Group 3 Class C - Parking Area of RSUP Dr. Sardjito

8/11/2019 Group 3 Class C - Parking Area of RSUP Dr. Sardjito

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COURSEWORK OF SYSTEM MODELLING AND SIMULATION

PARKING AREA OF RSUP DR. SARDJITO

By :

Group 3 - Class C

Akmal Fatah Fainusa 11/320145/TK/38979

Brithy Michelle Toar 11/312996/TK/37750

Ogissa Piertina Susilo 09/285235/TK/35694

Yunitha Ratnadilla 11/313560/TK/37951

DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERINGFACULTY OF ENGINEERING

GADJAH MADA UNIVERSITY

2014


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LIST OF CONTENTS

Chapter I : Introduction ..........................................................................................................1

1.1

Background of Study ...........................................................................................1

1.2Aims and Objectives ............................................................................................1

1.3Assumptions and Contraints ................................................................................2

Chapter II : Institution Profile and Methods of Observation ................................................3

2.1 Brief Description of Institution ............................................................................3

2.2 Flow of System ....................................................................................................3

2.3 Activity Cycle Diagram .......................................................................................4

2.4 Servers, Resources, and Capacity ........................................................................5

2.5 Date and Time of Observation .............................................................................5

Chapter III : Simulation Design .............................................................................................6

3.1 Data Collection ....................................................................................................6

3.2 Goodness of Fit Test and Selecting Distribution .................................................6

3.2.1 Inter-arrival Time of Cars ...........................................................................6

3.2.2 Processing Time in Entry Ticket Counter ...................................................7

3.2.3 Processing Time in Exit Ticket Counter .....................................................9

3.2.4 Duration of Cars Being Parked ...................................................................10

3.3 Model and Output ................................................................................................12

Chapter IV : Results and Discussion ....................................................................................13

4.1 Real System Simulation .......................................................................................13

4.2 Verification of System .........................................................................................14

4.2.1 Visual Inspection ........................................................................................144.2.2 Flow Diagram .............................................................................................15

4.2.3 Animation of Simulation.............................................................................15

4.2.4 Mistake and Error Check ............................................................................15


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4.3 Validation of System............................................................................................15

4.3.1 Utility of Staff in Entry Ticket Counter ......................................................16

4.3.1.1 Normality Test ................................................................................16

4.3.1.2 Statistic Test ....................................................................................17

4.3.2 Average Waiting Time in Entry Ticket Counter .........................................18

4.3.2.1 Normality Test ................................................................................18

4.3.2.2 Statistic Test ....................................................................................20

4.4 Simulation Results ...............................................................................................21

4.5 Experiments with Model ......................................................................................22

4.5.1 Alternative 1: Vending Ticket Machine .....................................................22

4.5.2 Alternative 2: Additional Entry Ticket Counter .........................................24

4.6 Analysis and Discussion ......................................................................................27

Chapter V : Conclusion ..........................................................................................................28

References ..............................................................................................................................29

Appendices .............................................................................................................................30


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CHAPTER I

INTRODUCTION

1.1Background of Study

Generally, every system is expected to work in its most optimum productivity, so that it

could generate more benefits for the firm or institution. Several tryouts should be carried out to

the system with the purpose of finding out which alternative gives the highest contribution to the

optimization of the system.

Trials conducted to the system can be categorized into two types, which are experiments

applied to the actual system and with a model of the real system. While the first category could be

risky, impractical, and costly, building a mathematical model of an actual system turns out to be

the most effective and efficient way of experimentation.

Mathematical models can perform a varied range of systems. In this study, the system to

be reproduced is the parking area system of a central hospital in Yogyakarta, known as RSUP Dr.

Sardjito. With various health facilities located in the area, it is assumed that thousands of people

come to this hospital every day for different needs. Such number of people will make use of the

parking area, but considering the limited capacity of the parking lot, it is inevitable that some

problems regarding the parking area system would arise. This study is conducted to build a modelof the parking area system of RSUP Dr. Sardjito, and hopefully could give beneficial proposals of

optimization for the problems regarding its parking area system.

1.2Aims and Objectives

In order to decide on the aims to be achieved, the problems occurring in the real system

should be taken into consideration. Among all others, the main problem arising in the parking area

system of RSUP Dr. Sardjito is about the waiting time (queuing time) of the vehicles (especially

cars in this study) in the entry ticket counter. While the process time in the entry ticket counter

varies from 2 seconds up to 25 seconds, the line can only provide for at most 10 cars. Furthermore,

it is highly unlikely to expand the capacity of either the waiting line or the entry ticket counter

since no more space is available in the area. Therefore, this study concerns in building a simulation

model of the parking area of RSUP Dr. Sardjito which has the objective of minimizing the waiting


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time of cars in the entry ticket counter. And based on the simulation, it is expected that some

alternatives of optimization can be established to overcome the problem.

1.3Assumptions and Constraints

In building the simulation model, there are some assumptions and constraints set, which

are:

a.

The system related to health facilities is excluded from the model.

b. The observed entities are only the four-wheeled vehicles (cars in general).

c. The existence of parking areas located outside RSUP Dr. Sardjito is neglected.

d. The model in this study is limited to simulate the parking area system of RSUP Dr.

Sardjito during visiting hours, in order to reduce the probability of visitors or patients

staying overnight.

e. Data collection for building the model is gathered only during visiting hours, which are

categorized into morning visiting hours (10.00-12.00 WIB) and evening visiting hours

(17.00-18.30 WIB).


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CHAPTER II

INSTITUTION PROFILE AND METHODS OF OBSERVATION

2.1Brief Description of Institution

RSUP Dr. Sardjito is the central hospital located in Kesehatan Street No. 1 Sekip, District

of Sleman, Province of Daerah Istimewa Yogyakarta, and sited between the Faculty of Medicine

and the Faculty of Engineering, Universitas Gadjah Mada. Built on 1982, this hospital has been

cooperating with Faculty of Medicine in conducting the subjects for students learning to be

doctors, specialists, and nurses. RSUP Dr. Sardjito owns various health facilities, ranging from

cardiology, orthopedic, neural operations, medical rehabilitation, and many others.

This hospital has a rather large parking area for four-wheeled vehicles which can provide

up to 352 vehicles. The parking building is located in the west side of the hospital, comprised of 6

floors of parking area with different capacity for each floor.

2.2Flow of System

The flow of the parking area system of RSUP Dr. Sardjito is explained as follows:

a. The system will be started when the car of patients or visitors enters the system through the

gate and queues in the waiting line to get entry ticket.b. In the entry ticket counter, a staff will input data of the car, including the cars license plate

and arrival time, and give a parking ticket.

c. After getting the ticket, visitors or patients are allowed to enter the system to find any empty

space and park their car.

d. Afterwards, visitors or patients can go directly to any health facilities for their respective needs.

The duration of visitors or patients stay inside the health facilities will determine the time of

cars being parked.

e. Once the visitors or patients are done, they will go back to the parking building to get into their

car and move towards the exit ticket counter.

f. In the exit ticket counter, visitors or patients will give the ticket back to the staff and pay the

fare.

g. The system will end once the car exits from the ticket counter.


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2.3Activity Cycle Diagram

In the typical activity cycle diagram (ACD) based approach, a simulation model is viewed

as a collection of interacting entities (Page, 1994). Entities are either idle - in notational or real

queues - or active - engaged with other entities in time consuming activities.

In the simulation model of parking area system of RSUP Dr. Sardjito, there are four

different entities involved in the system, which are the cars, the staff on entry ticket counter, the

staff on exit ticket counter, and the parking lot. List of entities with its assigned activities as well

as the flow diagram of the system is described in Table 2.1 and Figure 2.1 as follows.

Table 2.1 List of Entities and Activities

Entity Activity Symbol

Cars (temporary)

Arriving at the entry ticket counter ARRIVAL

Being processed by the staff on entry ticket counter IN

Being parked in parking area PARK

Being processed by the staff on exit ticket counter OUT

Staff on entry ticketcounter (permanent)

Processing cars which are entering hospital area IN

Staff on exit ticketcounter (permanent)

Processing cars which are leaving hospital area OUT

Parking lot (permanent) Being used for parking cars PARK

Figure 2.1 Activity Cycle Diagram of Parking Area System of RSUP Dr. Sardjito


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CHAPTER III

SIMULATION DESIGN

3.1 Data Collection

The data needed in building the model of parking area system of RSUP Dr. Sardjito are:

a. Inter-arrival time of cars

b. Processing time in the entry ticket counter

c. Processing time in the exit ticket counter

d. Duration of cars being parked

3.2

Goodness of Fit Test and Selecting Distribution

3.2.1 Inter-arrival Time of Cars

From the observation, the number of cars entering the system during evening visiting hours

was only 144 cars, while in the morning visiting hours it reached up to 194 cars. Considering that

the latter total amount of cars could represent the system better, the set of data used in later tests

are taken from the morning shift. Raw data of inter-arrival time during morning visiting hours is

shown in Appendix 1.

Before using the data for selecting distribution, it is preferred to check the uniformity andadequacy of the data set first. Test on the data uniformity reduces the total data from 194 to 192

cars, and test on the data adequacy gives the number of 2995 data needed in order to define more

accurate distribution. Since it is not possible to gather so much data, the original data set will still

be applied in selecting distribution.

As shown in Figure 3.1, test using StatFit results in no theoretical distribution exactly fits

the original data set. From this outcome, empirical distribution is applied for input in building the

model. The graph of the empirical distribution is shown in Figure 3.2.


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Figure 3.1 Auto-Fit Distribution Test of Inter-arrival Time Data

Class LB UB Freq. %

1 0 13 115 60%

2 14 27 14 7%

3 28 41 9 5%

4 42 55 15 8%

5 56 69 15 8%

6 70 83 9 5%

7 84 97 6 3%

8 98 111 2 1%

9 112 125 7 4%TOTAL 192 100%

Figure 3.2 Empirical Distribution of Inter-arrival Time Data

3.2.2 Processing Time in Entry Ticket Counter

The data set used in this section are picked out from the observation during morning

visiting hours. Raw data of processing time in the entry ticket counter can be seen in Appendix 2.

The test on data uniformity using control chart decreases the number of data to 187, while

the test on data adequacy ensues in the total of 285 data needed in order to define more accurate

distribution. Since it is not possible to gather more data, the original data set will still be applied

in selecting distribution.

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9

Inter-arrival Time


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As shown in Figure 3.3, test using StatFit results in four theoretical distributions have

passed the acceptance criteria. But before using any of four accepted distributions, it is preferred

to check the outcomes of the goodness of fit tests first.

Figure 3.3 Auto-Fit Distribution Test of Processing Time in Entry Ticket Counter Data

As can be seen in Figure 3.4, all four theoretical distributions which pass the auto-fit test

have at least one reject result from the three type of goodness of fit test. Based on this result, it

is preferred to use empirical distribution for input in building the model. The graph of the empirical

distribution is shown in Figure 3.5.

Figure 3.4 Goodness of Fit Test for Processing Time in Entry Ticket Counter Data


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Figure 3.4 Goodness of Fit Test for Processing Time in Entry Ticket Counter Data (cont.)

Class LB UB Freq. %

1 2 3 17 9%

2 4 5 41 22%

3 6 7 42 22%

4 8 9 39 21%

5 10 11 24 13%

6 12 13 17 9%

7 14 15 5 3%

8 16 17 2 1%

TOTAL 187 100%

Figure 3.5 Empirical Distribution of Processing Time in Entry Ticket Counter Data

3.2.3 Processing Time in Exit Ticket Counter

The data set used in this section are picked out from the observation during evening visiting

hours, since more data were obtained during this period. Raw data of processing time in the exit

ticket counter can be seen in Appendix 3.

The test on data uniformity using control chart decreases the number of data from 259 to

250, while the test on data adequacy ensues in the total of 288 data needed in order to define more

accurate distribution. Since the difference is not really wide, the original data set will still be

applied in selecting distribution.

0

10

20

30

40

50

1 2 3 4 5 6 7 8

Processing Time in Entry Ticket Counter


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As shown in Figure 3.6, test using StatFit results in no theoretical distribution exactly fits

the original data set. From this outcome, applying empirical distribution for input in building the

model is the last step. The calculation and graph of the empirical distribution is shown in Figure

3.7.

Figure 3.6 Auto-Fit Distribution Test of Processing Time in Exit Ticket Counter Data

Class LB UB Freq. %

1 3 4 40 16%

2 5 6 56 22%

3 7 8 65 26%

4 9 10 40 16%5 11 12 24 10%

6 13 14 13 5%

7 15 16 7 3%

8 17 18 5 2%

TOTAL 250 100%

Figure 3.7 Empirical Distribution of Processing Time in Exit Ticket Counter Data

3.2.4

Duration of Cars Being Parked

The data set used in this section are picked out from the observation during morning

visiting hours with the sample size of 50. Raw data of duration of cars being parked can be seen

in Appendix 4.

0

10

20

30

4050

60

70

1 2 3 4 5 6 7 8

Processing Time in Exit Ticket Counter


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The test on data uniformity using control chart indicates no data is being outlier, thus all

data can be used for later steps. The test on data adequacy ensues in the total of 185 data needed

in order to define more accurate distribution. Since it is not possible to gather more data, the

original data set will still be applied in selecting distribution.

As shown in Figure 3.8, test using StatFit results in nine theoretical distributions have

passed the acceptance criteria. But before using any of them, it is preferred to check the outcomes

of the goodness of fit tests first.

Figure 3.8 Auto-Fit Distribution Test of Duration of Cars Being Parked Data

As can be seen in Figure 3.9, from the top-three accepted distributions, lognormal

distribution is the only one having all do not reject results from the three type of goodness of fit

test. Based on this outcome, lognormal distribution will be applied for the input in building the

model.

Figure 3.9 Goodness of Fit Test for Processing Time in Entry Ticket Counter Data


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On the other hand, since the model is created using Flexsim 6.0 the distributions are cross-

checked using ExpertFit. The data of inter-arrival time, processing time in entry ticket counter,

and processing time in exit ticket counter have the similar results, which mean empirical

distributions are deemed as the fitting distribution. Meanwhile, the outcome of ExpertFit states the

duration of cars being parked could be defined better using Johnson-bounded distribution (min =

1002.309394; max = 8570.981104; shape 1 = 0.154941; shape 2 = 1.075610), so this result is the

one used for input in building the model.

3.3 Model and Output

After selecting the fitting distribution for each data, the following step is building the

model. The model of parking area system of RSUP Dr. Sardjito is created using Flexsim 6.0 and

the system layout is displayed in Figure 3.10.

Figure 3.10 Layout of Parking Area System of RSUP Dr. Sardjito


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CHAPTER IV

RESULTS AND DISCUSSION

4.1Real System Simulation

After building the model, a simulation is required in order to check whether the model

could work or not. Figure 4.1 displays the simulation of the parking area system of RSUP Dr.

Sardjito.

In this model, cars are symbolized with boxes. As can be seen from the Figure, cars need

to wait in the queue line before being processed in the entry ticket counter. A staff is assigned in

both entry and exit ticket counter as an operator for processing.

Figure 4.1 Running Simulation of Model

The running time for this simulation is set to 5.400 seconds, in order to create the similar

condition with the real system. On the other hand, setting the running time only up to an hour and

a half affects the results as the outcome in the exit ticket counter cannot be taken into further

analysis. Mainly caused by the operation time of a hospital which is 24 hours, the number of cars

exiting the system during the observation is most likely be the accumulation of cars staying

overnight. This explains the fact that there are entities (cars) which are already leaving the system

in time 0.


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On the contrary, when the simulation is started from time 0, the system is set to free from

holding any entities (cars). Since it is assumed that the parking lot is empty in the beginning of the

simulation, it is not possible that there will be any cars leaving the parking area in the first few

minutes. Thus, it is hardly possible that the end report of the simulation in terms of the exit ticket

counter can represent the real system condition.

In addition, observation of the real system indicates that problems regarding queue line in

the exit ticket counter is not as urgent as in the entry ticket counter. Other than having more space

for waiting line, problems in the exit ticket counter incline more to the extraneous circumstances,

such as the traffic happening in front of the hospital area, and less to the process. These are

basically the reasons on why the objective and further analysis of the simulation model will be

more focused in the entry ticket counter in the following sections.

Based on the simulation, the overall model works well without any error hindering the

process. Hence, the simulation model can be proceeded into the steps of verification and validation.

4.2Verification of System

Formally, verification is addressed to determine whether the model has satisfied the

conditions imposed (Calegari and Szasz, 2013). In other words, verification is the process of

proving that we are building the model in the right way. In doing the verification of the system,

there are four methods which are chosen. Each method is explained as follows.

4.2.1

Visual Inspection

Visual inspection has been done by a member of the group who did not partake in building

the model. Figure 4.2 exhibits the visualization of the simulation.

Based on the inspection, the model has successfully exemplified the real parking area

system of RSUP Dr. Sardjito. The model layout also has enough resemblances with the real

systems layout. The servers of the real system have been represented in the mode l as well,

including the existence of entry gate, entry ticket counter, parking lot, exit ticket counter, and exit

gate.


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Figure 4.2 Visual Inspection of Model

4.2.2 Flow Diagram

Verification with flow diagram uses activity cycle diagram (ACD) to check the logic for

each action in each event type. The list of activities with the activity cycle diagram is shown in

Table 2.1 and Figure 2.1.

4.2.3 Animation of Simulation

From the simulation, it can be seen that the model performs the exactly same process with

the real system. The system starts when there is an entity passing through the queue line towards

the entry ticket counter, before being processed and searching for available parking spot. During

the running, the simulation shows that there are entities queuing up in the waiting line.

4.2.4 Mistake and Error Check

While doing the running, there is no error found from the model. The model progresses

smoothly, which means that it can be said the model has been built right and worked well.

4.3Validation of System

Validation is generally considered as the process of determining whether the model has

satisfied specific requirement to some acceptable level compared to the real system. In other words,

validation is a process of proving that we are building the right model (Calegari and Szasz, 2013).

In validating the system, there are two types of data that will be set as the original parameter in


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this study, which are the utility of staff in the entry ticket counter and the average waiting time of

cars to enter the entry ticket counter.

4.3.1 Utility of Staff in Entry Ticket Counter

For validation, simulation of model is replicated for 30 times before being statistically

tested and compared to the initial outcome from the real system. Replication data of utility of staff

in the entry ticket counter can be seen in Appendix 5.

Test on the data adequacy states that the minimum number of data needed for validation is

11. Since the replication number is already three times the number of the data needed, it can be

directly proceeded to normality and statistic tests which both are performed using Minitab 15.

4.3.1.1 Normality Test

Figure 4.3 up to 4.5 show the Anderson-Darling, Ryan-Joiner, and Kolmogorov-Smirnov

normality tests applied to the replication data. With the initial sett ing of = 0.05, all three tests

give the results of p-value > . Therefore, the data on utility of staff in the entry ticket counter can

be dubbed as normal and able to be used in statistic test.

323028262422

99

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60

50

40

30

20

10

5

1

util

Percen

t

Mean 26.67

StDev 2.189

N 30

AD 0.578

P-Value 0.121

Utilitas Petugas Loket MasukNormal

Figure 4.3 Anderson-Darling Normality Test of Utility of Staff in Entry Ticket Counter


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323028262422

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30

20

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1

util

Percen

t

M ean 26.67

S tDev 2. 189

N 30

RJ 0.975

P-Value >0.100


Figure 4.4 Ryan-Joiner Normality Test of Utility of Staff in Entry Ticket Counter

323028262422

99

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50

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30

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util

Percen

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M ean 26.67

S tDev 2. 189

N 30

KS 0.125

P-Value >0.150


Figure 4.5 Kolmogorov-Smirnov Normality Test of Utility of Staff in Entry Ticket Counter

4.3.1.2 Statistic Test

The statistic test for system validation is performed using t-test. The value of parameter

from the observation is calculated from the total processing time per total observation time (an

hour and half). With the initial parameter of 26.02%, Figure 4.6 shows the one sample t-test done

to the simulation result. (H0: = 26.02 ; H1 : 26.02 ; = 0.05)


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Figure 4.6 One Sample T-Test for Utility of Staff in Entry Ticket Counter

As can be seen from the result, the p-value is stated to be 0.114, which is much higher than

the initial of 0.05. From this outcome, we fail to reject the H0with the statistical confidence level

of 95% and it can be said that the replication data have the similar mean compared to the original

data. Therefore, it can be concluded that outcomes in terms of utility of staff in the entry ticket

counter have been statistically validated.

4.3.2 Average Waiting Time in Entry Ticket Counter

Similar with the validation in the previous section, simulation of model is replicated for 30

times before being statistically tested and compared to the initial outcome from the real system.

Replication data of average waiting time in the entry ticket counter can be seen in Appendix 5.

Test on the data adequacy states that the minimum number of data needed for validation is

7. Since the replication number is already four times the number of the data needed, it can be

directly proceeded to normality and statistic tests which both are performed using Minitab 15.

4.3.2.1 Normality Test

Figure 4.7 up to 4.9 show the Anderson-Darling, Ryan-Joiner, and Kolmogorov-Smirnov

normality tests applied to the replication data. With the initial setting of = 0.05, all three tests

give the results of p-value > . Therefore, the data on average waiting time in the entry ticket

counter can be dubbed as normal and able to be used in statistic test.


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21201918171615

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40

30

20

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5

1

Validasi Ant rian

Percen

t

Mean 18,26

StDev 1,172

N 30

AD 0,435

P-Value 0,281

Probability Plot of Validasi AntrianNormal

Figure 4.7 Anderson-Darling Normality Test of Average Waiting Time in Entry Ticket Counter

21201918171615

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10

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Validasi Antrian

Percen

t

M ean 18, 26

S tDev 1,172

N 30

RJ 0,978

P-Value >0,100


Figure 4.8 Ryan-Joiner Normality Test of Average Waiting Time in Entry Ticket Counter


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21201918171615

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Validasi Antrian

Percent

Mean 18, 26

StDev 1, 172

N 30

KS 0,108

P-Value >0,150


Figure 4.9 Kolmogorov-Smirnov Normality Testof Average Waiting Time in Entry Ticket Counter

4.3.1.2 Statistic Test

The statistic test for system validation is performed using t-test. The value of parameter

from the observation is calculated from the total waiting time for all cars per the number of cars

who have to queue up in line. With the initial mean of 18.39 seconds, Figure 4.10 shows the one

sample t-test done to the simulation result. (H0: = 18.39; H1 : 18.39 ; = 0.05)

Figure 4.10 One Sample T-Test for Average Waiting Time in Entry Ticket Counter

As can be seen from the result, the p-value is stated to be 0.534, which is much higher than

the initial of 0.05. From this outcome, we fail to reject the H0with the statistical confidence level

of 95% and it can be said that the replication data have the similar mean compared to the original

data. Therefore, it can be concluded that outcomes in terms of average waiting time in the entry

ticket counter have been statistically validated.


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4.4Simulation Results

After being verified and validated, the model is again simulated in order to derive some

alternatives to answer the problem in the objective function. With the running time of 5.400

seconds, general reports from the simulation can be seen in Figure 4.11 and Figure 4.12 below.

Figure 4.11 Summary Report (Initial Condition)

Figure 4.12 State Report (Initial Condition)

With the objective function of minimizing the waiting time of cars in the entry ticket

counter, some variables are chosen to be the parameters of comparison in the following alternatives

of optimizations. These variables comprise of average content, maximum stay time, average stay

time, %blocked, and %empty of waiting line in entry ticket counter.

From the simulation, the waiting line has the average content of 0.79 entities (cars) per

second. Cars need to wait up to 65.41 seconds before being able to enter the entry ticket counter,

with the average time of waiting is 19.05 seconds. The percentage of blocked entities is fairly high,


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which is stated in 15.35%. Throughout the running for one and a half hour, the waiting line has

the percentage of 65.85% being in the state of empty. These parameters will be the value to be

appraised in deciding the optimal solution of optimization.

4.5Experiments with Model

Going by the objective of minimizing the waiting time before entering the entry ticket

counter, there are two major options which could be considered for optimizations, those are:

a. Replacing the entry ticket counter to vending ticket machine

b. Adding one more entry ticket counter and staff alongside the existing one

4.5.1 Alternative 1: Vending Ticket MachineThe idea of using vending ticket machine is derived from the real system condition in which

processing is still performed manually by an assigned staff and the time could vary from 2 to 25

seconds. The moderately high variability of processing time is mainly influenced by the lacking

of signs within the first few meters after the entry gate. Visitors or patients who have never visited

the hospital would be confused on how to reach their particular destination of health facility, thus

decide to ask the staff while getting their parking ticket. Figure 4.13 displays the layout of the

model after implementing this solution.

Figure 4.13 Layout of Alternative 1: Vending Ticket Machine


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Assuming that a vending ticket machine could perform a standardized processing time of

3 seconds, this alternative is expected to reduce the duration of waiting time of the cars before

being able to enter the hospital area. With the running time of one and a half hour, Figure 4.14 and

4.15 exhibits the summary and state report of the first offered solution.

Figure 4.14 Summary Report (Vending Ticket Machine)

Figure 4.15 State Report (Vending Ticket Machine)

Based on the reports, the average content of the waiting line is now 0.53 entities (cars) per

second. With a homogenous processing time, the maximum stay time of a car has significantly

decreased to 26.73 seconds and the average duration of being in the waiting line is 12.36 seconds.

Using a vending ticket machine also gives a low percentage of entities being blocked, which is

5.05% and during the simulation the waiting line has the percentage of 73.60% being in the state

of empty. Table 4.1 lists the comparison of the results between the initial system condition and the

first alternative of optimization using vending ticket machine.


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Figure 4.16 Layout of Alternative 2: Additional Entry Ticket Counter

Even with the varying processing time, adding one more entry ticket counter is expected

to somehow reduce the duration of waiting time of the cars before being able to enter the hospital

area. With the running time of one and a half hour, Figure 4.17 and 4.18 exhibits the summary and

state report of the second offered solution.

Figure 4.17 Summary Report (Additional Entry Ticket Counter)


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Figure 4.18 State Report (Additional Entry Ticket Counter)

After adding one more counter, the average content is seen to be decreasing to 0.58 entities

(cars) per second. The maximum stay time has reduced to 30.02 seconds and the average waiting

time is 12.41 seconds. With the existence of another server, the percentage of entities being

blocked is lowered to 5.23% and the waiting line has the percentage of 72.89% being empty. Table4.2 shows the comparison of the results between the initial system condition and the second

alternative of optimization with adding one more entry ticket counter.

Table 4.2 Comparison of Results - Initial Condition and Alternative 2

Parameter Initial Condition Additional Entry Ticket Counter

Average content 0.79 entities per second 0.58 entities per second

Maximum stay time 65.41 seconds 30.02 seconds

Average stay time 19.05 seconds 12.341seconds%Blocked 15.35% 5.23%

%Empty 65.85% 72.89%

Based on the table above, adding one more entry ticket counter also gives positive result

towards the effort to fulfil the objective function. More server means that more entities could be

processed at the same time, so cars need less time to queue up and also less entities being blocked

from entering the system.

In terms of investment, this solution is estimated to cost the management around US

$1.000-1.200, which would be spent in building the counter (estimated cost is US $500), buying

both hardware and software for integrated ticketing system (estimated cost is US $500), and also

hiring another employee to work in the counter (local minimum wage level is estimated to be US


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27

$120 per month). In addition, the management should also do bi-monthly maintenance for

checking up the hardware.

4.6

Analysis and DiscussionFrom the two alternatives of optimization, the results for each proposed solution could be

appraised one to another as figured in Table 4.3 below.

Table 4.3 Comparisons between Alternatives

Parameter Vending Ticket MachineAdditional Entry Ticket

Counter

Decrease of average content 0.26 0.21

Decrease of maximum stay time 59.13% 54.10%

Decrease of average stay time 35.12% 34.86%

Decrease of %blocked 10.30% 10.12%

Increase of %empty 7.75% 7.04%

From the results above, it can be concluded that the using of entry ticket counter with

vending ticket machine contributes to more significant outcomes in the objective of minimizing

the waiting time.

Substituting manual operator (staff) to automated one (vending machine) will affect the

occupancy rate of the parking lot, which has risen from the amount of 167 cars to 183 cars for the

running time of one and a half hour. But considering that this change can be considerably accepted,

the proposed solution of investing in a vending ticket machine to replace the existing entry ticket

counter is still advisable.


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28

CHAPTER V

CONCLUSION

The most crucial problem occurring in the parking area system of RSUP Dr. Sardjito

happens in the waiting line to enter the hospital area. With such confined space that can only

provide at most 10 cars in total, the simulation model has the objective of minimizing the waiting

time of cars in the queue line.

Verification and validation processes have been applied to the model in order to get as

accurate result as possible to the real system. The model has been verified using some methods as

well as validated with the variables of utility of staff and average waiting time both I the entry

ticket counter.

Taking the issues of available space and waiting time into consideration, there are two

proposed alternatives of system optimization. After comparing the results, the idea of replacing

the entry ticket counter to vending ticket machine gives more significant result in minimizing the

waiting time in the queue line. Thus, this option is more advisable to be applied in the real system.


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REFERENCES

Calegari, D., and Szasz, N., 2013, Verification of Model Transformations: A Survey of the State-

of-the-Art,Electronic Notes in Theoretical Computer Science, vol. 292, pp. 5-25.

Page, E.H., 1994, Simulation Modeling Methodology: Principles and Etiology of Decision

Support, Virginia Polytechnic Institute and State University, Virginia.


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APPENDICES

Appendix 1. Observation Data of Inter-arrival Time during Morning Visiting Hours

No Time IA No Time IA No Time IA No Time IA No Time IA

1 9:36:20 40 9:48:13 0 79 10:03:00 0 118 10:21:07 7 157 10:37:00 60

2 9:37:05 45 41 9:48:13 0 80 10:03:00 0 119 10:21:28 21 158 10:37:10 10

3 9:37:10 5 42 9:48:13 0 81 10:04:02 62 120 10:22:19 51 159 10:37:10 0

4 9:37:14 4 43 9:49:27 74 82 10:04:02 0 121 10:22:19 0 160 10:38:35 85

5 9:37:22 8 44 9:50:58 91 83 10:04:02 0 122 10:22:19 0 161 10:39:59 84

6 9:38:02 40 45 9:50:58 0 84 10:04:02 0 123 10:22:19 0 162 10:39:59 0

7 9:38:15 13 46 9:50:58 0 85 10:05:01 59 124 10:22:19 0 163 10:39:59 0

8 9:38:25 10 47 9:50:58 0 86 10:05:06 5 125 10:23:59 100 164 10:39:59 0

9 9:39:33 68 48 9:51:00 2 87 10:05:06 0 126 10:23:59 0 165 10:40:05 6

10 9:39:33 0 49 9:51:00 0 88 10:06:01 55 127 10:23:59 0 166 10:41:20 75

11 9:40:50 77 50 9:52:03 63 89 10:06:01 0 128 10:23:59 0 167 10:41:20 0

12 9:40:50 0 51 9:52:03 0 90 10:07:15 74 129 10:24:00 1 168 10:41:20 013 9:41:12 22 52 9:52:03 0 91 10:07:38 23 130 10:25:00 60 169 10:41:20 0

14 9:41:12 0 53 9:52:03 0 92 10:08:45 67 131 10:26:00 60 170 10:41:20 0

15 9:41:12 0 54 9:52:03 0 93 10:09:27 42 132 10:27:58 118 171 10:43:17 117

16 9:41:12 0 55 9:52:03 0 94 10:09:27 0 133 10:27:58 0 172 10:45:16 119

17 9:42:41 89 56 9:52:04 1 95 10:09:27 0 134 10:27:58 0 173 10:45:21 5

18 9:42:46 5 57 9:52:04 0 96 10:09:27 0 135 10:28:00 2 174 10:45:38 17

19 9:43:07 21 58 9:52:04 0 97 10:10:00 33 136 10:28:00 0 175 10:46:18 40

20 9:43:07 0 59 9:52:04 0 98 10:11:35 95 137 10:28:00 0 176 10:46:18 0

21 9:43:07 0 60 9:52:04 0 99 10:11:35 0 138 10:28:00 0 177 10:46:18 0

22 9:43:32 25 61 9:54:17 133 100 10:11:35 0 139 10:29:33 93 178 10:47:10 52

23 9:44:00 28 62 9:56:32 135 101 10:11:35 0 140 10:29:42 9 179 10:47:17 7

24 9:45:00 60 63 9:57:02 30 102 10:12:00 25 141 10:29:42 0 180 10:48:02 45

25 9:45:00 0 64 9:57:15 13 103 10:13:00 60 142 10:30:17 35 181 10:48:17 15

26 9:45:00 0 65 9:58:03 48 104 10:14:00 60 143 10:30:31 14 182 10:49:25 68

27 9:45:00 0 66 9:59:00 57 105 10:14:10 10 144 10:30:41 10 183 10:49:25 0

28 9:46:02 62 67 9:59:00 0 106 10:15:25 75 145 10:32:00 79 184 10:49:25 0

29 9:46:08 6 68 9:59:10 10 107 10:16:37 72 146 10:32:20 20 185 10:49:26 1

30 9:46:16 8 69 10:00:00 50 108 10:16:37 0 147 10:32:35 15 186 10:51:17 111

31 9:46:16 0 70 10:00:05 5 109 10:16:37 0 148 10:32:35 0 187 10:51:32 15

32 9:46:16 0 71 10:00:14 9 110 10:17:00 23 149 10:33:22 47 188 10:52:22 50

33 9:46:16 0 72 10:01:19 65 111 10:18:19 79 150 10:33:57 35 189 10:52:39 17

34 9:47:03 47 73 10:01:19 0 112 10:18:19 0 151 10:34:00 3 190 10:53:28 49

35 9:47:03 0 74 10:01:19 0 113 10:18:19 0 152 10:34:00 0 191 10:55:20 112

36 9:48:13 70 75 10:02:13 54 114 10:19:07 48 153 10:35:56 116 192 10:57:17 117

37 9:48:13 0 76 10:02:24 11 115 10:19:07 0 154 10:35:56 0 193 10:58:02 45

38 9:48:13 0 77 10:02:24 0 116 10:19:07 0 155 10:35:56 0 194 10:58:40 38

39 9:48:13 0 78 10:03:00 36 117 10:21:00 113 156 10:36:00 4 195 10:58:45 5


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Appendix 2. Observation Data of Processing Time in Entry Ticket Counter

No Time Process No Time Process No Time Process No Time Process No Time Process

1 9:36 3 40 9:48 14 79 10:03 12 118 10:21 4 157 10:37 5

2 9:37 4 41 9:48 11 80 10:03 10 119 10:21 6 158 10:37 5

3 9:37 3 42 9:48 6 81 10:04 9 120 10:22 6 159 10:37 8

4 9:37 5 43 9:49 20 82 10:04 8 121 10:22 10 160 10:38 3

5 9:37 6 44 9:50 6 83 10:04 13 122 10:22 9 161 10:39 11

6 9:38 3 45 9:50 7 84 10:04 9 123 10:22 10 162 10:39 5

7 9:38 4 46 9:50 7 85 10:05 4 124 10:22 3 163 10:39 8

8 9:38 7 47 9:50 8 86 10:05 12 125 10:23 5 164 10:39 8

9 9:39 6 48 9:51 11 87 10:05 13 126 10:23 6 165 10:40 6

10 9:39 6 49 9:51 8 88 10:06 12 127 10:23 4 166 10:41 24

11 9:40 5 50 9:52 11 89 10:06 6 128 10:23 15 167 10:41 7

12 9:40 7 51 9:52 12 90 10:07 7 129 10:24 15 168 10:41 9

13 9:41 4 52 9:52 8 91 10:07 11 130 10:25 8 169 10:41 28

14 9:41 3 53 9:52 7 92 10:08 6 131 10:26 9 170 10:41 7

15 9:41 4 54 9:52 5 93 10:09 20 132 10:27 7 171 10:43 5

16 9:41 2 55 9:52 8 94 10:09 8 133 10:27 13 172 10:45 4

17 9:42 5 56 9:52 9 95 10:09 10 134 10:27 26 173 10:45 4

18 9:42 6 57 9:52 6 96 10:09 5 135 10:28 9 174 10:45 3

19 9:43 5 58 9:52 4 97 10:10 8 136 10:28 9 175 10:46 18

20 9:43 12 59 9:52 11 98 10:11 5 137 10:28 12 176 10:46 7

21 9:43 13 60 9:52 6 99 10:11 4 138 10:28 5 177 10:46 20

22 9:43 3 61 9:54 14 100 10:11 8 139 10:29 3 178 10:47 5

23 9:44 5 62 9:56 7 101 10:11 9 140 10:29 5 179 10:47 4

24 9:45 17 63 9:57 4 102 10:12 9 141 10:29 4 180 10:48 625 9:45 3 64 9:57 10 103 10:13 12 142 10:30 8 181 10:48 3

26 9:45 9 65 9:58 9 104 10:14 8 143 10:30 6 182 10:49 7

27 9:45 10 66 9:59 11 105 10:14 5 144 10:30 6 183 10:49 5

28 9:46 3 67 9:59 8 106 10:15 11 145 10:32 3 184 10:49 6

29 9:46 5 68 9:59 3 107 10:16 7 146 10:32 6 185 10:49 10

30 9:46 9 69 10:00 4 108 10:16 4 147 10:32 13 186 10:51 5

31 9:46 13 70 10:00 7 109 10:16 11 148 10:32 10 187 10:51 3

32 9:46 11 71 10:00 5 110 10:17 6 149 10:33 9 188 10:52 4

33 9:46 18 72 10:01 10 111 10:18 17 150 10:33 4 189 10:52 9

34 9:47 10 73 10:01 8 112 10:18 10 151 10:34 7 190 10:53 7

35 9:47 9 74 10:01 8 113 10:18 7 152 10:34 8 191 10:55 8

36 9:48 14 75 10:02 8 114 10:19 12 153 10:35 3 192 10:57 8

37 9:48 7 76 10:02 13 115 10:19 12 154 10:35 7 193 10:58 6

38 9:48 9 77 10:02 12 116 10:19 10 155 10:35 9 194 10:58 4

39 9:48 11 78 10:03 6 117 10:21 5 156 10:36 10 195 10:58 6


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Appendix 3. Observation Data of Processing Time in Exit Ticket Counter

No Time Process No Time Process No Time Process

1 16:08 11 45 16:18 12 89 16:31 7

2 16:08 19 46 16:18 17 90 16:32 5

3 16:08 18 47 16:18 10 91 16:32 11

4 16:08 6 48 16:19 7 92 16:34 65 16:08 7 49 16:19 5 93 16:34 13

6 16:09 11 50 16:20 10 94 16:34 4

7 16:09 7 51 16:20 7 95 16:34 9

8 16:09 17 52 16:20 9 96 16:36 7

9 16:09 3 53 16:21 8 97 16:36 8

10 16:09 23 54 16:21 6 98 16:36 6

11 16:09 8 55 16:21 9 99 16:36 11

12 16:09 4 56 16:21 6 100 16:38 4

13 16:10 13 57 16:21 9 101 16:38 6

14 16:10 5 58 16:21 12 102 16:38 12

15 16:11 7 59 16:21 8 103 16:38 8

16 16:11 8 60 16:21 5 104 16:38 4

17 16:11 7 61 16:21 10 105 16:40 9

18 16:11 5 62 16:21 5 106 16:40 10

19 16:11 17 63 16:23 6 107 16:40 13

20 16:11 12 64 16:23 7 108 16:41 7

21 16:11 9 65 16:23 7 109 16:42 13

22 16:12 5 66 16:23 8 110 16:42 5

23 16:12 7 67 16:25 7 111 16:43 11

24 16:12 16 68 16:25 7 112 16:43 10

25 16:14 13 69 16:25 6 113 16:44 7

26 9:45 9 70 16:26 9 114 16:44 5

27 9:45 10 71 16:27 9 115 16:45 13

28 9:46 3 72 16:27 8 116 16:45 13

29 9:46 5 73 16:27 8 117 16:46 4

30 9:46 9 74 16:27 6 118 16:46 11

31 16:15 21 75 16:29 9 119 16:47 8

32 16:15 10 76 16:29 11 120 16:47 8

33 16:15 13 77 16:29 8 121 16:47 10

34 16:16 11 78 16:29 16 122 16:48 8

35 16:16 12 79 16:29 9 123 16:48 7

36 16:16 12 80 16:29 3 124 16:48 16

37 16:16 9 81 16:29 7 125 16:48 5

38 16:17 8 82 16:29 19 126 16:48 5

39 16:17 8 83 16:30 6 127 16:49 4

40 16:17 10 84 16:30 8 128 16:49 8

41 16:18 12 85 16:30 6 129 16:50 4

42 16:18 7 86 16:30 7 130 16:50 3

43 16:18 31 87 16:31 10 131 16:52 6

44 16:18 26 88 16:31 10 132 16:53 8


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Appendix 3. Observation Data of Processing Time in Exit Ticket Counter (cont.)

No Time Process No Time Process No Time Process

133 16:53 6 177 17:17 3 221 17:58 5

134 16:53 4 178 17:18 4 222 17:59 7

135 16:54 6 179 17:18 7 223 18:01 7

136 16:54 9 180 17:20 9 224 18:03 6137 16:54 11 181 17:20 15 225 18:03 3

138 16:55 11 182 17:20 5 226 18:03 3

139 16:56 4 183 17:21 12 227 18:03 8

140 16:56 8 184 17:21 6 228 18:04 9

141 16:57 9 185 17:22 5 229 18:05 9

142 16:57 8 186 17:22 13 230 18:06 8

143 16:58 7 187 17:22 6 231 18:06 10

144 16:58 9 188 17:23 14 232 18:08 7

145 16:59 9 189 17:24 13 233 18:08 18

146 17:00 12 190 17:25 7 234 18:08 4

147 17:03 22 191 17:25 12 235 18:09 3

148 17:03 16 192 17:25 10 236 18:10 24

149 17:03 10 193 17:26 11 237 18:12 4

150 17:03 6 194 17:26 13 238 18:12 3

151 17:03 18 195 17:29 5 239 18:14 8

152 17:03 4 196 17:29 7 240 18:17 8

153 17:03 6 197 17:29 7 241 18:17 3

154 17:04 4 198 17:30 6 242 18:21 4

155 17:05 5 199 17:30 8 243 18:21 15

156 17:05 12 200 17:30 7 244 18:22 3

157 17:06 10 201 17:30 20 245 18:22 3

158 17:06 8 202 17:31 5 246 18:22 5

159 17:07 4 203 17:31 6 247 18:22 5

160 17:07 6 204 17:31 6 248 18:23 8

161 17:08 7 205 17:31 11 249 18:23 6

162 17:08 7 206 17:33 4 250 18:23 4

163 17:08 9 207 17:33 13 251 18:24 7

164 17:08 5 208 17:36 10 252 18:24 3

165 17:09 12 209 17:37 9 253 18:24 5

166 17:09 9 210 17:37 7 254 18:26 4

167 17:09 8 211 17:39 4 255 18:26 9

168 17:10 7 212 17:40 5 256 18:27 5

169 17:12 3 213 17:45 3 257 18:28 4

170 17:13 5 214 17:45 5 258 18:30 3

171 17:13 6 215 17:47 3 259 18:30 8

172 17:14 8 216 17:51 6

173 17:16 6 217 17:51 9

174 17:16 4 218 17:53 7

175 17:17 3 219 17:56 10

176 17:17 10 220 17:58 6


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34

Appendix 4. Observation Data of Duration of Cars Being Parked

License Plate Number Duration (mins) License Plate Number Duration (mins)

AB1643BD 117 AD9123 37

AB1337DK 79 AB1397SE 104

K8903UC 40 AB9660WB 64

AB1399XX 118 AE9175AZ 66W1421BK 87 AB1991AY 99

R9334FH 76 AD8621LU 42

AB1049EN 77 AB1937HK 42

F1346B 34 AA171TA 112

AB1564EA 56 B1728TKR 112

B2475VE 56 B8671OE 69

AB1452MK 91 H1977NU 40

AB1686UZ 112 H9389YC 72

AB1582VA 89 AB1627KE 100

AB8909FA 61 AD9023UC 45

BE1945HK 89 AB1539GA 60

AB1371CE 39 AB1627UE 115

AB1470RQ 84 AA9090JT 100

AB8132C 69 AB1818 98

AB1435FQ 83 AA9219 47

AB1469YK 46 AD7362GC 34

AB1176F 96 AB10PM 69

B1855RB 88 AB1581JA 90

G1885RB 118 AB1983CN 78


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Appendix 5. Results of Simulations

Replication

n

Utility of Staff in Entry Ticket

Counter (%)

Average Waiting Time in Entry Ticket

Counter (seconds)

1 23.3 18.93

2 23.4 19.37

3 23.2 18.684 23.7 19.6

5 23.1 16.72

6 24.9 17.83

7 24.9 19.62

8 24.9 19.85

9 24.9 17.37

10 25.3 19.8

11 25.5 19.77

12 25.7 17.46

13 26 18.514 26.8 18.12

15 27.2 18.63

16 27.4 17.75

17 27.4 19.81

18 27.5 18.02

19 27.5 17

20 27.6 17.65

21 27.7 19.19

22 27.8 17.22

23 28.2 16.19

24 28.3 17.06

25 29.3 19.8

26 29.6 18.38

27 29.7 16.17

28 29.8 16.35

29 29.8 18.15

30 29.9 18.67

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Group 3 Class C - Parking Area of RSUP Dr. Sardjito

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