A Decision Support System Based on a Mixed-Integer Linear

Programming Model for Location of Routers in Open-Pit Mines

Matheus Ferreira Mandarino

1 a

, Tatianna Aparecida Pereira Beneteli

2 b

and Luciano Perdig

ao Cota

2 c

Vale S.A., Mariana, Brazil

Instituto Tecnol

ogico Vale, Ouro Preto, Brazil

Keywords:

Location of Routers, Mesh Networks, p-median, Open-Pit Mines.

Abstract:

In open-pit mines, it is very important to ensure network coverage for equipment in operation, which is located

in large areas. It should be noted that some of this equipment, such as trucks and drills, is autonomous;

therefore, access to the network is essential. This work presents a mathematical model for solving it based

on the p-median problem. The objective is to determine the location of the routers, minimizing the number

of routers and the sum of the distances between the operating points and the installed routers. We use real

data from the F

abrica Nova mine in Brazil to validate the mathematical model. The scenarios represent the

mining planning for 2023, 2024, and 2025. The results showed that the proposed model found the optimal

router location in a few seconds, providing more efﬁcient coverage for mining equipment using fewer routers.

1 INTRODUCTION

Open-pit mining is an activity that requires the use of

various high-tech equipment to ensure the safety and

productivity of the operation. One of the main chal-

lenges mining companies face is ensuring equipment

connectivity since the operation occurs in remote ar-

eas and often with limited access to communication

networks. One solution to this problem is the use of

mesh networks.

The mesh network is a wireless communication

technology that stands out for its ability to increase

network coverage and efﬁciency, offering more excel-

lent stability and security (Taleb et al., 2022). This

technology is an evolution of traditional networks,

which use a single access point, such as a router, to

connect to several devices. With the mesh network,

devices connect, forming a communication mesh,

which allows the network to be more robust and ﬂex-

ible.

According to Agrawal et al. (2023), mesh net-

works have several advantages over traditional net-

works, such as expanding the wireless network, cov-

ering remote areas, and solving connectivity problems

https://orcid.org/0009-0002-9248-0023

https://orcid.org/0000-0001-6419-0286

https://orcid.org/0000-0002-8385-7573

where the signal is weak or non-existent. These ad-

vantages make the mesh network exciting for large

environments like mining companies.

The location of routers in a mesh network is one

of the main factors that inﬂuence the efﬁciency and

signal quality of the network. Despite the economic

and operational importance of providing efﬁcient cov-

erage for mining equipment, the installation points for

routers in mines are generally determined empirically.

This adopted strategy may cause a signal loss, putting

operation and safety at risk. Figure 1 shows the struc-

ture used at the F

abrica Nova mine in Brazil to loca-

tion routers.

Figure 1: Trailer used to install routers at the F

abrica Nova

mine.

620

Mandarino, M., Beneteli, T. and Cota, L.

A Decision Support System Based on a Mixed-Integer Linear Programming Model for Location of Routers in Open-Pit Mines.

DOI: 10.5220/0012586400003690

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 26th International Conference on Enterprise Information Systems (ICEIS 2024) - Volume 1, pages 620-627

ISBN: 978-989-758-692-7; ISSN: 2184-4992

The problem of locating routers in mesh networks

can be classiﬁed as a p-median problem, where the

routers are the facilities and the mine operating points

are the customers. In the literature, the p-median

problem is widely treated in several applications, aim-

ing to minimize the distances between facilities and

customers. However, no study was found on the prob-

lem of locating routers in open-pit mines. In this prob-

lem, there are additional constraints, such as delimit-

ing the mine’s operating areas by four extreme points,

respecting the routers’ coverage radius, and allow-

ing redundancy of coverage, increasing network cov-

erage’s reliability. Furthermore, the objective func-

tion additionally deals with minimizing the number

of routers since the installation adds cost to the mine

infrastructure.

To ﬁll this gap, this work proposes a mixed-integer

linear programming model for router locations in

open-pit mines based on the p-median problem. To

validate the proposal, a case study was used with three

scenarios at the F

abrica Nova mine from Vale S.A in

Brazil. Scenarios represent mining planning for 2023,

2024, and 2025, respectively, and the results estimate

the network infrastructure necessary for the operation.

The main contributions of this work are: i) charac-

terization of the router locations in open-pit mines as a

variant of the p-median problem class; ii) introduction

of a mixed-integer linear programming formulation to

solve the problem using a solver.

The article is organized as follows: Section 2

presents a literature review. Section 3 shows the

characterization of the problem and provides a didac-

tic example. Section 4 presents the proposed model

for router location. Finally, in Section 5, the com-

putational experiments are reported, while Section 6

shows the conclusions of the work.

2 LITERATURE REVIEW

This section presents a literature review of some top-

ics related to the problem of the location of routers in

open-pit mines.

2.1 Mesh Networks

The use of routers in mesh networks has been studied

extensively in the literature. In particular, optimiza-

tion algorithms to determine the optimal router loca-

tion–allocation have proven effective in several con-

texts. In Zhang et al. (2009), the authors proposed

an optimization model for router location–allocation

in mesh networks in urban areas, aiming to minimize

the total cost of the network.

In Bueno (2021), the authors present a study on

router location–allocation in mesh networks in rural

areas. In this case, a mixed-integer linear program-

ming model approach was used to determine the op-

timal router location–allocation, considering several

constraints, such as installation cost and signal range.

Regarding the use of mesh networks in mining en-

vironments, a recent study by Shibalabala and Swart

(2020) highlighted the importance of using mesh net-

works for data transmission in underground mines,

aiming to improve the efﬁciency and safety of oper-

ations. However, more studies still need to be con-

ducted on the installation of routers in mesh networks

in open-pit mining environments.

2.2 The p-Median Problem

The p-median problem class is a combinatorial op-

timization problem that aims to ﬁnd the optimal lo-

cation of p medians in a set of possible locations,

minimizing the distance between the medians and the

demand points (Daskin and Maass, 2015). The p-

median problem has been used in several areas. Be-

low, we present some of these applications:

• Distribution Center Optimization: in logis-

tics and supply chain management, the p-median

problem is used to determine the strategic location

of distribution centers, minimizing transportation

costs and maximizing delivery efﬁciency of prod-

ucts (Ramadhanti et al., 2020).

• Health Services Planning: in healthcare, the p-

median problem approach is applied to determine

the ideal location of hospitals, clinics, or care cen-

ters, aiming to maximize access to medical ser-

vices and minimize patient travel times (Murad

et al., 2024).

• Reduction of Carbon Emissions: seeking sus-

tainable transport solutions, the p-median prob-

lem is used to optimize charging point locations

for electric vehicles, reducing carbon emissions

and improving infrastructure urban mobility (Kim

et al., 2022).

• Urban and Spatial Planning: the p-median

problem approach is used in urban planning to de-

termine the location of public services, such as

schools, libraries, or parks, seeking to ensure an

equitable distribution of these resources in the city

(Chen et al., 2023).

Location-allocation problems seek to ﬁnd the best

conﬁguration for installing one or more facilities to

meet the demand of a population. The term facility

can be replaced in the public sector by public ser-

vice units (schools, libraries, hospitals, bus stops) and

A Decision Support System Based on a Mixed-Integer Linear Programming Model for Location of Routers in Open-Pit Mines

621

emergency services units (ﬁre department, police sta-

tions, ambulance stations). In the private sector, the

term facility can be replaced, for example, by facto-

ries, warehouses, telecommunications antennas, and

routers (Barbosa et al., 2023; de Campos et al., 2020).

The problem of locating routers in mesh networks

is a critical issue that aims to ﬁnd the ideal location

for installing routers in a geographic area to ensure

maximum coverage and connectivity. This problem

is complex and involves several restrictions, such as

signal range, installation costs, and the limited num-

ber of routers to be installed. Several optimization

approaches have been widely studied and applied to

solve this challenge.

In Lorena and Pereira (2002), the p-median prob-

lem is applied to a facility location problem, simulat-

ing the installation of radio antennas for internet ser-

vice in S

ao Jos

e dos Campos, Brazil. Capdeville and

Vianna (2013) also proposed the implementation of

GRASP heuristics for the problem of locating access

points in a wireless mesh network, which is treated as

a problem capacitated p-median location based on the

structure of a new network that will be implemented.

Sandoval et al. (2021) consider the problem of max-

imizing user coverage for 5G/6G wireless communi-

cation networks subject to facility location and radial

distance constraints through two models. The ﬁrst

model maximizes the total number of users. The sec-

ond includes in the objective function the maximiza-

tion of users and the minimization of the number of

antennas to be activated. The numerical results ob-

tained show that the increase in the number of radius

allowed provides more ﬂexibility and accuracy to the

model, although at a higher computational cost. The

authors indicate that proposed models can be used for

future developments of 5G/6G networks to improve

coverage.

Therefore, the p-median problem formulation can

also solve the router location problem in mesh net-

works. In this context, the medians represent the lo-

cations of the routers, and the demand points are the

devices or areas that require connectivity.

Using the p-median problem approach to solve the

router location problem in mesh networks allows for

determining strategic positions for installing routers

to optimize network coverage and minimize associ-

ated costs. To that end, a new mathematical formula-

tion was developed based on the p-median problem.

The new objective function and problem constraints

seek to represent the speciﬁc characteristics of the

router location problem in open-pit mines. The pro-

posed new formulation will be presented below.

3 PROBLEM STATEMENT

Open-pit mines generally have a vast geographic ex-

tension, and mining activities may exist simultane-

ously in different regions of that mine. The mining

equipment used in the operation requires access to the

communication network to guarantee the safety and

productivity of the operation.

In this work, the operating points determine the ar-

eas where mining activities are being performed and

where mining equipment circulates and requires con-

nectivity. For each operational area, four extreme

points are deﬁned.

Figure 2 illustrates a region in which two opera-

tion areas are represented by the areas delimited by

the yellow lines. Each operating area is represented

by four extreme points, called operating points, in red

in the image.

Figure 2: Mapping of operating points.

Therefore, the router location problem in open-pit

mines consists of determining the minimum number

of routers needed to ensure that all operating points

are within the coverage radius of at least one router.

The characteristics of this problem are presented be-

low.

1. Operating points (J):

(a) A mine can have several areas of simultaneous

operation;

(b) In each operation area, there is a variety of

equipment that needs connectivity to perform

its activities;

treme points, called operation points;

(d) Each operating point j ∈ J has a location l p

;

(e) Each operating point j ∈ J needs to be attended

to one or more routers r ∈ R;

2. Routers (R):

(a) A communication network is made up of n

routers;

(b) Each installed router has a location lr

∈ I;

ICEIS 2024 - 26th International Conference on Enterprise Information Systems

622

ﬁed as radius;

(d) p

max

indicates the maximum number of routers

that can be installed.

3. Candidate locations for installing routers (I):

(a) There is a set of candidate locations for in-

stalling routers;

(b) Each location i ∈ I has a location lr

The objective is to locate routers r ∈ R serving all

operating points j ∈ J, seeking to minimize the num-

ber of routers installed and the sum of the distances

between the operating points and the routers.

Next, a small example of the problem is presented

to facilitate understanding.

In this example, represented in Figure 3, there are

two operation areas, represented by the areas delim-

ited in yellow. The two operating areas total eight

operating points j = {J1, J2, ·· · , J8}, represented in

red. There are six possible router installation points,

i = {I1, I2, ·· · , I6}, represented in blue. Each router

has an operating radius of 1000 meters, and the max-

imum number of routers that can be installed is four.

Figure 3: Operating points (J) and possible installation

points (I).

Table 1 presents the location matrix of the operat-

ing points in Cartesian coordinates (XYZ), while Ta-

ble 2 presents the location of possible router installa-

tion points.

Table 1: Operating points (J).

Points

Location

X Y Z

J1 662924,60 7763976,10 857,60

J2 662944,60 7763855,45 855,87

J3 663103,26 7763667,44 863,62

J4 663085,39 7763452,97 861,33

J5 662745,07 7763950,46 850,35

J6 662983,63 7763629,94 857,03

J7 663025,22 7763378,73 844,49

J8 663157,37 7763180,37 852,08

Table 3 presents the distance matrix between the

operating points and the possible router installation

points in meters.

A possible solution for the didactic example is to

install a router at point I3, which is show by Figure 4.

Table 2: Possible installation points (I).

Points

Location

X Y Z

I1 662672,16 7764069,48 854,63

I2 662848,54 7764001,51 857,08

I3 663018,54 7763651,51 862,22

I4 663101,99 7763358,01 865,70

I5 663176,98 7763235,03 871,57

I6 663262,39 7763096,90 876,83

Figure 4: Possible solution.

4 PROPOSED MATHEMATICAL

MODEL

In this section, we present the mixed-integer lin-

ear programming model to solve the addressed prob-

lem based on p-median. The main contributions of

this model are: i) minimize the number of installed

routers; ii) delimitation of mine operating areas by ex-

treme points; iii) respect the routers’ coverage radius;

iv) allow redundancy of router coverage.

Next, the input sets, indexes, parameters, and de-

cision variables used in the proposed formulation are

described.

• Sets:

J : set of operating points that must be met;

R : set of routers;

I : set of candidate locations for router installa-

tion.

• Indexes:

j : index of the set J;

i : index of the set I.

• Parameters:

i j

: distance from the operating point j to the

router located at i;

max

: maximum number of routers that can be in-

stalled;

radius : coverage radius of each router.

• Decision variables:

p : number of routers that will be installed;

A Decision Support System Based on a Mixed-Integer Linear Programming Model for Location of Routers in Open-Pit Mines

623

Table 3: Distance matrix.

J1 J2 J3 J4 J5 J6 J7 J8

I1 277,72 347,99 670,29 787,10 157,96 544,46 878,69 1019,42

I2 80,40 176,29 462,85 615,55 160,79 395,36 806,04 902,36

I3 359,54 257,19 88,18 210,27 546,07 67,90 587,14 593,94

I4 709,21 618,35 313,71 115,42 927,43 371,70 529,54 371,72

I5 979,04 908,97 501,79 341,15 1286,16 651,06 942,44 438,00

I6 1313,17 1261,83 766,80 637,82 1699,66 993,61 1414,54 746,96

i j











1, if the operating point j is assigned to

the router located at i;

0, otherwise;

(

1, if the router is installed at location i;

0, otherwise;

The objective function of the formulation is com-

posed of two parcels. The ﬁrst parcel minimizes

the number of open facilities, that is, the number of

routers installed. The second parcel minimizes the

sum of the distances between the operating points and

the installed routers. The equations (1) and (2) repre-

sent the objective function.

min α

|R|

+ β



∑

i∈I

∑

j∈J

i j

|J|radious



(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.

A set of constraints (3) has been implemented to

ensure that all operating points are within the cover-

age radius of the routers.

i j

≤ radius ∀i ∈ I, ∀ j ∈ J (3)

The set of constraints (4) ensures that each oper-

ating point is assigned to at least one router.

∑

i∈I

i j

≥ 1 ∀ j ∈ J (4)

The set of constraints (5) guarantees that each op-

erating point can only be assigned to installed routers.

i j

≤ y

∀i ∈ I, ∀ j ∈ J (5)

The constraint (6) determines the number of in-

stalled routers. The constraint (7) deﬁnes that the

number of installed routers must be less than the num-

ber of routers available p

max

∑

i∈I

≤ p (6)

p ≤ p

max

(7)

Finally, the set of constraints (8) and (9) deﬁne

the domain of the decision variables x

i j

and y

, re-

spectively.

i j

∈ {0, 1} ∀i ∈ I, ∀ j ∈ J (8)

∈ {0, 1} ∀i ∈ I (9)

5 CASE STUDY

The proposed mathematical model was implemented

in Lingo 10.0, version 4.01.100, and the computer

used in the computational experiments was an In-

tel(R) Xeon(R) W-10885M CPU @ 2.40 GHz note-

book, 64.0 GB RAM, and Windows 11 operating sys-

tem.

We used real data from three scenarios of the

abrica Nova mine in Mariana, Brazil, to evaluate the

proposed model. The operating points were collected

using geographic coordinates. The possible installa-

tion points were deﬁned in the existing roads from the

mine using the Deswik software.

5.1 Scenarios

Currently, in the F

abrica Nova mine, there are 12

routers available for implementing the network. In

this study, each router has a coverage radius of 1,000

meters. We used three scenarios to validate the pro-

posal: the ﬁrst represents the operations for 2023,

while the others represent the projection of the op-

erations for the following years, 2024 and 2025.

• Scenario 01: the ﬁrst scenario evaluated reﬂects

the mining planning for the year 2023. This sce-

nario has 12 operating areas represented by four

extreme points each, totaling 48 operating points.

Figure 5 shows the operating points for this year.

• Scenario 02: the second scenario analyzed rep-

resents mining planning for the year 2024. This

scenario is presented in Figure 6 and has nine op-

eration areas, totaling 36 operation points.

• Scenario 03: the last scenario analyzed is pre-

sented in Figure 7 and represents the mining plan-

ning for the year 2025. This scenario has six op-

eration areas, totaling 24 operation points.

In open-pit mines, the installation of routers is

only permitted at the mine’s access points, that is, on

the existing roads within the mine. To determine the

possible installation points for the routers, we use the

ICEIS 2024 - 26th International Conference on Enterprise Information Systems

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Figure 5: Operating points for the scenario 01.

Figure 6: Operating points for the scenario 02.

Figure 7: Operating points for the scenario 03.

Deswik software, version 2023.2.953. The topogra-

phy of the area with indications of existing accesses

is inputted into the software, as showed the red lines

in Figure 8. Thus, the software returns the number

of possible installation points to better the characteri-

zation of these accesses, as well as their geographic

coordinates. In the studies, we used the same ac-

cess topography across all scenarios and the software

identiﬁed 101 possible router installation points in the

mine.

A distance matrix, nxm, was created for each sce-

nario, where n is the number of operating points for

each scenario and m is the number of possible instal-

lation points. Due to the amount of data, a spread-

sheet with the matrices is available at https://encr.pw/

alocacao-roteadores

Figure 8: Possible installation points (in red).

5.2 Results

Table 4 summarises the results. As the objective func-

tion of the proposed mathematical model is composed

of two parcels, it was evaluated in three weight com-

binations for each scenario.

In all scenarios, the proposed mathematical model

quickly found the optimal solution (GAP = 0). It can

be seen that when one of the parcels has a weight

equal to 0, it is not considered in the optimization

process. Therefore, for this problem, it is suggested

to use a weight of 0.5 for each parcel of the objective

function.

The solution generated in each scenario is illus-

trated as follows, considering α = 0.5 and β = 0.5.

Figure 9 presents the solution for scenario 01. Five

routers were installed at the points indicated in green.

The solution for scenario 02 is presented in Fig-

ure 10. For 2024, nine routers were installed at the

points indicated in green. When ﬁnding solutions for

mine planning in the coming years, the model has

shown to be a valuable tool for predicting the infras-

tructure necessary for implementing the communica-

tion network in mine expansion.

Finally, for 2025, the installation of eight routers

was indicated. Figure 11 represents the solution for

scenario 03.

In scenarios 2 and 3, the installation of routers

overlaps more than in scenario 1. These situations are

due to the projection of the mine for 2023 and 2024,

A Decision Support System Based on a Mixed-Integer Linear Programming Model for Location of Routers in Open-Pit Mines

625

Table 4: Results.

Scenario

Weight # Operation

Areas

# Operation

Points

# Possible

Installation Points

Installed

Routers

Maximum

Distance

Average

Distance

GAP

Execution

Time (s)Parcel 1 (α) Parcel 2 (β)

0.0 1.0

12 48 101

12 592,019 219,684 0 13

0.5 0.5 5 836,646 360,746 0 12

1.0 0.0 5 908,457 588,192 0 21

0.0 1.0

9 36 101

12 958,006 388,08 0 1

0.5 0.5 9 958,006 465,878 0 1

1.0 0.0 9 958,006 657,681 0 7

0.0 1.0

6 24 101

12 972,767 622,021 0 0

0.5 0.5 8 972,767 659,385 0 0

1.0 0.0 8 992,281 774,993 0 3

Figure 9: Solution for scenario 01.

Figure 10: Solution for scenario 02.

in which the front mining will be more profound.

For all the scenarios evaluated, the proposed math-

ematical model was able to ﬁnd the optimum solu-

tion quickly, demonstrating that it is a suitable tool

for decision-making.

6 CONCLUSIONS

This work proposed a mathematical model based on

the p-median class to solve a router location prob-

Figure 11: Solution for scenario 03.

lem in open-pit mines. Open-pit mining is an activity

that requires the use of various high-tech equipment

in large areas. In this problem, it is necessary to de-

ﬁne the installation points for the routers, guarantee-

ing network coverage for all the mine’s equipment.

The objective is to minimize the number of routers

installed and the sum of the distances between the op-

erating points and the installed routers.

The proposed mathematical model brings the fol-

lowing new features: i) all equipment must be within

the overage radius of the routers; ii) one or more

routers can attend each mining equipment, i.e., cov-

erage redundancy is allowed; iii) and the objective

function involves additionally minimizing the number

of routers since a cost is associated with their instal-

lations.

We use real data from the F

abrica Nova mine in

computational experiments to validate the proposed

model. The results showed that the model found the

optimal router location in all scenarios, minimizing

the number of installed routers and providing more

efﬁcient coverage for mining equipment. Therefore,

the proposed mathematical model proved to be suit-

able for supporting decision-making in the locating

of routers in open-pit mines.

In future work, we suggest analyzing the uncer-

tainties present in the coverage radius of routers in

ICEIS 2024 - 26th International Conference on Enterprise Information Systems

626

large areas and network interference. In addition, we

also aim to explore other objective functions.

ACKNOWLEDGEMENTS

The authors are grateful for the support provided

by Vale S.A, Instituto Tecnol

ogico Vale, and by

the Coordenac¸

ao de Aperfeic¸oamento de Pessoal de

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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