 3 number of server,s
- 15. Graphical representation of effect of adding an extra counter for Tuesday Waiting time of customers, ws number of counter vs waiting time of customers in minute 100 90 80 70 60 50 40 30 20 10 0 96.664 33.923 9.217 2 3 2.911 4 5 number of server, s
- 16. Graphical representation of effect of adding an extra counter for Wednesday number of counter vs waiting time of customers in minute Waiting time of customers, ws 5 4.5 4 3.5 3 2.5 4.992 2 1.5 2.387 1 1.612 1.456 4 5 0.5 0 2 3 number of server, s
- 17. Graphical representation of effect of adding an extra counter for Thursday number of counter vs waiting time of customers in minute Waiting time of customers, ws 8 7 6 5 4 7.074 3 2 3.025 1.754 1 1.481 4 5 0 2 3 number of server, s
- 18. PROBLEM FORMULATION • It has been seen in the research that If waiting time increases then frustration level increases with this. In the scenario utilization factor is as high as 0.39 to 0.48 during busy days of the bank. It is clear that high utilization rate is not helping to reduce customer’s waiting time in queue. On high utilization factor customers have to wait more time in system as like as 26.58, 15.123, 96.664, 4.992, 7.074 minutes respectively from Sunday to Thursday. It seems that there is a problem in the operations which if not noticed could reduce business of bank.
- 19. RESULT AND DISCUSSION OF FORMULA 1 • The comparative analysis of adding an extra counter to the system and improving the service rate have shown in the above figures. • when one more counter is added (s=3) the waiting time in system reduces significantly to 9.5, 5.624, 33.923, 2.387, 3.025 minutes respectively from Sunday to Thursday. However, it can be seen that adding one more counter (s=3) does significantly change the waiting time of the system except for Tuesday. Using four counter for Tuesday significantly changes waiting time from 33.923 (when s=3) to 9.217. .
- 20. From this analysis, the optimum number of counter for the week Optimum number Utilization factor Day of the days are listed below Sunday of counter 3 0.30 Monday 3 0.29 Tuesday 4 0.24 Wednesday 2 0.39 Thursday 2 0.41
- 21. FORMULA 2 [IMPROVING THE SERVICE RATE BY SERVING THE CUSTOMER QUICKLY (INCREASE SERVICE RATE)] On another experiment, it has been found by meeting with the customers in waiting line that before they arrive at the bank they are mentally prepared for waiting 8 to 10 minutes in the bank for getting their service. From this point of view, for Wednesday and Thursday there is no need for adding an extra counter.
- 22. SERVICE RATE VS. WAITING TIME OF CUSTOMERS IN MINUTE service rate vs. waiting time of customers in minute 100 Waiting time of customers, ws 90 80 70 60 50 96.664 40 30 20 28.43 14.12 10 8.73 5.98 0 0.7 0.73 0.76 service rate 0.79 0.82
- 23. Result and discussion • The second way of reducing the waiting time in line is by improving the service rate. The above figure (8) indicates the ultimate effect of improving the service rate. From the comparative analysis, it can be seen that on Tuesday, if the service rate is improved from .70 to .76 then waiting time reduces to 96.664 to 14.12 (82.554minutes) without adding an extra counter thus adding no extra cost.
- 24. psychological View [Frustra
- 25. CONCLUSION The efficiency of commercial banks is improved by the following three measures: • the queuing number • the service stations number and • the optimal service rate which are investigated by means of queuing theory. By the example, the results are effective and practical. The time of customer queuing is reduced. The customer satisfaction is increased. It was proved that this optimal model of the queuing is feasible.
- 26. QUESTIONS?
- 27. THANK YOU!

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