Title


Science and Technology Indonesia
e-ISSN:2580-4391 p-ISSN:2580-4405
Vol. 7, No. 2, April 2022

Research Paper

Facility Location Problem of Dynamic Optimal Location of Hospital Emergency
Department in Palembang
Robinson Sitepu1, Fitri Maya Puspita1*, Ide Lestari1, Indrawati1, Evi Yuliza1, Sisca Octarina1
1Mathematics Department, Faculty of Mathematics and Natural Sciences, Sriwijaya University, Palembang, 30662, Indonesia
*Corresponding author: fitrimayapuspita@unsri.ac.id

AbstractThe Emergency Department (ED) is one part of a hospital that provides initial treatment for patients who suffer from illness andinjury, which can threaten their survival. The importance of integrated care in the ED is one of the keys to successfully treatingpatients at an advanced level. This becomes complex because the ED works in a team consisting of various multi-disciplinarysciences and limited human resources, facilities, and infrastructure. In the City of Palembang, 23 hospitals have emergency roomfacilities from 18 Sub-Districts, by using the TOPSIS (Technique for Others Reference by Similarity to Ideal Solution) method tovary the distance (radius) the optimal location of the emergency department is obtained according to the number of hospitals thathave emergency room facilities, namely Ilir Timur I District, Ilir Barat I District, Sukarami District, and Plaju District. Based on theformulation of the p-median model and the completion of the TOPSIS method, the order of Districts that have optimal locationsfrom 18 Sub-Districts that have emergency department facilities in the City of Palembang is obtained.
KeywordsOptimal Location, Emergency Department, P-Median Problem, TOPSIS Method, Palembang

Received: 3 January 2022, Accepted: 14 April 2022
https://doi.org/10.26554/sti.2022.7.2.251-256

1. INTRODUCTION

The optimal location problems deal with the nding of the
optimal location of the facilities (Guzmán et al., 2016), formed
the set covering problem (SCP) (Doungpan, 2020; Octarina
et al., 2020; Zhang and Zhang, 2015). In practical situations,
it deals with the set of public facilities such as hospitals (Sitepu
etal.,2019; MohriandHaghshenas,2021),wastebinallocation
(Puspita et al., 2019), gas stations, and so on (Özceylan et al.,
2017).

Some research focused on hospital or emergency unit (Ah-
madi et al., 2017; Priyandari et al., 2011; Sadatasl et al., 2016),
explain that ED is an emergency place in which a person needs
immediate help because if he does not get immediate help, it
can threaten his life or save him permanently. In these cir-
cumstances, the role of the hospital is very important (Chen
and Yu, 2016; Memari et al., 2018). One of the these are
hospital’s supporting facilities, namely the emergency room
and the availability and the closest location to reduce the risk
of death due to the distance of the hospital location that can be
reached. Most models of SCP only deal with the ability to set
optimal facility location if the only parameter known would be
the distance between facilities and distance between facilities
and population (Sitepu et al., 2019).

Some approaches are available to solve SCP using exact
(Sitepu et al., 2019; Sitepu et al., 2018), or heuristics methods
(Yuliza et al., 2021; Avrahami and Israeli, 2013; Octarina et al.,
2020; Puspita et al., 2019). Based on research that has been
done previously by Sitepu et al. (2018) in optimizing the loca-
tion of emergency installations at health facilities in Palembang
City, this study extends the research that has been done by
designing models with a criterion of unknown radius (Bashiri
and Fotuhi, 2009), that never described before in dealing with
ED di Palembang City of the facilities to be fullled by utiliz-
ing the TOPSIS method (Olugu et al., 2021; Sürmeli et al.,
2015; Surya, 2018; Zhang et al., 2020), compared previously
described by (Sitepu et al., 2019).

The TOPSIS method (Sürmeli et al., 2015), has an advan-
tage with the ability to nd the optimal alternative where the
alternative is closest to the positive ideal solution and farthest
from the negative ideal solution. TOPSIS requires an assess-
ment of the performance of each alternative Ai on each of the
normalized Cj criteria. The TOPSIS method is used to nd
the min-max value of the radius (Amaldi et al., 2013).

Then, the research is intended to seek the possible new
parameter concerning the unknown radius of the population
involved closest to the facilities that have never been discussed

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https://doi.org/10.26554/sti.2022.7.2.251-256


Sitepu et. al. Science and Technology Indonesia, 7 (2022) 251-256

Table 1. List of Names of Sub-Districts and Hospitals That Have ED

Sub-Districts ED Facilities of Hospital

Alang-Alang Lebar Ernaldi Bahar Psychiatric Hospital
Bukit Kecil RSU Dr. AK Gani Public Hospital

Mata Public Hospital
Gandus -
Ilir Barat I Bunda Public Hospital

Siti Khodijah Public Hospital
Bunda Noni Mother and Child Hospital

Siloam Sriwijaya Public Hospital
Ilir Barat II -
Kertapati RSIA Kader Bangsa Mother and Child Hospital

Seberang Ulu I Palembang Bari Regional Public Hospital
Seberang Ulu II Muhammadiyah Public Hospital
Ilir Timur I RSIA YK Madira Mother and Child Hospital

RK Charitas Public Hospital
Sriwijaya Public Hospital

Ilir Timur II Trinanda Mother and Child Hospital
Ilir Timur III -
Kalidoni Az-zahra Mother and Child Hospital

PUSRI Public Hospital
Kemuning Muhammmad Hoesin Public Hospital

Hermina Public Hospital
Plaju Pertamina Public Hospital

Marissa Mother and Child Hospital
Sako -

Sematang Borang Karya Asih Charitas Public Hospital
Sukarami Ar-Rasyid Public Hospital

Myria Public Hospital
Jakabaring -

Source : CBS in Palembang, year 2019

before in any research dealing with SCP of ED in Palembang
City. Lastly, the contribution of the research is to extend the
research which involves the new parameter of unknown radius
to be considered in solving the optimal location of ED, so
enable the population that are closest to the facilities to have
direct access immediately.

2. EXPERIMENTAL SECTION

2.1 Method
In this research, the type of data is secondary data from google
maps in August 2021, to nd the distance (in km) between
hospitals in each Sub-District (center of the Sub-District) in
the City of Palembang which has emergency facilities. While
the method used is a descriptive model with data collection
method approach that is using the document study method.

The steps taken in conducting the research are following:
(1) Describe the data used which is the distance between the
center point of the District and the ED location.
(2) Measure the mileage from each request location to the fa-
cility location using the help of google maps.

(3) Dene the p-median variables and parameters.
(4) Dene variables and parameters for Location Set Cover-
ing Problem (LSCP), Maximal Covering Location Problem
(MCLP), and p-median.
(5) Modeling using TOPSIS method.
(6) Finding a solution from the covering-based model.
(7) Analyzing the results of the covering-based model.
(8) Interpret the results obtained.

3. RESULTS AND DISCUSSION

Based on Palembang City Health Oce in 2018, from 18 Sub-
Districts, there are 23 hospitals that have ED facilities as in
CBS (Central Bureau of Statistics) website list.

Then, assumed that: x̃i = District name, ỹi = hospital name,
h̃i = number of hospitals in each District.

Then it canbeseenfromTable1, thenotationsofeachSub-
District are for example, Alang-Alang Lebar Sub-District (x̃1),
Bukit Kecil Sub-District (x̃2), and so on until Jakabaring Sub-
District (x̃18). Then, the notations continue for RSK Ernaldi
Bahar (ỹ1), RSU Dr. AK Gani (ỹ2), and so on until RSK Myria

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Sitepu et. al. Science and Technology Indonesia, 7 (2022) 251-256

Table 2. Distance between Request Point i to Alternative ED
Location j

d ỹ1 ỹ2 ỹ3 ỹ4 ỹ5 ... ỹ23

x̃1 1.7 13 8.6 10 11 ... 8
x̃2 14 3 4.9 2.7 3.2 ... 7.6
x̃3 18 12 14 12 11 ... 17
x̃4 12 3.7 6.5 4.3 3.8 ... 7.2
x̃5 14 3.2 7.1 4.9 6.2 ... 8.3
x̃6 19 12 14 12 11 ... 15
x̃7 13 3.6 3.9 2.4 2.9 ... 5.4
x̃8 12 5.6 3.3 3.4 3.8 ... 4
x̃9 5.9 11 6.2 7.7 8.1 ... 9.7
x̃10 23 4.1 8.9 8 8.5 ... 10
x̃11 17 3.8 8.7 7.8 8.3 ... 13
x̃12 16 5.5 7.7 6.8 7.3 ... 9.1
x̃13 14 6.5 5.1 5.1 5.6 ... 5,4
x̃14 18 8.4 8.9 9 9.4 ... 12
x̃15 22 8.2 13 12 13 ... 14
x̃16 16 9.7 8.3 8.3 8.8 ... 9
x̃17 19 11 10 10 11 ... 18
x̃18 25 8.9 14 13 13 ... 15
Source : Google maps, taken in August 2021

Table 3. Determination The Notation for Alternatives and The
Weight of The Criterion

Alternative Weight

h̃1 1
h̃2 2
h̃3 0
h̃4 4
h̃5 0
h̃6 1
h̃7 1
h̃8 1
h̃9 3
h̃10 1
h̃11 0
h̃12 2
h̃13 2
h̃14 2
h̃15 0
h̃16 1
h̃17 2
h̃18 0

(ỹ23). Furthermore, for the number of hospitals in each Sub-
District will be dened as (h̃i), for example, Alang-Alang Lebar
Sub-District has 1 hospital (h̃1), Bukit Kecil Sub-District has 2
hospitals (h̃2), and so on until the Jakabaring Sub-District has

0 hospitals (h̃18) as stated in Table 1.
Table 2 displays the distance between the request point

and ED location with a distance unit of kilometers (km), it can
be seen in the distance between Alang-Alang Lebar (x̃1) to
RSK Ernaldi Bahar (ỹ1) is 1.7 km, and so on until Jakabaring
(x̃18), (Myria Hospital) (ỹ23) is 15 km. To reduce the average
distance between the point of request and the point of ED
location, the p-median problem model is used, namely:

Zp-median = max
18∑︁
i=1

32∑︁
j=1

h̃id̃i jx̃i j (1)

Subject to

x̃1,1 + x̃1,2 + x̃1,3 + x̃1,4 + x̃1,5 + · · · + x̃18,23 = 1 (2)

ỹ1 + ỹ2 + · · · + ỹ23 = 4 (3)

x̃i1 + x̃i2 + x̃i3 + · · · + x̃i21 + x̃i22 + x̃i23 ≤ ỹj (4)

Based on the p-median model in determining the opti-
mal location of the emergency department with the highest
number of emergency installations completed in 4 Districts.
Furthermore, to nd the optimal location of the hospital by
using a radius to minimize the total allocation cost that does
not depend on the distance between the points, namely:

min max
18∑︁
i=1

32∑︁
j=1

h̃id̃i jx̃i j (5)

So:

min
©­«max

©­«
m∑︁
i=1

n∑︁
j=1

(x̃1,1 + x̃1,2 + x̃1,3 + ... + x̃2,1 + x̃2,2 + x̃2,3 + ... + x̃23)d̃i j
ª®¬
ª®¬ (6)

Using the min-max approach to assign service points so
that each customer should not travel too far to the service
point under consideration to nd the value of min-max using
the TOPSIS method. The optimal alternative solution in the
TOPSIS method will be the one that is closest to the positive
ideal solutionandfarthestawayfromthenegative ideal solution.
TOPSIS requires a performance rating of each alternative Ai
on each normalized Cj criterion, the steps of the TOPSIS
method:
a. Determine alternatives and criteria and their weights, where
alternatives (x̃i) Sub-District, namely Alang-Alang Lebar Sub-
District (x1), Bukit Kecil Sub-District (x̃2), and so on until
Jakabaring Sub-District (x̃18). For weight namely the number
of each hospital in each Sub-District, and for criterion (C)

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Sitepu et. al. Science and Technology Indonesia, 7 (2022) 251-256

Table 4. Determination The Normalized Decision Matrix

d C̃1 C̃2 C̃3 ... C̃23

x̃1 0.101025071 0.376677119 0.222016265 ... 0.168778249
x̃2 0.199204365 0.086925489 0.12649764 ... 0.160339337
x̃3 0.256119898 0.347701956 0.361421827 ... 0.35865378
x̃4 0.170746598 0.107208103 0.167802991 ... 0.151900424
x̃5 0.199204365 0.092720522 0.183292498 ... 0.175107434
x̃6 0.270348781 0.347701956 0.361421827 ... 0.175107434
x̃7 0.184975482 0.104310587 0.100681795 ... 0.316459218
...

...
...

... ...
...

x̃8 0.35572208 0.257878951 0.100681795 ... 0.316459218

Table 5. Weighted Normalized Matrix

d C̃1 C̃2 C̃3 ... C̃23

x̃1 0.101025071 0.376677119 0.222016265 ... 0.236403463
x̃2 0.39840873 0.173850978 0.252995279 ... 0.270175387
x̃3 0 0 0 ... 0
x̃4 0.682986392 0.428832412 0.671211965 ... 0.154385935
x̃5 0 0 0 ... 0
x̃6 0.184975482 0.347701956 0.361421827 ... 0.221929782
x̃7 0.170746598 0.104310587 0.100681795 ... 0.127850853
...

...
...

... ...
...

x̃8 0 0 0 ... 0

where C is the same as the hospital (yi = Cj), as stated in Table
2.

b. Create a normalized decision matrix, by doubling each
distance (ỹ1)2 on (x̃1) then adding up to (ỹ1)2 on (x̃2) until
(ỹ1)2 on (x̃18) then each entry distance (ỹ1) is divided by the
result summation above. Do the same for (ỹ23) to (x̃18) as
explained in Table 3.

c. Create a weighted normalized decision matrix, by mul-
tiplying each entry of the decision matrix is normalized with
each weight as Table 4 explained.

d. Determine the positive and negative ideal solution matri-
ces, by grouping the values of the normalized decision matrix
weighted in each column into two parts, namely positive (for
the value of largest) and negative (for the smallest value) as
Table 5 explained.

e. Determine the distance between the value of each al-
ternative and the ideal solution matrix positive and the ideal
solution matrix is negative. For the positive in a way subtract
each column of a positive matrix with entries in row (ỹ1) to
(ỹ23), then rooted. While for negative subtract each row (ỹ1) to
(ỹ23) to each entry in the negative matrix, as stated in Table 6.

f. Calculates the preference value foreach alternative. With

do
x̃−1

x̃−1 + x̃
+
1
it up to x̃18. Then sort from the most optimal to

the least optimal value, so that the most optimal location is

Table 6. Matrix of Positive Ideal Solution and Negative Ideal
Solution

Criteria Positive Negative

C̃1 0.682986392 0
C̃2 0.956390379 0
C̃3 0.671211965 0
C̃4 0.647086749 0
C̃5 0.657677381 0
C̃6 0.796052478 0
C̃7 0.706258955 0
C̃8 1.031308491 0
C̃9 1.206837006 0
C̃10 1.205411197 0
...

...
...

C̃23 0.75950212 0

obtained to the non-optimal location. Then we get x̃9 as the
most optimal location where (x̃9) Ilir Timur I District as stated
in Table 7.

From Table 8, it can be seen that the largest preference
value is located in (x̃9), so (x̃9) as the most optimal location
where (x̃9) Ilir Timur I Sub-District, namely RSIA YK Madira,

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Sitepu et. al. Science and Technology Indonesia, 7 (2022) 251-256

Table 7. The Dierence in Values Between Each Hospital Op-
tion and The Positive and Negative Ideal Solution Matrix

D+ Value D− Value

x̃1 2.953477 x̃1 1.550049
x̃2 3.207706 x̃2 1.364829
x̃3 4.381804 x̃3 0
x̃4 1.765836 x̃4 3.306415
x̃5 4.381804 x̃5 0
x̃6 3.028842 x̃6 1.515281
x̃7 3.892671 x̃7 0.557388
x̃8 3.763845 x̃8 0.667304
x̃9 0.761096 x̃9 4.229952
x̃10 3.686918 x̃10 0.902231
x̃11 4.381804 x̃11 0
x̃12 3.064979 x̃12 1.593795
x̃13 3.321605 x̃13 1.395468
x̃14 2.621008 x̃14 2.171972
x̃15 4.381804 x̃15 0
x̃16 3.386626 x̃16 1.116394
x̃17 1.824748 x̃17 3.008616
x̃18 4.381804 x̃18 0

Table 8. Preference and Rank Values for Each Alternative

Alternative Preference Rank

x̃1 0.344186 6
x̃2 0.298484 8
x̃3 0 14
x̃4 0.651863 2
x̃5 0 16
x̃6 0.33346 7
x̃7 0.125254 13
x̃8 0.150594 12
x̃9 0.847508 1
x̃10 0.196601 11
x̃11 0 16
x̃12 0.342106 5
x̃13 0.295833 9
x̃14 0.453157 4
x̃15 0 17
x̃16 0.247921 10
x̃17 0.622468 3
x̃18 0 18

RSU RK Charitas, and RSU Srivijaya. Figure 1 explains the
locations of the facilities obtained.

By applying the TOPSIS method in determining the loca-
tion of the hospital that has ER facilities in the City of Palem-
bang, it is obtained that the location of the ER in the Sub-
District are listed as follows: Ilir Timur I, Ilir Barat I, Sukarami,
Plaju, Kalidoni, Alang-Alang Lebar, Kertapati, Bukit kecil, Ke-

Figure 1. Map of Palembang and Sub-Districts

Source: Palembang Government, 2022

muning, Sematang Borang, Ilir Timur II, Sebrang Ulu II, Se-
brang Ulu I, Gandus, Ilir Barat II, Ilir Timur III, Sako, and
Jakabaring Sub-District.

Based on Figure 1, there are 4 Sub-Districts have hospi-
tals with the most optimal emergency facilities in the City of
Palembang, namely Ilir Timur I Sub-District, Ilir Barat I Sub-
District, Sukarami Sub-District, and Plaju Sub-District.

4. CONCLUSION

Based on the research, the optimal location of the hospital that
has emergency facilities in the City of Palembang is located in
the Ilir Timur I Sub-District. The setting up of the location
of the facilities enable population closest to the ED to reach
the facilities as soon as possible. The reduction the risk of
death that often occurs due to the distance from the location
of hospitals that have emergency facilities can be achieved.

Forfurtherresearch, it is suggestedtoalso includesomenew
parameters involved in designing the model of SCP in ED in
Palembang to also include the possibility of recent conditions
occurring in practical conditions. Such as how to reach the
facilities, the number of doctors involved in the hospital, or
possibilities of transportation means existed.

5. ACKNOWLEDGEMENT

On November23, 2020, DIPAof the Public Service Agencyof
Sriwijaya University 2021, SP DIPA-023.17.2.677515 /2021,
supported the publishing of this article. On April 28, 2021, the
Rector’s Decree Number: 0010/ UN9/ SK.LP2M.PT/2021
was issued.

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© 2022 The Authors. Page 256 of 256


	INTRODUCTION
	EXPERIMENTAL SECTION
	Method

	RESULTS AND DISCUSSION
	CONCLUSION
	ACKNOWLEDGEMENT