case study in queueing time of the development bank of the philippines

7/27/2019 Case Study in Queueing Time of the Development Bank of the Philippines

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QUEUING TIME

OF THE

AUTOMATED

TELLER

MACHINES OF

THEDEVELOPMENT

BANK OF THE

PHILIPPINES

CATARMAN

A

CASESTUDY

DIAZ, KAREN ROSALI

DONINA, ALLANGAVINO, JENNIFER

LABIAN, CHARISSE

RODELAS, JOY FRANCES


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INTRODUCTION

Queuing Theory is the mathematical study of waiting lines or queues. This theory

can be used to model and predict wait times and number of customer arrivals. Any time

there is more customer demand for a service than can be provided, a waiting line occurs.

Among the various services offered by banks is the use of automated teller machine

or ATM. ATM is an automatic teller machine which is used to save the cost and reachability

of a bank by satisfying customer needs. Customers can withdraw and deposit money

without any paper work and it facilitates them to reduce time and cost to go to bank in

person.

This case study focuses on the queuing time of the ATMs of the Development Bank

of the Philippines (DBP).

Currently, DBP have two ATMs, one is placed inside the bank and the other is placedoutside. During the our observation, the two ATMs were not used simultaneously. On the

first hour of the observation, the ATM inside the bank was the one used by the customers.

In the second and third hours, when the bank was closed, the ATM outside the bank was

used.

The figure below shows the queuing system of the Automated Teller Machines of the

DBP which is a single line system.

Figure 1

The single line set up keeps the workstations busy and distributes services fairly

among customers. This is most effective when all operations demanded by a customer can

be performed by a single workstation.

A first-come, first-served rule is applied in the ATMs where priority is given to those

that enter the line up first.

ARRIVALSSERVICE

FACILITY DEPARTURE

AFTER

SERVICE

SYSTEM


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QUEUING EQUATIONS

1. The average number of customers or work units waiting in line or being serviced:

2. The average number in the waiting line:

3. The average waiting time before service:

where,

B = average number of work units arriving in one unit of time

T = average number of work units serviced in one unit of time


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FIRST HOUR OBSERVATION2:27-3:27 P.M., WEDNESDAY, AUGUST 28,2013

Customer# WaitingTime TimeInterval ServiceTime TimeInterval1 2:27 2:27-2:28 1

2 2:29 2:29-2:30 1

3 2:30 2:30-2:31 1

4 2:33 2:33-2:33

5 2:35 2:35-2:36 1

6 2:40 2:40-2:42 2

7 2:41-2:42 1 2:42-2:44 2

8 2:42-2:44 2 2:44-2:45 1

9 2:43-2:44 1 2:44-2:44

10 2:45-2:46 1 2:46-2:47 1

11 2:54 2:54-2:54

12 2:54 2:54-2:55 1

13 2:56 2:56-2:57 1

14 2:58 2:58-3:00 2

15 2:59-3:00 1 3:00-3:01 1

16 3:00-3:01 1 3:01-3:04 3

17 3:06 3:06-3:08 2

18 3:07-3:08 1 3:08-3:09 119 3:09 3:09-3:10 1

20 3:10 3:10-3:11 1

21 3:10-3:11 1 3:11-3:12 1

22 3:15 3:15-3:16 1

23 3:16 3:16-3:16

24 3:16-3:17 1 3:17-3:17

25 3:20 3:20-3:22 2

26 3:22-3:23 1 3:23-3:24 1

27 3:24 3:24-3:25 1

TOTAL 11 minutes TOTAL 30 minutes

Figure 2


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SECOND HOUR OBSERVATION3:27-4:27 P.M., WEDNESDAY, AUGUST 28,2013

ustomer# WaitingTime TimeInterval ServiceTime TimeInterval28 3:29 3:29-3:33 4

29 3:35 3:35-3:41 6

30 3:35-3:41 6 3:41-3:42 1

31 3:38 3:38-3:39 1

32 3:39-3:43 4 3:43-3:43

33 3:39-3:43 4 3:43-3:44 1

34 3:40 3:40-3:40

35 3:41-3:42 1 3:42-3:43 1

36 3:43-3:44 1 3:44-3:45 1

37 3:46 3:46-3:48 2

38 3:47-3:48 1 3:48-3:51 3

39 3:47-3:51 4 3:51-3:53 2

40 3:52 3:53-3:53

41 3:57 3:57-4:01 4

42 4:00-4:01 1 4:01-4:02 1

43 4:01-4:02 1 4:02-4:03 1

44 4:03 4:03-4:04 1

45 4:03 4:04-4:05 146 4:06 4:06-4:07 1

47 4:06-4:07 1 4:07-4:08 1

48 4:13 4:13-4:!4 1

49 4:13-4:14 1 4:14-4:18 4

50 4:14-4:18 4 4:18-4:19 1

51 4:16-4:19 3 4:19-4:22 3

52 4:19-4:22 3 4:22-4:23 1

53 4:20-4:23 3 4:23-4:25 2

54 4:21-4:25 4 4:25-4:27 2

55 4:21-4:27 6 4:27-4:30 3

56 4:23-4:30 7 4:30-4:31 1

TOTAL 55 TOTAL 50

Figure 3


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THIRD HOUR OBSERVATION4:27-5:27 P.M., WEDNESDAY, AUGUST 28,2013ustomer # Waiting Time Time Interval Service Time Time Interval

57 4:30 4:30-4:32 2

58 4:31-4:32 1 4:32-4:33 1

59 4:32-4:33 1 4:33-4:34 160 4:32-4:34 2 4:34-4:35 1

61 4:33-4:35 2 4:35-4:36 1

62 4:33-4:36 3 4:36-4:37 1

63 4:34-4:37 3 4:37-4:38 1

64 4:35-4:38 3 4:38-4:39 1

65 4:37-4:39 2 4:39-4:40 1

66 4:37-4:40 3 4:40-4:43 3

67 4:39-4:43 4 4:43-4:44 1

68 4:39-4:44 5 4:44-4:45 1

69 4:39-4:45 6 4:45-4:46 1

70 4:41-4:46 5 4:46-4:47 1

71 4:44-4:47 3 4:47-4:53 6

72 4:44-4:54 10 4:54-4:55 173 4:44-4:53 9 4:53-4:54 1

74 4:45-4:55 10 4:55-4:56 1

75 4:46-4:56 10 4:56-4:58 2

76 4:47-4:58 11 4:58-5:00 2

77 4:54-5:00 6 5:00-5:02 2

78 4:54-5:02 8 5:02-5:03 1

79 4:56-5:03 7 5:03-5:04 1

80 4:57-5:04 7 5:04-5:05 1

81 4:57-5:05 8 5:05-5:08 3

82 4:59-5:08 9 5:08-5:10 2

83 4:59-5:10 11 5:10-5:13 3

84 5:00-5:13 13 5:13-5:16 385 5:03-5:09 6 5:09-5:13 4

86 5:03-5:13 10 5:13-5:14 1

87 5:05-5:14 9 5:14-5:17 3

88 5:06-5:16 10 5:16-5:17 1

89 5:06-5:17 9 5:19-5:20 1

90 5:07-5:19 12 5:19-5:20 1

91 5:07-5:18 11 5:18-5:21 3

92 5:07-5:21 14 5:21-5:23 2

93 5:08-5:20 12 5:20-5:21 1

94 5:08-5:24 16 5:24-5:25 1

95 5:13-5:25 12 5:25-5:27 2

96 5:13-5:27 14

97 5:13-5:30 1798 5:15-5:31 16

99 5:19-5:33 14

100 5:19-5:34 15

101 5:22-5:35 13

102 5:23-5:37 14

TOTAL 372 TOTAL 66Figure 4


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Figure 5

Figure 6

The data shows that more customers arrived at 5:00pm and beyond. This is because the employees time out

or free time is 5:00pm onwards. This data may also yield the same result during lunch breaks.

0

2

4

6

8

10

12

14

16

18

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

WAITING TIME

First Hour Second Hour Third Hour

0

1

2

3

4

5

6

7

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

SERVICE TIME

First Hour Second Hour Third Hour


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CALCULATIONAverage number of customers waiting in line or being served

0

N= 1.307

Average number of customers in the waiting line

0 0

5

0

5

50

NQ = .74

Average waiting time before service

.

W= .02179 or 1.305 minutes


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NOTE 1: AVERAGE NUMBER OF CUSTOMERS THAT ARRIVED (B)Time # of customers

2:27-3:27 27 Page # 3

3:28-4:27 29 44:28-5:27 46 5

Total customers arrived 102

Average # of customers that arrived =

=

= 34 customersNOTE 2: AVERAGE NUMBER OF CUSTOMERS BEING SERVED (T)The used value of T is an estimated value of the average number of customers an ATM can serve at a

given time. Figures 2, 3 and 4 show that a normal transaction, without delay, is 1 minute per

customer. In normal transactions, the ATM can accommodate an average of60 customers per hour,or 1 customer per minute assuming there is no delay in their transactions.

NOTE 3The actual computed average number of served customers for an hour is

computed as follows:

Time # of customers

2:27-3:27 27

3:28-4:27 274:28-5:27 41

Total customers served 95

Average # of customers served =

=

= 31.67 or 32 customersThe average actual computed value of 32 customers is different from the average

estimated value of 60 customers per hour due to factors such as:

1. Customers dont know how to use ATMs causing delays;2. Customers who fall in line only to find out they dont have sufficientbalance in their account;3. Customers indulge in paniningit with other customers in queue;4. The delay in transaction of electronic responses from one bank to another

when a customer withdraws not in the principal bank. There is delay, thus,

lesser customers will be accommodated at a given time;

5. Peak season. Data gathered during ordinary days is different during peakseasons (remuneration days, distribution of 4Ps).


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1

CONCLUSION

This case study uses queuing theory to study the waiting line or queuing time inthe Bank ATM of DBP Catarman. The bank provides two ATMs in the main branch.

The data computed shows that an average of 34 customers arrives and 60

customers are being served (assuming no delay in transaction) in an hour. The average

number of customers in line and being served for a minute is 1.307. The average number of

customers waiting in line is .74 per minute and the average waiting time for every

customer before service is 1.305 minutes.

This case study can contribute to the betterment of a bank in terms of its

functioning through ATM. Waiting line models are important to banks because they

directly affect customer service perception and the costs of providing a service. Quick

service or response can be a competitive advantage. Long waits suggest a lack of concern

by the company or can be linked to a perception of poor service quality.

The average number of customers waiting in line and in the system. The number

of customers waiting in line can be interpreted in several ways. Short line ups can

translate as good customer service, or it could mean too much capacity. Alternatively, long

line ups can indicate poor service, or not enough capacity utilization. The number of

customer in a line up also relate to the process efficiency and capacity. Long waiting lines

can result from poor server efficiency inadequate system capacity and/or significantsurges in demand.

The average time customers spend waiting, and the average time a customer

spends in the system. Customers often link long waits to poor-quality service. If too much

time is spent in the system, customers might perceive the competency of the service

provider as poor.

Managements goal is to have enough servers to assure that waiting is within

allowable limits but not so many servers as to be cost inefficient.

case study in queueing time of the development bank of the philippines

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