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2014 International Conference on Advances in ICT for Emerging Regions (ICTer) :
11th - 12th December 2014 International Conference on Advances in ICT for Emerging Regions ICTer2014
A Simulation for Reduced Outpatient Waiting Time
N. Algiriyage#1, R. Sampath#2, C. Pushpakumara#3, G. Wijayarathna#4
# Department of Industrial Management, University of Kelaniya
Kelaniya, Sri Lanka
1rangika.nilan i@gmail.com
3chamli@kln.ac .lk
2sampathrangana@gmail.com
3gamini@kln.ac .lk
Abstract— Extended waiting time for treatment in National
hospitals is very common in Sri Lanka. This situation has
created several problems to patients, doctors and even to other
health workers. The quality of service leaves a lot to be desired
and is costly to the economy. This study analyses different
queues which create bottlenecks in the Out Patient Department
at national eye hospital in Sri Lanka and critically evaluate
several appointment scheduling rules with the help of a
simulation model to come up with a solution which minimises
the total patient waiting time. Our results shows that total
patient waiting time can be reduced more than 60% using
proper appointment scheduling system with process
improvement.
Keywords— OPD, waiting time, simulation, scheduling.
I. INTRODUCTION
Waiting time in outpatient departments has become a
problem in healthcare industry all over the world. In Sri
Lanka most of the government hospitals have long queues in
OPDs and this creates a high waiting time for the patient. The
ma jor caus e for this problem is the as sumption that doctor’s
time is more valuable than the patient’s time. It seems that
sufficient attention is not paid to this matter in the Sri Lankan
context and no other studies have been undertaken so far.
Most government hospitals don’t use any appointment
systems for Out Patient Departments. Patients come as early
as possible and wait in the queue before the hospital work
starts. From the time of registration until they leave the
hospital, patients have to wait longer periods for every
examination, test, and diagnosis they face.
This area of patient waiting time analysis has been chosen
by many researchers in the world and important solutions
have been introduced throughout the past. But most of these
solutions cannot be directly adapted to other hospitals as the
solutions are specific to the hospital which is considered for
their analysis. Some of these studies are discussed in the
literature review.
During this research the process of National Eye Hospital
is thoroughly studied and possible appointment scheduling
rules are proposed in order to minimize patient waiting time
in the hospital. And we have focused on resecuring of the
process such as introducing new workstations, reducing
patient routing time in the hospital premises etc in order to
improve the overall process.
II. LITERATURE REVIEW
According to Kaandorp and Koole[1], all Appointment
Scheduling (AS) literature is divided in to two main groups;
evaluated schedules and evaluated algorithms to uncover
improved schedules. Simulations are mostly used to test
evaluated schedules, whereas analytical methods are used to
test evaluated algorithms.A comprehensive literature review
on appointment scheduling is found in Cayirli and Veral [2].
The types of appointment systems vary from single block
appointment to individual appointments. Most systems are
concentrated on modifying and combining these two
appointment systems in different forms. An appointment rule
is created using any of the following schemas:
Single Block System – This allows all patients to arrive
in a block at the beginning of the clinic session. This
system allocates a date rather than allocating a specific
appointment time. Babes and Sarma[3] introduced this
system. Single block system creates long waiting times
for patients but shortens idle time for doctors.
Individual-block/fixed-interval system – This system
calls patients individually at intervals equal to the mean
consultation time Klassen, Rohleder,Cayirli,Veral, and
Rosen has done research on this.[4],[5],[6].
Individual-block/fixed-interval with an initial block
system -This is similar to the above method, but the
number of patients assigned to the initial block is
greater than one. Bailey in 1952[7] introduced this rule
to the Appointment Scheduling literature, setting two
patients at the beginning of the session. Ho and Lau [8]
evaluated and made additional amendments to the
original Bailey rule. Many people used this system in
their studies. Klassen and Rohleder[4]Yang, Lau, and
Quek [8] Cayirli, Veral, and Rosen [5],[6],
Wijewickrama and Takakuwa [11] evaluated these
rules in their studies. Kaandorp and Koole [1]
introduced initial block in their queuing model.
Multipleblock/fixed-interval rule – This divides the
patients in to m number of blocks and calls a fixed
number of patients at the beginning of each block.
Soriano[13] introduced this system to the Appointment
Scheduling Literature. This system schedules two
patients at a time with an interval of twice the
consultation time. The two at a time rule was
extensively studied with its original counterpart and its
variations by Ho and Lau [8] and Cayirli, Veral, and
Rosen [5], [6].
Multiple block/Fixed-interval with an initial block rule
- Cox, Birchall, et al.[14] investigated this rule with an
initial block rule,introducing an initial block to the
above rule studied by Soriano.
Variable-block/fixed -interval –This rule assigns a
different number of patients in a fixed appointment
interval during the clinical Lang Khiong et al. [11]
Using a dynamic programming approach, Lin (2000)
optimized a quota AS.
Sample ICTer Conference Paper (Paper Title) 2
12th-13th December 2013 International Conference on Advances in ICT for Emerging Regions ICTer2013
Individual-block/variable-interval rule - Calls patients
individually with unequal appointment intervals. Ho
and Lau [8] introduced this rule by concluding that the
variable-interval system, which sets an increasing
appointment intervals rate towards the latter part of the
session. This system works well in most environmental
conditions. Many scholars have tested this rule using
either analytical method or applying simulations
Cardoen, Brecht et al. [12] identified the some pattern
of inter-arrival times which optimized the solution.
This pattern made inter-arrival times shorter at the
beginning and the ending part of a session and longer
in the middle, which represents a slight variation of
variable interval rule.
Multiple-block/variable-interval rule - Cayirli, Veral,
and Rosen [5] introduced this method to the
Appointment Scheduling literature. They modeled the
multiple-block/variable-interval rule by combining the
dome pattern of inter-a rrival to ―the two-at-a time rule‖
and Bailey rules.
Most of the above studies concentrated only on
appointment rule disregarding the patient characteristics in
designing the appointment systems. A number of studies
considered the use of patient classification to sequence
patients by classifying consultation time or type of procedure
into groups based in order to design the Appointment
Scheduling [5], [6].
Klassen and Rohleder [4] proposed a sequencing rule in
scheduling based on the consultation time variance, whether a
patient was considered ―low variance‖ or ―high variance.‖
The empirical research showed that setting low variance
patients at the beginning of the session and high variance
patients at the end of the session would minimize both patient
waiting time and doctor idle time in most instances.
Later they [4] identified that this rule is still effective when
the scheduler is unable to identify the low variance and high
variance patients proportionately. Incorporating patient
classification into AS (Appointment Scheduling) rules, a
number of AS rules were designed under a wide range of
clinical environments by Cayirli, Veral et al.[5] by grouping
patients as new and returning. They concluded that
―sequencing decisions have a more definite impact on
performance than the choice of an appointment rule‖
By extending the scope of their previous research, Cayirli,
Veral, and Rosen [6] introduced well-designed ASs with
adjusting appointment intervals to match the consultation
time characteristics of different patient classes.
We have focused on implementing schedule rules to
minimize total waiting time not only considering the patient
types but also the routing times inside the hospital. In the Sri
Lankan context doctor’s id le time is not a matter. In our work
we have done modifications to prevailing Appointment
Scheduling rules.
III. MODEL CONSTRUCTION
This section provides an introduction to the processes that
were considered in building the simulation model. The OPD
process of the hospital includes patient registration, eye
checking, searching for prev ious diagnosis receipts, and
finally the doctor’s examination. In the later part of this
section it describes how the simulation model was built using
the gathered information with the help of Rockwell Arena
simulation software [15].
A. Description of OPD
1) Patient Registration: There are two types of patients at
the OPD. They are the first time and follow up/second visit
patients. Patient registration process starts at 6.00 am every
Monday to Saturday. Any first time patient has to visit Room
No 10 and get the ticket after registering there before 10 a.m.
An attendant at the counter takes basic details from the
patient and assigns him/her a unit and a registration number.
First patient in a Monday morning receives K1, second one
receives K2. Third patient is assigned with unit B1 and fourth
one is B2. Fifth patient gets unit F1 and sixth one gets unit F2.
The seventh person starts the cycle by having unit K1 again.
This pattern is same for other days and the only difference is
that on Mondays, Wednesdays and Fridays they assign
patients with units K, B, F and on Tuesdays Thursdays and
Saturday the operating units are MP, G, and S. These units
have been named according to the consultant at the clinic on
that day. A patient receives two different receipts after the
registration process. One receipt is consisted with the details
of the patient and he has to keep it securely during the stay in
the hospital.
2) Eye Checking: Registered patients visit Room No 13
where his/her eyes are checked. An attendant checks the left
eye and right eye and measurements are written on the other
receipt which was received by patients at the registration
counter.
3) Searching Previous Diagnosis Documents:Second visit
patients have to provide the receipt with their details to the
counter and get the previous diagnosis from Room No 10.
4) Doctor’s Examination (OPD): Patients wait in a
waiting area according to the registration number order, until
doctors arrive. Patients are taken in to the OPD room in a
FIFO pattern. First visit patients are examined by a junior
doctor and second visit patients are examined by a senior
doctor. During the examination patients may receive
diagnosis and leave, they may ask to go for test rooms, or
have to visit OPD again in another day after using the
medication.
B. The Performance Measures
The performance measure considered under this study was
the patient waiting time for each type of patient. Times are
measured in seconds. The total waiting time of a patient was
calculated using a spread sheet.
C. Data and Simulation Model
Data was co llected for a period of one month and the main
source of information gathering was through observation
since an electronic database was not available. Table I shows
the distribution patterns of data, which was generated by the
Arena Input Analyzer. Other than these waiting times routing
times inside the hospital for various purposes were also
considered in building the simulation model.
D. Animation
In addition to the simulation model an animation was used
to clearly identify and analyse the process and the behaviour
of each entity. This animation model is shown in the Fig. 1.
3 First A. Author#1 , Second B. Author*2, Third C.D. Author#3
12th-13th December 2013 International Conference on Advances in ICT for Emerging Regions ICTer2013
TABLE I
ARRIVAL AND SERVICE TIME DISTRIBUTION
Description
Distribution/Expression
Inter arrival time of first
visit patients
9 + GAMM(4.67, 3.23)
Inter arrival time of second
visit Patients
TRIA(220, 398, 474)
Service time at Room
no 10
7 + ERLA (7.3, 2)
Service time at Room
no 13
10 + GAMM (10.5, 1.36)
Doctor service time at OPD
Rooms
35 + 385 * BETA
(0.916, 0.97)
E. Verification and Validation of the Model
Model verification and validation is the most important
and hardest activity in any simulation project. In this scenario
several techniques were used to verify and validate the model.
An animation view was created with dynamic statistics and
graphs. This was used to examine whether the animation
depicts the real system behavior. And statistics generated
through the computer simulation model was examined
against the statistics that were collected from the real system.
IV. EXPERIMENTAL ANALYSIS
This section provides a comprehensive summary of
schedule rules and results of each are discussed.
Fig. 2 depicts the average waiting time in each queue for
the original model (the model generated with the data
gathered from the current OPD proces s).
Average total waiting time of a first visit patient in the
original model is about 13673.8 seconds. That is 3.79 hours.
For a second visit patient it is about 6802.62 Seconds.
Fig. 1 Patient waiting time in queues for original model
To reduce the total waiting time of a patient four schedule
rules were introduced.
Following section demonstrates each schedule rule with
the output statistics generated through the model. In the Fig1.
No of the queue axis represent check eye sight.Queue1, check
eye sight.Queue2, examine time-first visit11, examine time-
first visit5, examine second-visit11, examine-second
visit5,get ticket, wait until doctors arrive, search ticket, wait
until getting space respectively.
A. Schedule Rule 1(Equal intervals/Equal blocks)
TABLE II
SCHEDULE RULE 1
Patient type
Time
period
(Seconds)
Number
of patients
Total
First Visit Patient
3600
50
50
3600
50
50
…
…
…
Patient waiting time
No of the queue
Fig. 1 The animation of the OPD process
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12th-13th December 2013 International Conference on Advances in ICT for Emerging Regions ICTer2013
3600
50
50
Second Visit Patient
K1,K2,B1,B2,F1,F2
7200
10 from
each type
60
K1,K2,B1,B2,F1,F2
7200
10 from
each type
60
…
…
…
K1,K2,B1,B2,F1,F2
7200
10 From
each Type
60
Schedule Rule 1 has 50 first visit patients per half an hour
and 60 second visit patients per hour. Second visit patients
are 10 from each type.
According to the calculations Schedule Rule 1 gives an
average waiting time of 1270.425 seconds for first visit
patients and 1320.63 seconds for second visit patients. It is a
very higher reduction of total patient waiting time when
compared with the original model. Fig II shows variations of
waiting time in the Schedule Rule 1.
Fig. 2 Patient waiting time in queues for schedule rule 1
B. Schedule Rule 2(Equal Intervals Repeating/Equal Blocks)
TABLE III
SCHEDULE RULE 2
Patient type
Time
period
(Seconds)
Number
of patients
Total
First Visit Patient
3600
100
100
3600
100
100
…
…
…
3600
100
100
Second Visit Patient
K1,K2,B1,B2,F1,F2
7200
20 From
each Type
120
K1,K2,B1,B2,F1,F2
7200
20 From
each Type
120
…
…
…
K1,K2,B1,B2,F1,F2
7200
20 From
each Type
120
Schedule Rule 2 is a variation of the Schedule Rule 1 with
different block size and time intervals. The values for the first
visit and second visit patients are shown in Tab le III. This
rule also has reduced most of the waiting times and but it has
a long waiting times in get ticket and search ticket queues
compared to the original model.
C. Schedule Rule 3(Unequal Intervals Repeating/Unequal
Blocks)
TABLE IV
SCHEDULE RULE 3
Patient type
Time
period
(Seconds)
Number of
patients
Total
First Visit Patient
1800(6.00)
45
50
3600(6.30)
109
50
1800(7.30)
56
3600(8.00)
92
50
1800(9.00)
49
3600(9.30)
105
1800(10.30)
56
3600(11.00)
95
Second Visit Patient
K1,K2,B1,B2,F1,F2
3600(6.00)
9,10,8,12
10,11
60
K1,K2,B1,B2,F1,F2
7200 (7.00)
19,25,15,22
20,19
120
3600 (9.00)
6,15,9,12
10,8
60
K1,K2,B1,B2,F1,F2
7200(10.00)
20,16,27,19
12,26
120
K1,K2,B1,B2,F1,F2
3600(12.00)
5,9,17,12
8,9
60
Schedule Rule 3 is somewhat different from other two
schedule rules discussed earlier. The schedule allows unequal
amount of patients for each interval. These intervals are one
hour and half an hour repeated. These intervals are repeating
one after another.
The average waiting t ime for a first visit patient in
Schedule Rule 3 is 2232.01seconds and for a second visit
patient it is about 1904 seconds.
No of the queue
Patient waiting time
Patient waiting
time
No of the queue
Fig. 3 Patient waiting time in queues for schedule rule 2
Fig. 4 Patient waiting time in queues for schedule rule 3
Patient waiting time
No of the queue
5 First A. Author#1 , Second B. Author*2, Third C.D. Author#3
12th-13th December 2013 International Conference on Advances in ICT for Emerging Regions ICTer2013
D. Schedule Rule 4(Unequal Intervals Repeating/Unequal
Blocks)
TABLE V
SCHEDULE RULE 4
Patient type
Time
period
(Seconds)
Number
of
patients
Total
First Visit Patient
1800(6.00)
50
50
900(6.30)
25
50
2700(6.45)
75
900(7.30)
25
50
900(7.45)
25
900(9.00)
25
2700(9.15)
75
2700(10.00)
75
3600(10.45)
100
Second Visit Patient
K1,K2,B1,B2,F1,F2
1800(6.00)
10 From
each Type
60
K1,K2,B1,B2,F1,F2
3600 (6.30)
10 From
each Type
60
K1,K2,B1,B2,F1,F2
7200 (7.30)
10 From
each Type
K1,K2,B1,B2,F1,F2
1800 (9.30)
10 From
each Type
K1,K2,B1,B2,F1,F2
1800(10.00)
10 From
each Type
K1,K2,B1,B2,F1,F2
3600(10.30)
10 From
each Type
K1,K2,B1,B2,F1,F2
1800(11.30)
5 From
each Type
60
Schedule Rule 4 is also somewhat similar to Schedule
Rule 3. The only difference is that it has a varying number of
patients in different time intervals for both first visit and
second visit patients. With schedule rule 4 first visit patients
take 2639.05 seconds and second visit patients take 1913.32
seconds.
Fig. 5 Patient waiting time in queues for schedule rule 4
E. Problems with Schedule Rules
The main aim of this study was to find the method that
could minimize total patient waiting time without creating
other large queues. Although the Schedule Rules (SRs) 1, 2,
3 and 4 were successful in minimizing total waiting time they
generated large queues in some other p laces. The next
analysis was conducted with more attention focusing on
reducing the total waiting time at the expense of particular
queues. Since they are carried out based on the schedule rules
they have been named as Experiment1 [SR1], Experiment2
[SR1]...etc.
Spreading the load in the various queues was achieved by
modifying the number of agents in the get and search ticket
counters at Room No 10. In the first two experiments it has
been used the previous data that was gathered and for the
next two an assumption has been made that service time in
Room No 10 and 13 is equal to the half of the original data
with increment of agents inside each room.
Seven experiments were carried out to identify the best
appointment scheduling method. Schedule rule 1 was
checked for four experiments with changes to the number of
servers. Experiment1 [SR1] has two attendants at the first
visit patient registration and one attendant at the search ticket
for second visit patients. Experiment 2[SR1] has two
attendants for both counters in the Room no 10. In the
experiment 3 another two attendants were added to the first
visit patient registration counter. The same model was tested
assuming the service time would reduce to half when the
appointment system is introduced.
TABLE VI
DATA ANALYSIS
Mode
l
Total Wai ting time
Differ ence
Percentag e
Differ ence
FV
SV
FV
SV
FV
SV
Origi
nal
13673.81
6802.62
SR1
1270.43
1320.63
12403.38
5481.99
91
81
SR2
2436.13
2610.91
11237.68
4191.71
82
62
SR3
2232.01
1903.99
11441.79
4898.63
84
72
SR4
2639.05
1913.32
11034.75
4889.3
81
72
Ex1-
SR1
4450.29
2910.3
9223.52
3892.32
67
57
Ex2-
SR1
1234.41
1256.06
12439.4
5546.56
91
82
Ex3-
SR1
1325.79
1247.97
12348.02
5554.65
90
82
Ex4-
SR1
1399.44
1973.76
12274.37
4828.86
90
71
Ex5-
SR2
2142.17
1867.57
11531.64
4935.05
84
73
Ex6-
SR3
1948.29
2421.63
11725.52
4380.99
86
64
Ex7-
SR4
1856.67
2421.63
11817.14
4380.99
86
64
With the first four experiments it was clear that experiment
2 reduced the both first and second visit patient waiting time
in a higher rate. Therefore the next 3 experiments were
carried out based on this, which is to include two servers for
No of the queue
Patient waiting
time
Sample ICTer Conference Paper (Paper Title) 6
12th-13th December 2013 International Conference on Advances in ICT for Emerging Regions ICTer2013
both get ticket and search ticket counters. Schedule Rule 2, 3,
4 were analysed according to the model shown in figure 8.
All statistical out puts were collected and imported to a
spread sheet using the arena simulation model. This data was
used to calculate the percentage reduction compared with the
statistics for the original model.
Table VI summarizes the final analysis of the output
generated by the model. Experiments are shown as ―Ex‖ . It
shows that the introduction of schedule rules helps to reduce
the total waiting time to a great extent and that the reduction
rate of most of the rules are greater than 80%. According to
the observations first visit patients have the major problem of
a high waiting time for the treatments. It is obvious that
―Ex2‖decreases the waiting time of a first visit patient by
91% and 82% from a second visit patient. Therefore the final
analysis suggests that the best schedule rule for the national
eye hospital to implement is E2 [SR1]; that is an appointment
system of 50 patients per half an hour for the first visit patient
type and 10 patients from each K1,K2,B1,B2,F1,F2 per an
hour as second visit patients. There should be two counters
for the registration of first visit patients and two counters to
search tickets of second visit patients.
V. CONCLUSIONS
This research has focussed on reducing extended waiting
times in queues of National Eye Hospital in Sri Lanka.
Different types of appointment scheduling rules have been
tested. According to the simulation model it is obvious that
significant amount of total patient waiting time has been
reduced. The optimum solution which is proposed by our
findings for the hospital is 50 patients per half an hour for the
first visit patient type and 10 patients from each
K1,K2,B1,B2,F1,F2 per an hour as second visit patients
The importance of this work is, it has considered both
reducing waiting times and routing times in the hospital
premises while improving the whole process. And also
experiment schedules show how resources can be allocated in
order to achieve efficient and effective service.
As for the future work these improved schedule rules can
be implemented to see how they operate in the practical
world. This model can also be used by the internal staff to
test new scenarios in future.
ACKNOWLEDGMENT
Author wishes to acknowledge the inputs of Dr.Roshan
Hewapathirana, Ms. Nadee De Silva and other staff members
at National eye hospital, Colombo for the success of this
study.
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[15] (2014) The Rockwell Arena official website. [Online]. Available:
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