A Mixed-Integer Linear Programming Model for Repeaters and Routers
Location-Allocation Problem in Open-Pit Mines
J
´
essica Cristina Teixeira da Costa
1 a
, Arthur Francisco Emanuel Borges Pereira
3
,
Higor Cassiano Sousa Milan
ˆ
es
3
, Tatianna Aparecida Pereira Beneteli
2 b
and Luciano Perdig
˜
ao Cota
2 c
1
Programa de P
´
os-Graduac¸
˜
ao em Instrumentac¸
˜
ao, Controle e Automac¸
˜
ao de Processos de Minerac¸
˜
ao,
Universidade Federal de Ouro Preto e Instituto Tecnol
´
ogico Vale, Ouro Preto, Brazil
2
Instituto Tecnol
´
ogico Vale, Ouro Preto, Brazil
3
Vale S.A., Parauapebas, Brazil
Keywords:
Mixed-Integer Linear Programming, Open-Pit Mines, P-Median, Repeaters and Routers Location-Allocation.
Abstract:
In open-pit mines, communication network coverage is required throughout the operating area to ensure con-
tinuous operation of equipment such as drills, trucks, shovels, and loaders, in addition to communication be-
tween teams. Although the location-allocation problems have been widely studied in various contexts, there is
a significant gap in its application to open-pit mines. This study proposes a Mixed-integer linear programming
formulation based on the p-median problem to optimize the location-allocation of repeaters and routers. The
objective is to minimize the number of network equipment installed and reduce distances between operating
points and network equipment, increasing efficiency and coverage in mining environments. We use nine large
instances to validate the mathematical formulation. These instances vary the number of candidate locations for
installation and operation points, reflecting scenarios from large open-pit mines. The results demonstrate that
the proposed method can find optimal solutions with low computational time, less than 5 minutes, ensuring
efficient coverage of the operation area.
1 INTRODUCTION
In open-pit mining environments, large-scale opera-
tions rely on a stable network to ensure the operation
of equipment such as drills, trucks, and shovels. The
lack of a reliable infrastructure can compromise the
continuity of activities, generate operational failures,
and increase risks to worker safety. In addition, con-
stant communication between teams is essential for
effective coordination of tasks and a rapid response to
emergencies.
Currently, the location of repeaters and routers
in mining environments is performed empirically
through on-site testing. However, this manual ap-
proach has significant limitations, mainly due to the
variation of operating points over time and the mo-
bile nature of the facilities, which makes adjusting the
a
https://orcid.org/0009-0003-0759-8201
b
https://orcid.org/0000-0001-6419-0286
c
https://orcid.org/0000-0002-8385-7573
location of devices time-consuming and often ineffi-
cient. In addition, the vast extension of the areas and
the presence of physical barriers make it even more
challenging to achieve adequate network coverage,
resulting in operational failures that can compromise
system performance and increase the risk of mining
activities.
To mitigate these issues, adopting an efficient pro-
cess to determine the optimal locations of repeaters
and routers is necessary, ensuring continuous net-
work coverage throughout the mining environment.
The application of combinatorial optimization meth-
ods, such as the p-median problem, presents itself as
a promising solution to strategically define the posi-
tions of these devices, maximizing coverage and min-
imizing costs.
P-median is a classical location problem, which
aims to find the optimal location of p facilities (Chap-
pidi and Singh, 2023). This problem belongs to the
NP-hard class (Liotta et al., 2005). In essence, this
problem seeks the efficient distribution of resources to
724
Costa, J. C. T., Pereira, A. F. E. B., Milanês, H. C. S., Beneteli, T. A. P. and Cota, L. P.
A Mixed-Integer Linear Programming Model for Repeaters and Routers Location-Allocation Problem in Open-Pit Mines.
DOI: 10.5220/0013221700003929
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 27th International Conference on Enterprise Information Systems (ICEIS 2025) - Volume 1, pages 724-731
ISBN: 978-989-758-749-8; ISSN: 2184-4992
Proceedings Copyright © 2025 by SCITEPRESS – Science and Technology Publications, Lda.

optimize demand fulfillment, being widely applied in
contexts such as logistics, infrastructure, urban plan-
ning, health, and education.
Although the p-median problem has been widely
studied in various contexts, there is a significant gap
in its application to mining environments, especially
in open-pit mines, where only some studies address
router location problems. Recently, in Mandarino et
al. (Mandarino et al., 2024), the authors addressed the
router location-allocation problem (RLP) in open-pit
mines, in which they proposed a mixed-integer linear
programming (MILP) formulation to represent it. In
this work, the focus is on mines that use only routers
to implement the communication network. However,
it was identified that larger mines need to use re-
peaters in conjunction with routers to ensure network
coverage throughout the territory. Basically, repeaters
receive the signal generated by routers and amplify
it, allowing the network to reach a larger area than
would be possible without using these devices. Due
to the lower cost and less operation complexity, re-
peaters are a good alternative to guarantee coverage in
large areas, especially in large open-pit mines where a
single router cannot guarantee complete connectivity.
Including repeaters imposes new constraints, such as
requiring each repeater to be within the coverage ra-
dius of at least one router.
Thus, this work proposes an extension of the study
of Mandarino et al. (Mandarino et al., 2024), with a
new MILP formulation to optimize the variant of the
problem with repeaters, called repeaters and routers
location-allocation problem (RRLP). This problem
seeks to minimize the number of installed devices and
reduce the distances between the operating points and
the network equipment, providing greater efficiency
and coverage in open-pit mining environments.
The paper is organized into several sections that
explore different aspects of the study. Section 2
presents a literature review about the repeaters and
routers location-allocation problem. In Section 3,
the location-allocation problem is described in detail,
along with the definition of the parameters used in
the MILP formulation. Section 4 discusses the pro-
posed mathematical formulation, presenting the vari-
ables, constraints, and the objective function. Then,
Section 5 examines the results of the computational
experiments, and finally, Section 6 shows the conclu-
sions and proposals for future research.
2 LITERATURE REVIEW
The strategic decision of facility location is crucial for
both private companies and public organizations. In
the public sector, this includes the selection of loca-
tions for essential services, such as healthcare centers,
schools, and fire stations. In the private sector, loca-
tion decisions pertain to productive facilities such as
factories, warehouses, and distribution centers (Are-
nales et al., 2007).
Various approaches and algorithms have been ap-
plied to solve location problems across different sec-
tors, such as healthcare, public safety, transportation,
logistics, education, and electrical energy.
In the mining field, Lotfian and Najafi (Lotfian
and Najafi, 2019) presented a solution to determine
the optimal location of emergency facilities in under-
ground mines based on a case study of a coal mine in
Tabas, Iran.
From another perspective, Oyola-Cervantes and
Amaya-Mier (Oyola-Cervantes and Amaya-Mier,
2019) proposed the design of a reverse logistics net-
work for off-the-road tires discarded by the mining
sector.
In the context of open-pit mining, Paricheh and
Osanloo (Paricheh and Osanloo, 2016) investigated a
case study of a copper mine in Iran. The study aims
to determine the optimal location of in-pit crushers in
open-pit mining operations.
The repeaters and routers location-allocation
problem is often addressed using p-median problems.
These problems seek to identify the optimal location
of p facilities to minimize distances or travel times
between these facilities and demand points.
P-median problems have been applied in a wide
variety of contexts, such as in the location of vaccina-
tion centers (Zapata et al., 2023) and public schools
(Nascimento et al., 2023). Furthermore, several stud-
ies explore combining heuristic methods or hybrid ap-
proaches to solve complex problems, such as those
investigated in Silva and Mestria (Silva and Mestria,
2018) and Pinto et al. (Pinto et al., 2023), which ex-
amined the use of metaheuristics combined with the
p-median problem.
In addition to traditional location problems, op-
timizing connectivity in complex environments de-
pends on advanced technological solutions such as
mesh networks. Mesh networks are an advanced, self-
configuring, and self-organizing wireless connection
technology, offering advantages such as low initial
cost, easy maintenance, robustness, and reliable cov-
erage. (Akyildiz et al., 2005; Qian et al., 2023).
The use of routers in mesh networks has been
widely studied in the literature. In particular, opti-
mization algorithms to determine these routers’ ideal
location and distribution have proven highly effective
in various contexts. Codato and Souza (Codato and
de Souza, 2021) applied the Maximum Coverage Lo-
A Mixed-Integer Linear Programming Model for Repeaters and Routers Location-Allocation Problem in Open-Pit Mines
725

cation Problem to the location-allocation of wireless
network access points at the Federal Institute of Edu-
cation, Science, and Technology of S
˜
ao Paulo, aiming
to find the optimal positions for the access points and
the maximum coverage of areas of interest.
Jansang et al. (Jansang et al., 2023) proposed an
optimization mechanism based on MILP for the lo-
cation of energy-aware wireless mesh routers. The
objective is to determine the appropriate location of
mesh routers and maximize network lifetime.
Wang et al. (Wang et al., 2017) proposed a
method based on the p-median problem combined
with heuristic methods to determine the location of
nodes in a mesh network in an industrial context.
Oda (Oda, 2023), in turn, presented a solution
for the location of mesh routers in evacuation cen-
ters, considering a disaster scenario in the city of
Kurashiki, Japan. The objective is to maximize net-
work connectivity and client coverage.
In the mining context, various approaches have
been developed to optimize the placement of routers
in mesh networks. Mandarino et al. (Mandarino
et al., 2024) presented a recent approach to allocat-
ing telecommunications devices in open-pit mines. In
a case study for the F
´
abrica Nova mine in Mariana-
MG, the p-median problem was used to minimize the
number of installed routers, ensuring necessary cov-
erage and reducing costs. However, this study only
considered the router location-allocation problem.
Although numerous studies focus on facility lo-
cation in several contexts, were not found specific
research addresses the simultaneous repeaters and
routers location-allocation problem for open-pit min-
ing applications. Including repeaters in the p-median
problem formulation, especially in this context, rep-
resents a highly relevant and unexplored contribution
to the literature. This approach will optimize net-
work coverage and improve communication robust-
ness and efficiency in challenging environments like
large-scale open-pit mines. This methodology can re-
duce operational costs, increase safety, and improve
operational efficiency when applied to open-pit min-
ing projects.
2.1 Comparison of Our Proposal with
the Reviewed Papers
Table 1 provides a comparative view of the main char-
acteristics of our proposal with the studies reviewed
in the literature. The works are listed chronologically
in the first column, from the oldest to the most recent
publications. The subsequent columns (2 to 7) present
the objective functions addressed in each study, col-
umn 8 identifies the application sector, and column 9
specifies the location-allocation facilities. Finally, the
last three columns detail the solution methods applied
in each work, classified as exact, heuristic, or hybrid.
Thus, the main differentiation of our proposal is
the inclusion of repeaters in the localization problem,
aiming to minimize two facilities simultaneously. In
addition, little research focuses on the location of
routers or repeaters in open-pit mining applications,
highlighting the need for new studies in this context.
3 PROBLEM STATEMENT
This section presents the characteristics of the
repeaters and routers location-allocation problem
(RRLP) in open-mines, as follows:
1. An open-pit mining iron ore complex is formed
by a set of mines (M );
2. Each mine k ∈ M is formed by a set of mining
fronts (F );
3. Each mining front z ∈ F has a set of operation
areas (A):
(a) Each operation area a ∈ A indicates a polygon
of the mining front z ∈ F that is in operation;
(b) In each area of operation a ∈ A, a set of min-
ing equipment needs connectivity to perform its
activities adequately. The set of mining equip-
ment consists of drills, trucks, cargo equipment
(loaders and shovels), infrastructure and sup-
port equipment;
(c) Each operation area a ∈ A is represented by a
set of J extreme points, or operation points;
(d) Each operation point j ∈ J has a location l p
j
;
(e) Each operation point j ∈ J needs to be serviced
by one or more network equipment r ∈ E.
4. A communication network is composed of a set of
network equipment (E):
(a) The set of network equipment (E ) has a subset
of routers R and a subset of repeaters T , which
means that E = R ∪ T .
5. Set of routers (R ):
(a) Each router installed has a location LR
i
∈ I ;
(b) Routers have a coverage radius identified as
RR;
(c) PR
max
indicates the maximum number of
routers installed.
6. Set of Repeaters (T ):
(a) Each installed repeater has a location LT
i
∈ I ;
(b) Repeaters have a coverage radius identified as
RT ;
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Table 1: Summarizing the main characteristics of our proposal in comparison with the reviewed studies.
Works
Objective Functions
Application Facility
Solution Methods
[1] [2] [3] [4] [5] [6] Exact Heuristic Hybrid
Paricheh and Osanloo (2016) ✓ ✓ open-pit mining in-pit crusher ✓
Wang et al. (2017) ✓ ✓ industry routers ✓ ✓
Silva and Mestria (2018) ✓ - service stations ✓
Lotfian and Najafi (2019) ✓ ✓ ✓ underground mining emergency stations ✓
Oyola-Cervantes and Amaya-Mier (2019) ✓ open-pit mining power generation plant ✓
Codato and de Souza (2021) ✓ education routers ✓
Nascimento et al. (2023) ✓ ✓ education municipal public schools ✓
Jansang et al. (2023) ✓ rural area routers ✓
Oda (2023) ✓ evacuation center routers ✓
Yang et al. (2023) ✓ ✓ electrical energy power stations ✓
Zapata et al. (2023) ✓ healthcare vaccination center ✓
Pinto et al. (2023) ✓ transportation hubs ✓
Mandarino et al. (2024) ✓ ✓ open-pit mining routers ✓
Our Proposal ✓ ✓ open-pit mining repeaters and routers ✓
Legend: [1]: Minimize distance; [2]: Minimize one facility; [3]: Minimize two facilities; [4]: Minimize costs;
[5]: Minimize losses or Maximize profit; [6]: Others.
(c) Each repeater t ∈ T must be directly connected
to a router r ∈ R ;
(d) PT
max
indicates the maximum number of re-
peaters installed.
7. There is a set of candidate locations for network
equipment installation (I ):
(a) Each place i ∈ I has a location l
i
.
The objective of this problem is to install repeaters
t ∈ T and routers r ∈ R to meet all operation points
j ∈ J , seeking to minimize the number of network
equipment installed (r and t) and the sum of the dis-
tances between the operating points and the installed
network equipment.
Figure 1 presents a didactic example to facilitate
understanding of the RRLP. The scenario includes
an operating area bounded by four operation points
j = {J1, J2, J3, J4}, both shown in green. Eight can-
didate locations for installing network equipment i =
{i1, i2, ·· · , i8} are considered, indicated in red. In ad-
dition, the routers have a coverage radius of 140 me-
ters and repeaters 80 meters, allowing the installation
of one router and up to four repeaters.
I1 I2 I3 I4 I5 I6 I7 I8
J1
J2
J3
J4
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
0 40 80 120 160 200 240 280 320 360 400
Figure 1: Mapping of operating points (J) and candidate
locations for installation (I) for the didactic example.
Table 2 shows the Cartesian coordinates (X and
Y) of the candidate locations for installing network
equipment.
Table 2: Candidate locations for installing (I).
Points
Location
X Y
I1 40 140
I2 80 140
I3 120 140
I4 160 140
I5 200 140
I6 240 140
I7 280 140
I8 320 140
Table 3 details the operation points that define the
area that the network must meet.
Table 3: Operating points (J).
Points
Location
X Y
J1 20 160
J2 220 220
J3 200 60
J4 380 140
Table 4 displays the matrix of distances between
the operating points and the locations that are candi-
dates for installing network equipment.
Table 4: Distance matrix.
J1 J2 J3 J4
I1 28.3 197.0 178.9 340.0
I2 63.2 161.2 144.2 300.0
I3 102.0 128.1 113.1 260.0
I4 141.4 100.0 89.4 220.0
I5 181.1 82.5 80.0 180.0
I6 220.9 82.5 89.4 140.0
I7
260.8 100.0 113.1 100.0
I8 300.7 128.1 144.2 60.0
Table 5 also presents the distance matrix between
all pairs of candidate locations for installing network
equipment.
Figure 2 illustrates a possible solution for this di-
dactic example. In this configuration, the router was
A Mixed-Integer Linear Programming Model for Repeaters and Routers Location-Allocation Problem in Open-Pit Mines
727

Table 5: Equipment distance matrix.
I1 I2 I3 I4 I5 I6 I7 I8
I1 0 40 80 120 160 200 240 280
I2 40 0 40 80 120 160 200 240
I3 80 40 0 40 80 120 160 200
I4 120 80 40 0 40 80 120 160
I5 160 120 80 40 0 40 80 120
I6 200 160 120 80 40 0 40 80
I7 240 200 160 120 80 40 0 40
I8 280 240 200 160 120 80 40 0
allocated at point I5, shown in red, while the repeaters
were installed at points I2 and I8, shown in blue, en-
suring coverage of all operating points. In addition, it
is noteworthy that the repeaters installed in I2 and I8
are within the coverage radius of the router installed
in I5, as delimited by one of the problem’s constraints.
J1
J2
J3
J4
I5I2 I8
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
0 40 80 120 160 200 240 280 320 360 400
Figure 2: Possible solution for the didactic example.
4 MILP FORMULATION
This section presents the proposed MILP formulation
to represent the RRLP. The input sets, indices, param-
eters, and decision variables are described below.
• Sets:
A : set of the areas of operation;
R : set of routers;
T : set of repeaters;
E : set of network equipment (E = R ∪T );
J : set of operation points that must be met;
I : set of candidate locations for installing net-
work equipment.
• Indexes:
j : index for a element of the set J ;
i, a, k : index for a element of the set I .
• Parameters:
D
i j
: distance from the operating point j to the can-
didate location i for installation of a network
equipment;
DE
ki
: distance between all pairs k and i of candi-
date locations for the installation of a network
equipment;
PR
max
: maximum number of routers that can be in-
stalled;
PT
max
: maximum number of repeaters that can be in-
stalled;
RR : coverage radius of each router;
RT : coverage radius of each repeater.
• Decision variables:
pr : number of routers installed;
pt : number of repeaters installed;
x
i j
:





1, if the operating point j is attended by
the network equipment installed in i;
0, otherwise;
yr
a
:
(
1, if the router is installed at location a;
0, otherwise;
yt
k
:
(
1, if the repeater is installed at location k;
0, otherwise;
The objective function of the proposed formula-
tion is composed of two parcels. The first parcel min-
imizes the number of open installations, that is, the
number of network equipment installed. The second
parcel minimizes the sum of the distances between
the operating points and the installed network equip-
ment. The Equations (1) to (3) represent the objective
function.
minα

σ
pr
|R |
+ φ
pt
|T |

+ β

∑
i∈I
∑
j∈J
d
i j
x
i j
|J | max(RR, RT )

(1)
α + β = 1 (2)
where α indicates the weight of the first parcel and β
indicates the weight of the second parcel of the objec-
tive function.
σ + φ = 1 (3)
where σ indicates the weight in the objective function
of router installation and φ indicates the weight of re-
peater installation.
The constraints (4) ensure that all operating points
are within the coverage radius of installed network
equipment.
D
i j
x
i j
≤ RR yr
i
+ RT yt
i
∀i ∈ I , ∀ j ∈ J (4)
The constraints (5) ensures that each operating
point is attended by at least one network equipment.
ICEIS 2025 - 27th International Conference on Enterprise Information Systems
728

This way, we allow coverage redundancy, increasing
the network reliability.
∑
i∈I
x
i j
≥ 1 ∀ j ∈ J (5)
The constraints (6) defines that each operating
point can only be attended by a location where it has
a repeater (yt
i
= 1) or a router (yr
i
= 1) installed.
x
i j
≤ yr
i
+ yt
i
∀i ∈ I , ∀ j ∈ J (6)
The constraints (7) ensures that in each candidate
location can be installed at most one network equip-
ment, a repeater (yt
i
= 1) or a router (yr
i
= 1).
yr
i
+ yt
i
≤ 1 ∀i ∈ I (7)
The constraint (8) determines the number of
routers installed, while the constraint (9) defines that
the number of routers installed must be less than
the number of available routers PR
max
. The con-
straint (10) ensures that at least one router will be in-
stalled.
∑
a∈I
yr
a
= pr (8)
pr ≤ PR
max
(9)
pr ≥ 1 (10)
Similarly, the constraint (11) determines the num-
ber of repeaters installed, while the constraint (12) de-
fines that the number of installed repeaters must be
less than the number of available repeaters PT
max
.
∑
k∈I
yt
k
= pt (11)
pt ≤ PT
max
(12)
The constraints (13) ensure that the repeater in-
stalled in k is within the coverage radius of a router
installed in a. The term (M × (1 − yr
a
)) ensures that
this equation is only valid if there is a router installed
on a. Otherwise, the Big M will be activated, and the
equation will be respected.
DE
ka
yt
k
≤ RRyr
a
+ (M × (1 − yr
a
))
∀k, a ∈ I (13)
Finally, the Equations (14), (15) and (17) define
the domain of the variables.
x
i j
∈ {0, 1} ∀i ∈ I , ∀ j ∈ J (14)
yr
a
∈ {0, 1} ∀a ∈ I (15)
yt
k
∈ {0, 1} ∀k ∈ I (16)
α, β, σ, φ ≥ 0 (17)
5 COMPUTATIONS
EXPERIMENTS
We implement the proposed MILP formulation in
Lingo 10.0, version 4.01.100. The computational ex-
periments were conducted on a computer with an 11th
Gen Intel(R) Core(TM) i5-1135G7 CPU @ 2.40GHz,
8.0 GB of RAM, and the Windows 11 Pro operating
system.
To evaluate the proposed method, we used nine
instances varying the number of candidate locations
for installing network equipment and the number of
operating points.
5.1 Instances
Table 6 presents the data of the instances used in de-
tail. Column one shows the number of instances,
while columns two and three show, respectively, the
number of candidate locations for network equipment
installation and the number of operating points. Fi-
nally, columns four and five show the maximum num-
ber of repeaters and routers available for installation
in each experiment. In these scenarios, the number of
routers was restricted to one unit due to the higher cost
and complexity of operation compared to repeaters.
Table 6: Characteristics of the instances.
Instances
#Installation
Points
#Operating
Points
#Max
Repeaters
#Max
Routers
1 150 20 10 1
2 300 20 10 1
3 450 20 10 1
4 150 35 10 1
5 300 35 10 1
6 450 35 10 1
7 150 50 10 1
8 300 50 10 1
9 450 50 10 1
In all the experiments performed, we adopted the
coverage radius of the repeaters as 120 meters and the
routers as 140 meters.
To illustrate the set of instances, we detailed the
largest them (Instance 9). This instance has 450 can-
didate locations for the installation of network equip-
ment and 50 operating points. The mapping of the op-
eration points and the candidate locations for installa-
tion of the network equipment are shown in Figure 3.
In this scenario, five operation areas were delimited,
each with 10 points of operation, totaling 50 points
j = {J1, J2, J3, . . . , J50}, highlighted in green. Ad-
ditionally, this instance has 450 candidate locations
for the installation of network equipment, identified
as i = {I1, I2, . . . , I450} and highlighted in red.
A Mixed-Integer Linear Programming Model for Repeaters and Routers Location-Allocation Problem in Open-Pit Mines
729

0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300 350 400 450
Figure 3: Mapping of operating points (green) and candi-
date locations for installation (red) for the Instance 9.
A distance matrix, nxm, and an equipment dis-
tance matrix, mxm, were generated for each in-
stance, where n represents the number of oper-
ating points and m indicates the number of can-
didate locations for installation. All instances
are available at https://github.com/tatiannabeneteli/
ICEIS2025/blob/main/Instances.zip.
5.2 Results
Table 7 summarizes the results. Column one shows
the instance, while column two shows the best bound
value. Columns three and four indicate the number
of repeaters and routers installed in the found solu-
tion. Finally, columns five and six report the GAP
and execution time in seconds for each instance. The
weights adopted for the objective function parcels
were: α = 0.5, β = 0.5, σ = 0.1, and φ = 0.9.
Table 7: Results for instances.
Instances
Best
Bound
Repeaters
Installed
Routers
Installed
GAP
Execution
Time (s)
1 0.31047 2 1 0 2
2 0.31008 2 1 0 14
3 0.31008 2 1 0 56
4 0.41486 3 1 0 8
5 0.41486 3 1 0 84
6 0.41345 3 1 0 458
7 0.46351 4 1 0 13
8 0.46351 4 1 0 111
9 0.46291 4 1 0 381
In all instances, the solver found the optimal solu-
tion (GAP = 0) in low computational time, less than
five minutes.
We chose Instance 9, which was detailed in the
previous section, to analyze the results. Figure 4
presents the optimal solution found by the solver for
this instance. In this solution, the router was allocated
to point I224, highlighted in red, while the repeaters
were positioned at points I115, I133, I315, and I333,
indicated in blue. Thus, the solution of this instance
requires one router and four repeaters to ensure cov-
erage of all operating points. The best objective func-
tion found was 0.46291 and the computational time
was 381 seconds.
Ponto
Limites
Rot1
Limites
I224
I115 I133
I315 I333
0
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250 300 350 400 450
Figure 4: Optimal solution for the Instance 9.
These results demonstrate the feasibility of the
proposed mathematical modeling to determine the op-
timal location-allocation of repeaters and routers in
open-pit mines, ensuring an efficient coverage even
in large-scale scenarios.
6 CONCLUSIONS
This study explores a new variant of the p-median
problem, the repeaters and routers location-allocation
problem in open pit mines. We proposed a MILP for-
mulation to minimize the number of network equip-
ment installed and the distances between operating
points and network equipment. The proposed for-
mulation was tested in nine instances, using differ-
ent combinations of operation points and candidates
location for installation. The results demonstrate the
solver’s effectiveness in finding optimal global solu-
tions with low computational times in all instances.
These results reinforce that the proposed model is a
strategic tool to support decisions, enabling a network
infrastructure capable of covering the entire area of
operation of large open-pit mines. Additionally, the
proposed model can be adapted to other industrial
sectors, reinforcing its applicability in large-scale op-
erations and under diverse operational conditions. In
future work, we intend to adapt the proposed model to
other industrial environments, such as ports and rail-
ways. We also suggest to explore other optimization
approaches, such as using metaheuristics to solve this
problem.
ICEIS 2025 - 27th International Conference on Enterprise Information Systems
730

ACKNOWLEDGEMENTS
The authors are grateful for the support provided
by Vale S.A, Instituto Tecnol
´
ogico Vale, Univer-
sidade Federal de Ouro Preto, Coordenac¸
˜
ao de
Aperfeic¸oamento de Pessoal de N
´
ıvel Superior
(CAPES, Finance Code 001), and Conselho Nacional
de Desenvolvimento Cient
´
ıfico e Tecnol
´
ogico (CNPq,
grant 302629/2023-8).
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