p–ISSN: 2723 - 6609 e-ISSN: 2745-5254
Vol. 5, No. 5 Mei 2024 http://jist.publikasiindonesia.id/
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2142
Analysis and Modeling of Queuing System Simulation in
Payment Process at Minimarket (Case Study of Minimarket
X Yogyakarta)
Trinopi Melani
1*
, Yani Iriani
2
Universitas Widyatama Bandung, Indonesia
Email: [email protected]
1*
2
*Correspondence
ABSTRACT
Keywords: Antrian,
Anylogic, Minimarket,
Simulasi.
This study aims to analyse the queue queuing system at
Minimarket X to minimise the number of queues. The
method in this writing uses a discrete event simulation
method with the help of Analogic software. Simulation is
used as a method to analyse problems that exist in the
payment system at the Minimarket. At the same time,
Analogic software is an illustration that can facilitate the
queuing system to make it more transparent and accessible
to understand. Observations conducted for 20 days show that
the queuing system applied by Minimarket X is Multi-
Channel – Single Phase and First Come, First Served (FCFS)
or First In, First Out (FIFO) with four cashier officers
(M/M/4). Each cashier is tasked with serving customers and
processing purchased products by scanning them and
packing each grocery. The average number of Minimarket
visitors daily is 22 customers per hour with a queue length
of 10 to 11 customers per hour, and the average waiting time
for customers to be served is around 27 to 30 minutes. Using
any logic software, the simulation obtained error results
within 67 minutes and 43 seconds.
Introduction
Minimarket is a form of retail business with the concept of daily shopping in a
practical, effective, and efficient way (Lope, 2023). The growth of the national retail
industry encourages local retailers to develop the retail industry in their area (Hariyadi,
2016). Thus, minimarkets participate in enlivening the retail industry in Indonesia
(Yosefhine et al., 2022). Minimarket is a convenient shopping place where we can buy
everything we need. The minimarket is a place to do the shopping process, replacing
traditional markets. In the past, people often shopped at traditional markets or stalls close
to where they lived, but because of the busyness and comfort provided, people preferred
to shop at minimarkets (Lopez et al., 2023).
Minimarkets are usually managed with a modern and computerised system, making
service and check prices easier. Shopping at a minimarket seems more practical, where
we do it independently because information about the items we are looking for has been
Analisis Dan Pemodelan Simulasi Sistem Antrian Pada Proses Pembayaran Di Minimarket
(Studi Kasus Minimarket X Yogyakarta)
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2143
provided in detail. Although it seems more practical and efficient, shopping at
minimarkets also often has obstacles, namely in the form of payment processes that tend
to be extended. So, the incident caused a long queue and led us to queue longer (Ramdani
et al., 2021).
Today, queuing is an activity or event that we often encounter. The queue is one of
the events where the number of service resources is not greater than the number of
customers. In other words, the queue is an event caused by the absence of a balance
between arrival patterns and the capacity how to serve customers (Lestari, 2021); in an
era that is starting to develop, practical and modern causes many consumers who shop at
minimarkets to want fast and precise service. However, the large number of customers
who will be served in the queue causes customers who come not to be served
immediately. In this case, customer satisfaction and loyalty are the main things (Azizi,
2022).
The same applies to Minimarket X, located in Bantul Regency, Yogyakarta.
Minimarket X has ten branches in Yogyakarta. Minimarket X is also known as a
comfortable shopping place, with relatively complete daily necessities and relatively
cheap price offers. However, Minimarket X has a problem that often repeats in the form
of a reasonably long payment queue. So, when the primary purpose of shopping at
minimarkets is comfort, it becomes less comfortable because the queues are pretty long,
especially on weekends, the beginning of the month, the end of the month, the afternoon,
the evening and the approach of certain holiday celebrations.
Minimarket X usually operates every day from 08.30 WIB to 21.30 WIB. The data
for this writing is taken from December 23, 2023, to January 11, 2024, for 20 days from
15.30 WIB to 17.30 WIB every day. Minimarket X generally serves many customers, so
it experiences a long queue, and the time to be served in the queue is also quite long.
Queues arise when an unbalanced condition exists between customers served and their
servers (Lestari, 2021). The average number of Minimarket visitors daily is 22 customers
per hour, with a queue length of 10 to 11 customers per hour, and the average waiting
time for customers to be served is around 27 to 30 minutes.
The queuing system implemented by Minimarket X is Multi-Channel – Single
Phase and First Come, First Served (FCFS) or First In, First Out (FIFO) with several
cashier officers, as many as four people who are tasked with serving customers and
processing the products purchased by scanning them and packing each grocery item.
Because of the long queue, it raises the writer's curiosity about problems that often occur.
So, in this study, a simulation will be carried out on the payment process at Minimarket
X using a discrete event simulation model with the help of Analogic software. Simulation
is used as a method to analyse problems that exist in the payment system at the
Minimarket.
Discrete Event System (DES) concerns modelling a system that evolves by a
representation whereby state variables change instantaneously at separate points in time
(in more mathematical terms, it can be said that a system can change only at a quantifiable
number of points in time.) With the help of Analogic software, the author thinks that it
Trinopi Melani
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2144
can make a more transparent and easier-to-understand picture of the queuing system and
make it easier for cashiers to minimise the number of queues during the payment process.
The author also hopes this research can provide an understanding of minimarket X to
improve the future queuing system in the payment process (Sopha & Sakti, 2021).
The previous research relevant to this study's problems can be seen in the following
table.
Table 1
Previous Research
No
Researchers
Heading
Purpose
Conclusion
1
Murthy,
Surasthya,
Don Liquid
(2018)
Simulation
of Alfamart
Pucangsawit
Cashier
Queue
Model
Enhancing
Arena
Software
Knowing the
queue model
of Alfamart
Pucangsawit
cashiers using
Arena
software
simulation and
making
program
simulations
from the
queuing
system at
Alfamart
Pucangsawi
cashiers
After modeling and
using Arena software,
the number of cashiers
available is not qualified
to reduce the length of
queuing time at
Alfamart Pucangsawit.
Therefore, to maximise
the number of
consumers served,
improvements can be
made by increasing the
number of cashiers to
minimise waiting time.
2
Arafah,
Wijayanti,
and
Runanto
(2024)
Queuing
System
Analysis at
Alfamart
Ahmad Yani
Purworejo
Obtain an
overview and
proof of the
performance
of the queuing
system in the
queue process
of Alfamart
Ahmad Yani
Purworejo
The use of the queuing
system at Alfamart
Ahmad Yani is optimal
by using the Multiple
Channel System. This is
evidenced by the data
obtained showing that,
on average, no people
are waiting in the
system.
Based on previous research described in the table above, it can be seen that there
are differences between each title and the research the author examined
(Sulistiyoningrum, 2018). The author's research compared the queue formula and the
Anylogic application. In this method, the author sees the results of calculations, and the
application produces the same or different results. As for the data analysis, the author
reanalysed by adding 1 number of cashiers to compare with the number of cashiers in the
field.
The goal of this study is for the author to represent the modelling of the queuing
system in an analysed system. So that the specific objectives of this writing include the
following:
Analisis Dan Pemodelan Simulasi Sistem Antrian Pada Proses Pembayaran Di Minimarket
(Studi Kasus Minimarket X Yogyakarta)
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2145
1. Analyze efforts that can be applied in optimising customer service to reduce queues in
the payment process at Minimarket X using queuing theory.
2. Identify the average time each customer needs in the payment process until each
cashier serves it at Minimarket X.
3. Analyze the optimal number of cashiers to reduce long queues at Minimarket X's
payment process.
Research Methods
Unit Analisis Data
The time referenced in this writing is rush hour, around afternoon to evening, on
December 23, 2023. So, the object of research in this writing is visitors who decide to
visit Minimarket X to look for their daily needs in Bantul, Yogyakarta.
Data Collection Methods
The data collection methods used by the authors in this study are:
1. Interview
Interviews are flexible tools for data collection, allowing the use of multi-sensory
channels: verbal, nonverbal, seen, spoken, heard, and conducted online or offline, live or
written interviews. The sequence of material that becomes interview material can be
controlled but still provides room for spontaneity (Rahman, 2021).
2. Observation
One of the data collection methods widely used in qualitative research is planned
observation, recording, analysis, and interpretation of behaviour, actions, or
events/phenomena (Sekaran & Bougie, 2016).
3. Study Book
Data is collected by reading literature books, journals, the internet, magazines, and
previous research related to the research (Ginting, 2019).
In addition, the author also made direct observations, but from a short distance, by
measuring the arrival time of customers and the length of time they were queued until
they were served at each cashier using a stopwatch. The data observed is in the form of
the number of customer arrivals at each cashier, a specific time interval (arrival rate), and
service time data (service time) per person.
Data Analysis Methods
Data analysis is an effort made by the author to collect data, process, and analyse
it.
Trinopi Melani
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2146
Figure 1 Research Flow
Results and Discussion
Data Processing Using Formulas
After the data collection, the author can obtain the number and average arrival of
Time Union customers and the number and average Time Union customer service. The
data is used for performance or queue performance. The queuing system at minimarket X
is Multi-Channel—Single Phase, with the queue model used being (M/M/4) and First
Come, First Served (FCFS) or First In, First Out (FIFO), so the data analysis carried out
is as follows.
Average customer arrival rate in a unit of time
Student Literature
Field Observation
Identification
Masalah
Problem Statement
Research
Objectives
Data Collection
interview
Observation
Study Book
Data Processing
Validas
iii
Data Analysis
Conclusions and
Suggestions
no
Ye
s
Analisis Dan Pemodelan Simulasi Sistem Antrian Pada Proses Pembayaran Di Minimarket
(Studi Kasus Minimarket X Yogyakarta)
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2147
Based on the calculation results, the average customer arrival rate is 22
customers/hour.
Average customer service per unit of time (μ)
The average service time required to serve one customer is {(9,58 + 9,42 + 11,33 + 10,33):
4)} = 10,16 atau ten menit.
/perkasir
Based on the calculation results, the average customer service in a unit of time is as
many as six customers/hour or as many as 24 customers/hour for four cashiers.
City of service facilities (s = cash, i.e.)
=
Based on the calculation results, the level of water intensity or cashier busyness in
serving customers is 0.92 or 92%.
The probability of certainty n customers in the system or P0 is equal to an empty
cashier (P0)
Based on the calculation results, the time the cashier has to rest if the customer is
not there or there are 0 customers (P0) is 0.08, or 8% of his busy time.
Average number of subscribers in the system (Ls)
Based on the calculation results, the average number of customers in a system is 11
people/hour, so the system must be able to accommodate as many as 11 people/hour.
parent won the queue (Lq)
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Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2148
Based on the calculation results, the average number of customers in the queue or
customers waiting to be served and in the queue is ten people/hour.
Average customer time in a system (Ws)
Based on the calculation results, the average time customers need to be in the
system is 0.5 hours or 30 minutes.
Average time in queue (Wq)
W_q=λ/(μ(μ-λ))
=22/ (24(24-22))
=22/48
=0,45 hours or 27 minutes.
Based on the calculation results, the average time needed for customers to be in the
queue is 0.45 hours or 27 minutes.
Data Processing Using Anylogic Software
The processing results found for Multi-Channel - Single Phase simulation with four
cashiers running for 120 minutes using Anylogic Software have the following results.
1. The simulation that was run resulted in an error caused by the large number of
customers contained in the queue (queue overload), where the maximum capacity of
the number of queues in one cashier is 12 customers.
2. The error results of the simulation or overload of the number of customers occurred
within 67 minutes and 43 seconds.
3. The number of customers entered during that period was 77 customers.
4. There are 12 customers at each cashier who is queuing.
5. The number of customers being served by each cashier is one customer.
6. The number of customers who have finished being served and have left is 25
customers.
The results of the review can be seen in picture 2 below.
Analisis Dan Pemodelan Simulasi Sistem Antrian Pada Proses Pembayaran Di Minimarket
(Studi Kasus Minimarket X Yogyakarta)
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2149
Figure 2 Simulation of Queue 4 Cashier Using Anylogic Software
Analysis of 5 Cashiers Using the Formula Average customer arrival rate in time
units λ=22 people/hour
In this case, there is no difference in the number of customers who use 4 cashiers
or five cashiers.
Average customer service per unit of time (μ)
μ=6 Customer/Clock/Cashier
In this case, the average number of customers serviced in a unit of time is six for
one cashier and 30 for five cashiers.
Level of service facility intensity (s = many servers or cashiers, ie 5)
ρ=λ/(s.μ)
ρ=22/(5*6)=22/30 = 11/15
ρ=0,73=73%
Based on the calculation results, the level of waiter intensity or cashier activity after
adding one cashier to serving customers is 0.73 or 73%.
The probability of certainty n customers in the system or P0 is equal to an empty
cashier (P0)
P0=1-P
P0=1-0,73
P0=0,27=27%
Based on the calculation results, the time obtained after adding one cashier to the
rest of the customers is unavailable, or 0 customers (P0) is 0.27 or 27% of the busy time.
Average number of subscribers in the system (Ls)
Ls=ρ/(1-ρ)
= (11/15)/(1-11/15)
=11/15 x 15/4
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Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2150
=165/60
=2,75 orang/jam
Based on the calculation results, a system's average number of customers is 2.75
people/hour.
The average number of customers in the queue (Lq)
Lq=λ^2/(μ(μ-λ))
=22^2/(30(30-2))
=22^2/(24(2))
=484/840
=0,02 person/hour or 1.6 person/minute
Based on the calculation results, the average number of customers in the queue or
customers waiting to be served and in the queue is 0.02 people/hour or 1.6 people/minute.
Average customer time in a system (Ws)
Ws=1/(μ-λ)
=1/(30-22)
=1/8
=0,125 Hours or 7.5 Minutes
Based on the calculation results, the average time needed for customers to be in the
system is 0.125 hours or 7.5 minutes.
Average time in queue (Wq)
W_q=λ/(μ(μ-λ))
=22/(30(30-22))
=22/240
=0,09 Hours or 5,5 Menit
Based on the calculation results, the average time needed for customers to be in the
queue is 0.09 hours or 5.5 minutes.
The comparison between using four cashiers or adding one cashier to 5 cashiers can
be seen in the following table to make it easier to see.
Table 2
Comparison of Calculations with 4 Cashers and 5 Cashiers
s = 4
s = 5
22 Orang/Jam
22 Orang/Jam
24 Orang/Jam
30 Orang/Jam
92%
73%
P0
8%
27%
11 Orang/Jam
2,75 Appelsínugulur/sulta
10 Orang/Jam
0,02 Person/Hour or 1,6 Person/Hour
0.5 hours or 30 minutes
0.125 hours or 7.5 minutes
0.45 hours or 27 minutes
0.09 hours or 5.5 minutes
Analisis Dan Pemodelan Simulasi Sistem Antrian Pada Proses Pembayaran Di Minimarket
(Studi Kasus Minimarket X Yogyakarta)
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2151
Based on Table 2, the results of adding one cashier have a significant impact on
Minimarket X. Among them is the level of waiter intensity or cashier activity before
adding cashiers, which reaches 92%. At the same time, after the addition of cashiers, the
level of busyness of each cashier decreases by 19% to 73%. That way, the number of
customers in the queue, the time of customers in the queue, and the time of customers in
the system also seem significantly reduced by adding one cashier.
The calculation data on the average number of customers in the queue for four
cashiers is 11 per hour, while there are 2.75 customers per hour with five cashiers. At the
same time, the calculation results on the average customer time in a system for the use of
four cashiers are 30 minutes and 7.5 minutes. In addition, the calculation results on the
time it takes the average customer in the queue for four cashiers are 27 minutes and 5.5
minutes.
After calculating and comparing the 4 and 5 cashiers presented in the table above,
it can be said that the addition of 1 cashier in Minimarket X can speed up the customer
payment service process. In addition, using five cashiers can reduce the length of the
queues and optimise the service process for customers. Thus, it is expected to maintain
the sense of loyalty of customers who shop at Minimarket X.
Analysis of 5 Cashiers Using Anylogic Software
Data processing analysis by adding one cashier to 5 cashiers for Multi Channel-
Single Phase simulation, which was run for 120 minutes using Anylogic Software, had
the following results.
Figure 3 Simulation of Queue 5 Cashier Using Anylogic Software
Based on the picture above, the conclusions obtained are as follows.
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Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2152
1. The simulation results, which were run with five cashiers for 120 minutes, did not
experience any problems or could be considered optimal.
2. The number of customers entered during this period was 92 customers.
3. The number of customers queuing at each cashier varies between the six lowest and
the seven most customers.
4. The number of customers being served by each cashier is one customer.
5. The number of customers have finished being served and have left is 56 customers.
6. At each cashier, the number of queues long enough to meet the maximum of 12
customers was not increased.
Conclusion
Based on the results of research that the author has conducted from December 23,
2023, to January 11, 2024, with a case study at Minimarket X Yogyakarta, things that can
be concluded are:
1. To reduce the queue length, the author conducted an analysis test of data obtained
directly from the field and processed using a simulation calculation of the queuing
system. The queuing system at minimarket X is in the form of a Multi-Channel - Single
Phase with the queue model used (M/M/4) and First Come, First Served (FCFS) or
First In, First Out (FIFO). In addition to processing data using formulas for simulation,
the author also uses logic software to analyse problems in the payment system at
Minimarket X.
2. The average number of customer service in a unit of time if using four cashiers is 24
customers/hour, while with five cashiers, as many as 30 customers/hour. The
simulation results obtained using any logic software obtained error results for four
cashiers within 67 minutes and 43 seconds, while the results for five cashiers that were
run for 120 minutes did not find many problems, and there was no increase in the
number of queues at each cashier.
3. Efforts that can be made in optimising service to customers and reducing the number
of queues are to increase the number of cashiers from four to 5 cashiers. This is proven
by the analysis carried out in the level of server intensity or the level of cashier activity
before the addition of the cashier reaches 92%. At the same time, after the addition of
the cashier, the level of busyness becomes 73%. The calculation data on the average
number of customers in the queue for four cashiers is 11 per hour, while there are 2.75
customers per hour with five cashiers. At the same time, the calculation results on the
average customer time in a system for the use of 4 cashiers is for 30 minutes and five
cashiers, 7.5 minutes. In addition, the calculation results on the time it takes the
average customer in the queue for four cashiers is 27 minutes and for five cashiers 5.5
minutes.
Analisis Dan Pemodelan Simulasi Sistem Antrian Pada Proses Pembayaran Di Minimarket
(Studi Kasus Minimarket X Yogyakarta)
Jurnal Indonesia Sosial Teknologi, Vol. 5, No. 5, Mei 2024 2153
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