Scientia et Technica Año XVI, Vol.30 No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira. ISSN 0122-1701 16
Abstract— Natural disasters have long affected populations
worldwide, resulting in significant consequences for both people
and their environments. Most disasters occur suddenly, and
several studies have highlighted logistical weaknesses in both the
prevention and response to such events. In Colombia, flooding is
the leading cause of death from hydrometeorological phenomena.
Based on this context, the present research proposes a mixed-
integer linear programming model for the location of temporary
relief centers and the routing of specialized personnel. These
decisions were addressed in two phases. In the first phase, the
location of temporary shelters was determined, considering
designated safe zones as candidate sites. In the second phase, route
planning for specialized personnel was carried out, using a local
distribution center as a reference point. The results indicate that
addressing both decision-making processes and their interrelation
contributes to minimizing response times for vulnerable
populations.
Index Terms— Aid distribution, Humanitarian logistics,
Location of shelters, Mixed integer linear programming, Natural
disasters.
Resumen— Los desastres naturales han afectado a la población
mundial, provocando consecuencias relevantes para las personas
y su entorno. La mayoría de los desastres ocurren repentinamente,
por lo que varios estudios han detectado deficiencias logísticas en
el momento de prevenir y afrontar estos casos.En Colombia, las
inundaciones son la principal causa de muertes por fenómenos
hidrometeorológicos. Con base en lo anterior, la presente
investigación propone un modelo de programación lineal entera
mixta para la localización de albergues temporales y enrutamiento
de personal especializado. Estas decisiones se abordaron en dos
fases. En la primera fase se estableció la localización de albergues
temporales considerando como sitios candidatos las zonas seguras
destinadas para el emplazamiento de estas instalaciones. Los
albergues seleccionados, permitió establecer en la segunda fase la
configuración de rutas del personal
This manuscript was submitted on November 23, 2023. Accepted on
February 19, 2025. And published on March 31, 2025.
Karen Vanessa Marín Gómez: Escuela de Ingeniería Industrial, Universidad
del Valle Cali, Colombia, Postal code 760042. (email:
karen.vanessa.marin@correounivalle.edu.co).
Jessica Dayan Morales Corredor: Escuela de Ingeniería Industrial,
Universidad del Valle Cali, Colombia, Postal code 760042. (email:
jessica.dayan.morales@correounivalle.edu.co).
especializado, considerando un centro local de distribución. Como
resultado obtenido se pudo establecer que abordar ambos
esquemas de decisión y su interrelación, contribuye a la
minimización de los tiempos de respuesta a la población
vulnerable.
Palabras claves— Distribución de ayuda, Logística humanitaria,
Localización de albergues, Programación Lineal Entera Mixta,
Desastres naturales.
I. INTRODUCTION
A
natural disaster is defined as a phenomenon caused by
nature, influenced by human activity. In 2011, there were
more than 30,000 fatal victims, and 245 million people affected
worldwide. This caused economic losses estimated at 386
trillion dollars, due to various disasters. In Colombia, 28
thousand events have been recorded in the last 40 years, 60%
of which happened between 1990 and 2011; damage costs
amounted to 623 billion dollars for the 2010-2011 winter season
[1]. This shows that there has been an increase in the occurrence
of disasters, which directly and indirectly affect the population
and their environment.
From an engineering point of view, the most important
challenge concerning humanitarian logistics is coordinating
logistics activities [2] and managing resources in chaotic
environments together with the uncertainty of emergency
situations, which is a complex logistical task [1].
In Colombia, according to the National Risk and Disaster
Management Unit, some of the most common disasters include
floods, earthquakes, and landslides. These events have a
negative effect on communities, and cause infrastructure
damage and endanger human lives.
Carlos Alberto Rojas Trejos: Departamento de Ingeniería de Sistemas e
Industrial, Facultad de Ingeniería, Universidad Nacional de Colombia ,
Bogotá, Colombia, Postal code 111321.
Escuela de Ingeniería Industrial, Universidad del Valle, Cali, Colombia,
Postal code 760042. (email: crojast@unal.edu.co).
Model for Location of Temporary Shelters and Routing
of Specialized Personnel for Assisting Vulnerable
Population in case Sudden Natural Disasters
Modelo de localización de albergues temporales y ruteo de personal especializado para la
atención de población vulnerable ante un desastre natural súbito
K. V. Marín-Gómez ; J. D. Morales-Corredor ; C. A. Rojas-Trejos
DOI: https://doi.org/10.22517/23447214.25487
Scientific and technological research paper
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
17
Table 1 shows the distribution of these disasters that occurred
in Colombia between 1906 and 2019. This also shows that
floods, landslides, and earthquakes have the highest
accumulated percentage of occurrences, totaling 81.77%.
TABLE I
DISTRIBUTION OF EVENTS IN COLOMBIA (1906-2019).
Type of
Natural
Disaster
Absolute
Frequency
(# events)
Relative
Frequency
Total
frequency
affected (#
persons)
Total
deaths (#
persons)
Total
damages
(thousands
of dollars)
Flooding
86
44.79%
16.356,3
3.585
3.591,353
Landslide
43
22.40%
76.082
3.460
102.400
Earthquake
28
14.58%
1.460,39
3.972
2.318,666
Volcanic
activity
11
5.73%
56.964
22,826
1,000,000
Storm
9
4.69%
140.415
49
53.050
Epidemic
6
3.13%
121.194
672
0
Forest fire
3
1.56%
200
31
0
Mass
movement
(dry)
3
1.56%
2.411
247
0
Drougth
2
1.04%
100.000
0
0
Insect
infestation
1
0.52%
0
0
104.000
Total
192
100%
18,314,58
34,842
7.169,469
Source: UNGRD
The most significant type of disaster is flooding, which occurs
due to heavy or sudden rainfall, causing the rising and
overflowing of rivers. These events happen abruptly and, in
many cases, are difficult to control, causing material losses and
affecting people’s health. This may cause the loss of human
lives. During a flood, the current of rivers often carries
everything in its path such as animals, trees, rocks, and various
debris.
Since floods are difficult to be controlled, in necessary to
have a contingency plan for efficient and timely post-disaster
response. To achieve this purpose, it is important to know the
affected area and its limitations. Help centers and resource
distribution centers should be strategically located, and trained
personnel efficiently deployed so that they can respond to
emergencies of this nature.
To fulfill this purpose, it is necessary to go to a branch of
logistics that is responsible for providing timely aid to
populations that may be affected before, during and after a
disaster. This branch is called Humanitarian Logistics, which
have the same fundamental principles logistics: planning,
implementing and controlling the flow of information,
resources or personnel from a point of origin to a destination.
While logistics aims to meet customer needs, humanitarian
logistics aims to alleviate the suffering of affected populations
in a timely manner.
Based on this, this project aims to develop a mixed-integer
linear programming model whose objective is to minimize
response time for victims by optimizing the distribution of
resources between relief centers and temporary shelters.
Specialized personnel are also present to provide timely
assistance to victims in a municipality of the Valle del Cauca
department, Colombia. Thus, a diagnosis of the area will be
conducted to assess the effects of natural disasters and identify
the most relevant dangers, which will be the bases for
formulating the mathematical model.
II. LITERATURE REVIEW
Humanitarian logistics according to [3] is the process of
planning, implementing and efficiently controlling the flow of
products, materials and information from individuals and donor
organizations to victims, so that their survival needs are met.
Humanitarian logistics emerged as a response to the increase of
natural disasters worldwide, which have affected some
populations. According to data from the International Strategy
Program for Disaster Reduction (ISDR), in 2004, there were
305 natural disasters in the world. As these natural disasters
continue to increase, and consequently the survival needs of
affected populations increase as well. Populations affected by
these adversities face such multiple problems as inadequate
shelter, lack of food, limited access to medical care, insufficient
drug supply and the need for psychological support, particularly
in cases of family loss. [4].
The authors [4] identify the challenges facing humanitarian
logistics today are increasing, and they are much more
complex; these issues are the speed aid of delivery, the
movement of affected populations in conflict areas, the
influence of humanitarian teams, deficiencies in ONG`s
capabilities, lack of knowledge, limited investment in
technology and communication.
Humanitarian logistics is generally divided into three stages,
which are aligned with the well-known traditional risk
management model: pre-disaster, during the disaster, and post-
disaster. These stages have several subcategories [5]. These are
shown in Fig.1.
Fig. 1. Traditional Risk Management Model Source: Adapted of [5]
Authors such as [6] state that in natural disasters such as
floods, the affected population is partially isolated and
vulnerable. Research in Colombia highlights the importance of
providing timely post-disaster support. According to IFRC
(2010), cited by [7], such "organizations as the Red Cross in
Colombia play an important role in developing training
programs for both the population and institutions: These
organizations have also established a series of protocols and
guidelines to effectively manage crisis situations".
The post-disaster situation occurs in an environment
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
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characterized by uncertainty regarding aid resources and
shelters for victims. The latter is critical, since many houses are
damaged or destroyed. Therefore, families are forced to seek
alternative accommodation until a permanent housing solution
can be found [8].
Regarding humanitarian logistics [9], this presents a
qualitative analysis of inventory management strategies in the
humanitarian logistics operations. They state that, each year,
many natural and human-induced disasters affect thousands of
people around the world. During these disasters, both
government agencies and humanitarian organizations face
logistical challenges; their main objective is to meet the needs
of affected people and alleviate their suffering. To achieve this,
an effective inventory management strategy plays a crucial role
at every stage of the supply chain.
In terms of routing trained personnel and vehicles for the care
of vulnerable populations, some authors have researched this
topic, including:
In the emergency logistics planning, natural disaster [10]
pose one of the most common problems in logistics: the
Vehicle Routing Problem (VRP), which involves a set of clients
(each represented as a destination node) that must be served by
m identical vehicles located at a warehouse. Each vehicle is to
return to the depot after completing its route, and its load cannot
exceed its capacity at any point of the trip. Additionally, each
client can be visited only once, and it is assumed that the
vehicle’s carrying capacity exceeds the demand of any
individual client. Thus, the main objective is to minimize the
total distance traveled on each route.
According to [11], specialized literature has enough
information on the application of metaheuristics in route
planning route. However, most research in this field have been
conducted under normal conditions (e.g., standard weather
conditions). The problem of route planning for repairing
electrical faults can be basically modeled Capacitated Multiple
Traveling Salesman Problem (CMPS), due to some significant
similarities with this well-known variant of the theoretical VRP.
These similarities are related to the dispatching of a
homogeneous fleet of vehicles (with repair technicians
deployed in vulnerable areas), where each vehicle is assigned a
set of nodes (affected areas) similar to MTSP (Multi-Traveling
Salesman Problem). Each node is once visited by a single
vehicle (or salesman).
Other authors as [12] have developed a structured plan for
distributing humanitarian aid through vehicle routing in the
event of a major earthquake in Lima Metropolitan and Callao.
They use the Great Route method together with Linear
Programming, as this minimizes the actual distance traveled
and reduces transportation costs. The number of victims was
also considered to optimize the allocation of resources and
supplies to be used for each trip by the terrestrial vehicular fleet.
In the work of [13], a bi-level optimization model is
presented for sending, receiving and distributing in-kind
assistance after a natural disaster has occurred. This aims to
determine the optimal configuration of shipments and the most
efficient distribution method for delivering supplies affected
areas through various transportation modes.
A key issue in humanitarian logistics, widely recognized by
researchers, is the strategic location of temporary relief or
facilities to provide timely resources and specialized assistance
in affected areas.
Concerning this issue, [14] propose an approach to the
problem of locating temporary relief facilities for households
affected by severe natural disasters. They characterize both the
demand and supply of temporary relief, identifying high-risk
areas based on the type of disaster that may occur. The model’s
performance function seeks to minimize the weighted distances
between temporary relief facilities and affected households,
considering constraints such as ensuring full demand from each
household type, facility capacity limitations, and the maximum
number of temporary shelters that can be built.
Similarly, author [15] propose a bi-criteria model for the
location of temporary relief centers. This model includes the
design an evacuation plan to support and ensure the safety of
the affected population in case of a flood. This includes the
opening of a temporary relief and distribution centers, pre-
positioning of aid package inventories, and the assignment of
individuals to temporary shelters and evacuation routes.
Some of the optimization models in humanitarian logistics
used for facility location, which is the focus of this research,
include deterministic single-objective modes developed by [16-
19], and stochastic models developed by [20-22], among others.
Based on the analyses of previous studies, it is necessary to
analyze the interrelationship between decisions related to the
location of distribution points and temporary shelters, and the
distribution of humanitarian aid. This analysis is to consider
limitations in the availability and capacity of humanitarian
assistance or support units in affected areas.
Unlike the reviewed literature on humanitarian logistics this
research considers the following:
✓ A mathematical formulation with hierarchical
approach that allows integrating decisions on the
location of temporary relief centers and the routing of
specialized personnel.
✓ The allocation of temporary shelters and assignment
of homeless individuals to the temporary shelters.
✓ Supplies allocation according to the number of victims
assisted by open temporary shelters
✓ The routing of specialized personnel and their
assignment to open temporary shelters
✓ Capacity constraints in temporary shelters and
limitations in specialized personnel availability.
Therefore, this research proposes a two-level mode. The first
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
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level aims to determine the optimal location of a distribution
point and temporary shelters to assist populations that have
been affected by a sudden natural disaster. The second level has
to do with decisions on the distribution of humanitarian aid in
the last-mile by considering limited resources and capacity
issues in care units.
III. METHODOLOGY
A review of the literature on location and routing models will
be conducted by various authors who have addressed these
topics related to natural disasters. This review will be of great
help as a basis for developing mathematical models to achieve
an optimal post-disaster solution Fig. 2.
Fig. 2. Description of Methodology. Source: Authors
The formulation of mathematical models will be presented,
defining input parameters, decision variables, the objective
function, and constraints. These models are validated through a
case study to determine whether the results are aligned with
real-world contexts.
The methodology is structured in two phases. First, the
location model is solved by using information provided by the
case study; thus, output variables are obtained, which serve as
input parameters for the routing model following a hierarchical
approach. This produces output variables or model results that
are to be analyzed to verify if they meet the objectives of each
component. Finally, conclusions are reached based on these
findings.
A. Model of location for temporary relief centers
This location model is a mathematical model formulated as a
mixed-integer linear programming (MILP), which has been
designed to determine the best location of a distribution center
and different temporary relief centers. This done to minimize
travel time for delivering supplies from the distribution center
to temporary shelters, ensuring timely assistance to vulnerable
populations.
Assumptions.
• The municipality in this study case lacks specialized and
adequate infrastructure for establishing temporary relief
centers during a flood disaster. Therefore, some
educational facilities in both urban and rural areas are used
instead.
• The areas affected and requiring evacuation due to such
disasters are known with certainty.
• The victims are not relocated to the homes of relatives,
friends or neighbors.
• Victims arrive at the assigned temporary relief.
• Supplies include temporary kits (including a pillow, mat
and blanket), which is required by each victim.
• It is assumed that each victim uses only one kit.
• The kits are donated and managed by national and
departmental institutions.
• The kits are pre-positioned at the Distribution Center.
• Travel times and number of victims are considered
deterministic.
Main Sets
•
       
•
        
•
      
•
        
•
      
•
         
•
   
Parameters
•


:      
        
  
•

      
•
       
Number of victims who can be assisted
•
    
•
  
(

)
  
•
:      
Decision Variables
•

1 if the distribution center is located
in zone
; 0 otherwise.
•

1 if the temporary relief center is located in
zone j; 0 otherwise
•


1 if the distribution center serves
the temporary relief center j; 0 otherwise
•

:
number of victims in area k who are served
in the temporary relief center in zone j
•


1 if the victims of the area k
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
20
are assigned to the temporary relief center in zone j;0 otherwise
•

:
quantity of supplies sent from the
distribution center in zone j
Objective Function
Minimize travel time from the distribution center to the
temporary relief centers so that affected victims can be assisted
[minutes].
,



+
,

,

Constrains
+
1

,

,
=
(1)

=
1
(2)


=

(3)





(4)

=



,

(5)


=
1

(6)


0.1

(7)




(8)



,

(9)



(10)




(11)




(12)



(13)






(14)
{
0,1
}

(15)
{
0,1
}

(16)

{
0,1
}

,

(17)

{
0,1
}

,

(18)

0

,

(19)

0

,

(20)
Where (1) is a zone that can only be used to locate a
distribution center or temporary relief center; (2) Ensures the
opening of a single distribution center i; (3) The distribution
center can serve a temporary relief center j only if the temporary
relief center is open; (4) Ensures that victims from each zone k
are accommodated in a temporary relief center only if it is open;
(5) The temporary relief center can serve the victims of a zone
only if it has been designated to do so; (6) Victims from each
affected area k must be assigned to a single temporary relief
center j; (7) A temporary relief is opened only if the number of
victims to be served exceeds 10% of its capacity; (8) Each open
temporary relief center must have sufficient capacity to
accommodate the victims from an affected area k; (9) supplies
are sent from a distribution center to the temporary relief center
only if the distribution center serves the temporary relief center;
(10) The amount of supplies sent from a distribution center to a
shelter should not exceed the distribution center’s capacity; (11)
The quantity of supplies sent from distribution centers for to
temporary relief centers should not exceed the temporary relief
center’s capacity; (12) The total number of victims
accommodated in temporary relief centers in zone j of k must
be at least equal to the total number of victims in that area; (13)
Ensures that the number of temporary relief centers is sufficient
to serve the affected population; (14) Ensure that sufficient
supplies are sent to meet the demand of the shelter; (15), (16),
(17), (18), (19) and (20) Define the range of values that
variables can take.
B. Specialized Personnel Routing Model
To develop the model shown below, the Capacitated Vehicle
Routing Model with a homogeneous fleet was used as aa
reference.
Assumptions
•
Three support groups (Red Cross, Civil Defense and Fire
Department) have the same skill and capacity to serve the
victims of such disasters and are equipped with all
necessary tools.
•
Specialized people form a single support unit.
•
The capacity for assistance is determined based on the
number of victims and available staff.
•
Restrictions on access roads are not considered.
•
All specialized personnel are available at the distribution
center.
•
Travel times are deterministic
•
Support unit transport all specialized personnel required to
assist victims.
Main Sets
•

Set of input vertices(distribution center
and
temporary relief
centers
indexed
by
i and j
•

Set of available support units indexed by k
Parameters
•

:
Travel time from the CDA i to the CDA j (Minutes)
•


 

 
•
:
Shelter demand associated with each CDA i (Victims)
•

Number of s
pecialized personel available in each
s
upport
unit
(Personnel)
Decision Variables
•


1 if support unit k travels through
the route from i to j; 0 otherwise
•

:
Demand at the Temporary Relief Center supplied by the support unit
(Personnel)
•
:
Additional variable that represents the
unit
s load capacity
of the support unit after visiting the temporary relief
center i (Personnel)
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
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Objective Function
Minimize travel time from the distribution center to all
temporary relief centers.
,, 


Constraints
, 

1

(1)

=



,

:
1
(2)
:

=

(3)
:



(4)
 

 

=
0

,

(5)
+



,

,

:
,
0 ,
0
(6)

:
0
(7)


:
0
(8)

{
0,1
}
,

,

(9)

0

,

(10)
0

(11)
0 

(12)
Where (1) ensures that the specialized personnel arrives at
the temporary relief center; (2) indicates that the temporary
relief center i can be served by specialized personnel if k passes
i; (3) Ensures that the demand of each open temporary relief is
fully satisfied ; (4) determines that the quantity of specialized
personnel assigned to each temporary relief center does not
exceed the available personnel; (5) Flow balance, which
indicates that the support unit leaving the distribution center
returns; (6), (7) and (8) Avoid sub-routes; (9), (10), (11) and
(12) define range of values that the variables can take.
IV. CASE STUDY
The case study is framed within the municipality of Tuluá is
located in southwestern Colombia, in the center of Valle del
Cauca department between the Central Mountain Range and the
Cauca River (CVC, 2017). It has territorial area 1,014.96 km
2
.
The total land area of the municipality is 910.55 km
2
of which
98.78% corresponds to the rural sector and the urban sector
1.22% (Municipality of Tulua, 2017).
According to figures from DANE, Tuluá has a population of
216,619 inhabitants, 187.121 live in the municipal capital and
29,483 in rural areas. (Tuluá Chamber of Commerce, 2016).
To validate the proposed models, the municipality of Tuluá was
chosen as a reference, particularly those areas affected by the
2022 rainy season. Floods occur during the winter season due
to the overflow of Tuluá River, which initially affects the
following neighborhoods: Tomas Uribe (CV1), La Trinidad
(CV2), Siete de Agosto (CV3), San Antonio (CV4), La
Inmaculada (CV5), Villa Nueva (CV6), Casa Huertas (CV7),
Portales Rio in urban area (CV8), the village of Bocas de Tulua
(CV9), Tres Esquinas (CV10); Morales River affecting
neighborhoods: Urbanization Villa (CV11), El Bosque (CV12)
and Santa Rita (CV13). (CMGR, Consejo Municipal de Gestión
del Riego de Desastres Municipio de Tuluá – disaster risk
managment -, 2012). These places can be seen in fig. 3.
The proposed models provide an optimal solution that meet
the needs of the affected population, safe areas were identified,
where temporary relief centers could possibly be located. These
safe places are: Coliseo de Ferias Manuel Victoria Rojas(CA1),
Salesiano High School San Juan Bosco (CA2), Coliseo Benicio
Echeverry (CA3), Stadium Doce de Octubre (CA4), Institución
Educativa Aguaclara (CA5) Institución Educativa Técnica
Occidente Tulua (CA6), Health Center La Independencia
(CA7), Rubén Cruz Vélez (CA8), Institución Educativa Julia
Restrepo (CA9), Gimnasio del Pacifico School (CA10),
Institución Educativa Julio Cesar Zuluaga, Tres Esquinas
Village (CA11), Institución Educativa Julio Cesar Zuluaga in
the village Bocas de Tulua (CA12). These places can be seen in
Figure 4. A distribution center was also identified, which has
become a safe potential place: these are Coliseo de Ferias
Manuel Victoria Rojas (CD1) and Salesiano High School San
Juan Bosco (CD2), which can be seen in Figure 5 as well; the
municipality of Tulua Secretary of government lacks suitable
facilities of temporary relief centers; that is the reason why
some state-owned educational institutions and some health
centers are used. Although it is known that, when an emergency
occurs, these centers should not be used since doing do would
disrupt academic and labor activities, these have been used in
this study due to the lack of alternative facilities.
They can be observed in Fig. 4; in the municipality of Tulua
Secretary of government lacks suitable for the location of
temporary shelter facilities, which is why we make use of
official educational institutions and some health centers,
although it is known that when an emergency that requires
locating temporary relief should not resort to educational
institutions and health centers, because this way we would be
intervening in academic and labor activities, but as mentioned
above the city and this work they will resort to facilities because
they are not they have other available. The entities or groups
equipped with specialized disaster relief personnel include the
Fire Department, Civil Defense, and Red Cross.
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
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Fig. 3. Areas Flood irrigation. Source: Google Maps
Fig. 4. Safe Zones for the location of temporary relief centers
Source: Google Maps
Fig. 5. Safe areas for the location of distribution centers.
Source: Google Maps
V. RESULTS
This section presents the results obtained based on the
methodology developed. The results thrown by the CPLEX
software in the NEOS Server platform and the mathematical
programming language AMPL, indicate that the location model
determined the opening of a Distribution Center No. 1 (CD1)
and Temporary Relief Centers No. 5 and 11 (CA5, CA11).
These temporary locations ensure a minimum travel time of 93
minutes while guaranteeing assistance for the entire vulnerable
population.
Fig. 6 shows the location of the distribution center and
temporary relief centers, while Figures 7 and 8 show the
assignment of affected areas to each of the temporary relief
center.
Fig. 6. Location of the distribution center and temporary relief
Source: Google Maps
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
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Fig. 7. Mapping affected areas to CA5.Source: Google Maps
Fig. 8. Allocation of areas affected by CA11. Source: Google
Maps
The number of victims and supplies assigned to each
temporary relief center are shown in Table 2. Table 3 presents
the results of supplies allocation from the distribution center to
each temporary relief center.
TABLE II
VICTIMS OF EACH AFFECTED SITE THAT WILL BE TREATED AT EACH
TEMPORARY RELIEF
AC
CV
5
11
1
0
47
2
0
21
3
27
0
4
32
0
5
21
0
6
25
0
7
25
0
8
30
0
9
16
0
10
32
0
11
26
0
12
27
0
13
25
0
Source: Authors
TABLE III
SUPPLIES ALLOCATED FROM THE DISTRIBUTION CENTER FOR EACH
TEMPORARY RELIEF
CD
AC
1
5
286
11
68
Source: Authors
These results show that all affected areas within where the
victims are in the municipal head are assisted by Institución
Educativa Aguaclara Sede principal (CA5), which is also
located in the city center and close to the distribution center
Coliseo de Ferias Manuel Victoria Rojas (CD1). Meanwhile,
affected rural areas are served by Institución Educativa Julio
Cesar Zuluaga (CA11), which also receives supplies from the
same distribution center (CD1).
The routing model that has been designed to minimize travel
time and provide timely assistance to victims, determined that
the support unit with specialized personnel leaves the Coliseo
de Ferias Manuel Victoria Rojas (CD1), goes to the Institución
Educativa Aguaclara temporary relief (CA5), where 96
specialized personnel are left. After that, it goes Institución
Educativa Julio Cesar Zuluaga (CA11), where other 23
specialized personnel are left. Finally, it returns to point of
departure (CD1). Table 4 shows the results produced by the
model.
TABLE IV
RESULTS MODEL ROUTING OF SPECIALIZED PERSONNEL.
Specialized personnel (D) temporary relief
(CA) open
AC
CA5
CA11
D
96
2. 3
Source: Authors
• Travel time: 40 minutes
• Route: CD1 → CA5 → CA11 → CD1
It is observed in the base model of routing that the path that
specialized staff starts at the distribution center CD1, there is
going to lodge to CA5 where 80% of specialist staff meets the
demand of the temporary relief because most (+ - 80%) of the
victims are concentrated there, so that is necessary more
specialist staff to alleviate the suffering of those affected by a
disaster natural, thence he goes to meet the other temporary
shelter open CA11 which has 20% of victims, generating a time
minimum of 40 minutes of transfer from support unit with
specialized personnel to temporary relief.
These models determine the number of temporary relief
centers that are to be opened by, identify optimal locations and
distribution centers with good capacity, assign victims to
shelters, and also identify the routing of specialized personnel.
This is aimed to seek a solution that generates the shortest
possible time in assisting the affected victims. The combined
results related to Location and Routing are shown in Fig. 9.
Scientia et Technica Año XVI, Vol.30, No 01, Mes enero-marzo de Año 2025. Universidad Tecnológica de Pereira
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Fig. 9. Results Model Location and routing of specialized
personnel.Source: Google Maps
Although the location model provides a decision-making
decision solution for placing temporary relief centers to assist
flood victims in the municipality of Tulua, and the routing
model ensures a solution that meets the objective of minimizing
travel time for the support unit and specialized personnel. Thus,
further scenario analysis is required based on the variation of
parameters of interest, so that the behavior of the location and
routing model can be evaluated to improve response strategies
and optimize decision-making in the event of a flood.
Addressing the decisions about the location of temporary
shelters and the configuration of routes for specialized
personnel together recognizes the connection between both
decision-making processes. This integrated approach helps
improve response times for affected populations compared to
tackling these decisions separately, as shown in the studies
conducted by [8], [16], and [17]. Treating these decisions
individually may lead to suboptimal solutions [2].
VI. CONCLUSION
In emergency situations caused by natural disasters, the most
important issue is to have a well-structured emergency response
to meet victims’ needs and assist them as soon as possible. The
objective of this study is to minimize time from the occurrence
of a disaster to the arrival of aid in affected areas.
To achieve this, a location model was proposed to determine
the number and location of temporary shelters, which should be
served by a single distribution center. This model also took into
account allocation of victims and necessary supplies; this also
accounts for the capacity of both shelters and the distribution
center. A routing model was also designed to optimize the
movement of specialized personnel to provide timely assistance
to vulnerable population and the assignment of personnel,
according to the needs of each shelter.For this purpose, the
mathematical programming language AMPL was used, as well
as the NEOS Server platform and the CPLEX solver to obtain
and analyze quantitative results of the proposed models.
Unlike previous studies in humanitarian logistics, this research
employs a mathematical hierarchical approach, which allows
the integration of location decisions for distribution centers and
temporary shelters with the routing of specialized personnel.
This model considers issues related to victim assignment to
shelters, supply assignment according to the number of victims
served by open shelters, and assignment of specialized
personnel, while accounting for the limited capacity of relief
units.
For future research, it is necessary to improve models for
temporary relief centers and routing of specialized personnel by
incorporating stochastic travel and setup times and number of
victims. Future studies could also include cost models related
to opening and operating a temporary shelter and distribution
centers. Furthermore, the impact environmental factors in the
performance function are considered as well.
ACKNOWLEDGMENT
The study was funded by Bicentennial Doctoral Excellence
Scholarship Program of the Ministry of Science, Technology
and Innovation, defined in Article 45 of Law 1942 of 2018 of
the General System of Royalties in Colombia. The authors of
the research would like to acknowledge to SEPRO and
GEDESC research groups of Universidad Nacional de
Colombia and Universidad del Valle, respectively, for their
valuable comments.
Acknowledgment the National Risk and Disaster
Management Unit (UNGRD, by its Spanish acronym) of Tulua
city, Colombia.
DECLARATION OF INTERESTS
The authors declare no conflict of interest.
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Karen Vanessa Marín Gómez
Industrial Engineer - Universidad del
Valle, Colombia. She has worked in
projects related to humanitarian
logistics, logistics and supply chains at
industrial and commercial level, through
mathematical models approaches. The
areas of knowledge are: project
management, logistics, production,
quality management and operations
research.ORCID: https://orcid.org/0009-0003-9155-418X
Jessica Dayan Morales Corredor
Industrial Engineer - Universidad del
Valle, Colombia. Experience in process
optimization, continuous improvement
and management of operational and
technological projects in sectors such as
manufacturing, logistics and
pharmaceuticals. Specialized in Lean
Manufacturing, Six Sigma and digital
transformation through Agile Project
Management, she is currently
responsible for the Progreso process with a focus on projects
with impact on competitiveness, expansion and business
sustainability .ORCID: https://orcid.org/0009-0000-3776-1557
Carlos Alberto Rojas Trejos
Industrial Engineer and Magister in
Engineering of Universidad del Valle,
Colombia. PhD in Engineering -
Universidad Nacional de Colombia,
Bogotá, Colombia. Actually, he is
professor in Operation's Research, of
academic program of Industrial
Engineering in Universidad del Valle,
Colombia. His research interests
include applied mathematical modeling, humanitarian logistics,
hospital logistics and optimization using metaheuristics.
ORCID: https://orcid.org/0000-0002-5440-5631