=Paper=
{{Paper
|id=Vol-1743/paper15
|storemode=property
|title=A Clustering Optimization Approach for Disaster Relief Delivery: A Case Study in Lima-Peru
|pdfUrl=https://ceur-ws.org/Vol-1743/paper15.pdf
|volume=Vol-1743
|authors=Jorge Vargas-Florez,Rosario Medina-Rodriguez,Rafael Alva-Cabrera
|dblpUrl=https://dblp.org/rec/conf/simbig/FlorezRA16
}}
==A Clustering Optimization Approach for Disaster Relief Delivery: A Case Study in Lima-Peru==
https://ceur-ws.org/Vol-1743/paper15.pdf
A clustering optimization approach for disaster relief delivery: A case
study in Lima-Perú
Jorge Vargas-Florez, Rosario Medina-Rodrı́guez, Rafael Alva-Cabrera
Pontificia Universidad Católica del Perú
jorge.vargas@pucp.edu.pe , {r.medinar,rafael.alva}@pucp.pe
Abstract dispatch is more oriented to beneficiary communi-
ties in a timely manner, while waiting for the ini-
During the last decade, funds to face tial disaster assessment to be completed. Klibi and
humanitarian operations have increased Martel (2012), described that under a state of dis-
approximately ten times. According to aster the depots network is not expected to respond
the Global Humanitarian Assistance Re- adequately, because its storage and distribution ca-
port, in 2013 the humanitarian funding re- pacity loses its nominal operability.
quirement was by US$ 22 billion, which Moreover, Martinez et al. (2011) confirms
represents 27.2% more than the requested that transport is the second largest general bud-
in 2012. Furthermore, the transportation get of humanitarian organizations, after staff.
cost represents between one third to two- Thus, planning transportation routes (VRP, Ve-
thirds from the total logistics cost. There- hicle Routing Problem) is one of the most im-
fore, a frequent problem in a disaster re- portant problems of combinatorial optimization
lief is to reduce the transportation cost by and it is widely studied with many applications
keeping an acceptable distribution service. in the real world, like distribution logistics and
The latter depends on a reliable delivery transport (Toth and Vigo, 2002). The humanitar-
route design, which is not evident con- ian delivery in disasters cases are concerned to
sidering a post-disaster environment. In optimize; maximizing unsatisfied demand, min-
this case, the infrastructures and sources imizing travel time and minimizing total deliv-
could be inexistent, unavailable or inop- ery delay (Beamon and Balcik, 2008). There are
erative. This paper tackles this problem, three basic approaches for modeling the problem:
regarding the constraints, to relief delive- (i) the vehicle route is represented by a binary
ry in a post-disaster environment (like an variable of multiple indexes, that define the ve-
eight degree earthquake) in the capital of hicle and route identification; (ii) the construc-
Perú. The routes found by the hierarchi- tion of a dynamic network flow model whose
cal ascending clustering approach, which outputs are the vehicle and material flows, that
has been solved with a heuristic model, have to be parsed in order to construct vehicle
achieved the best result. routes and loads and; (iii) to enumerate all fea-
sible routes between all pairs of supply and de-
1 Introduction
mand nodes (Özdamar and Demir, 2012). The lat-
Humanitarian response recognizes two phases ter open a data analysis utilization based on pattern
after a disaster: the life-saving and the life- mining, data mining or clustering to optimize de-
sustaining actions (Thevenaz and Resodihardjo, livery routes. For our purposes, we decided to use
2010). The first one, consists in carrying activi- the last mentioned approach.
ties that aim to preserve life, like removal debris In literature, numerous works have been pro-
and rescue victims. The second one, involves the posed to deal with the problem of spatial cluste-
provision of aid kits and services such as: food, ring on data associated to natural disasters. Early
water, temporary shelter, medical care, and pro- papers attacked the problem of emergency eva-
tection (Assessment and Coordination, 2006). As cuation, for example, Pidd et al. (1996) presented
it was mentioned in (Hall, 2012), the initial relief a spatial decision support system to emergency
122
planning. Their approach, based on Geographical lighted: (1) the high risk that would suffer the Pe-
Information System (GIS) software, evaluated two ruvian capital in a potential major earthquake due
issues: (i) static, processing the data from a math- to its sociodemographic and seismic location; (2)
ematical, statistical and logical point of view and; the failed National delivery relief case described
(ii) dynamic, establish the terrain for evacuation before and; (3) the importance of supplies trans-
under certain assumptions and with some speci- portation to humanitarian operations. Therefore,
fied policies. Then, in (Gong and Batta, 2007), an it is necessary to provide an optimal, efficient and
ambulance allocation to improve the rescue pro- resilient route design regarding the constraints of
cess of victims, was proposed. The authors used a a post-disaster environment. For this purpose, we
spatial clustering combined with fuzzy logic in or- propose an approach based on the hierarchical as-
der to allocate the correct number of ambulances cending classification that seems the best option
to each spatial objects grouped into a cluster after considering the expected bad conditions of the
an earthquake. roads in a post disaster environment.
Later, Tai et al. (2010) described a method to Following this brief introduction and review,
evacuate Shin-Hua city, Taiwan, after an earth- the paper is organized as follows: Section 2, de-
quake. They analyze the spatial correlation be- scribes the followed methodology. Then, Sec-
tween objects taking into account six indexes tion 3, exposes the medical aid relief delivery to
associated to route characteristics. Moreover, Lima and Callao in an eventual earthquake, ana-
Özdamar and Demir (2012), proposed a hierar- lyzing the Hierarchical Ascending Classification
chical cluster and route procedure (HOGCR) for approach for humanitarian distribution. At the
coordinating vehicle routing in large-scale post- end, we conclude with an analysis of the solution
disaster distribution and evacuation activities. Re- with the lowest travel time and also some future
cently, Matthew et al. (2015) evaluated the sur- research works are described.
vival Kobe-1995-earthquake manufacturing plants
2 Methodology
and their post-earthquake economic performance.
They used a geographical clustering technique In order to find an approximate solution to the pro-
combined with a micro-econometric approach. cess of delivery humanitarian relief in Lima, we
In Perú, from 1582 to 2007, occurred 47 earth- propose an efficient and resilient approach. The
quakes with magnitudes between 6.0 to 8.6 on efficiency is related to the ability to provide the
the Richter scale. At least 10 were greater than service with fewer resources, while resilience con-
8.0 and 100% of them occurred between the dition is related to the ability to retain the ope-
center and the south coast area of Perú; where ration in time, even whether infrastructures and
Lima is located. Leseure et al. (2010), presented sources are inexistent. Our methodology is com-
the 7.9 earthquake in Pisco-Perú in 2007, which posed by the following stages:
killed more than 500 people and affected more
than 655 thousand people; who demanded water, 1. Obtain the information about the actual Peru-
food, shelter, clothes, etc. The assistance for vic- vian humanitarian system from government
tims was distributed through multiple civil defense entities (i.e. INDECI).
committees, leaded by the Instituto de Defensa 2. Perform an analysis about cartography in the
Civil (INDECI). territory of study, to identify the most vulner-
Despite the efforts, they could not manage a able, exposed and threatened areas.
proper relief delivery, however the authors stand
out the following conclusions: (i) humanitarian 3. Carry out a study about available models to
donations reception and transport were impro- solve the vehicle routing problem.
vised; (ii) humanitarian aid was distributed hap-
4. Identify the costs following a cluste-
hazardly; (iii) duplication of supplies in some
ring approach (Hierarchical Ascending
closer areas, while the more isolated ones, re-
Classification-HAC).
ceived partial support and; (vi) distribution of in-
appropriate aid relief and unfit food for consump- Our goal is to identify the routes to be used
tion (rotten food, expired date drugs, etc.). for the distribution of humanitarian aid. Whereas
From these statements, three points can be high- these routes be comprised by pre-positioned by
123
INDECI warehouses which are: the Medical Sup-
Table 1: INDECI scale values corresponding to
plies (AM, “Almacén de Insumos Médicos”, in
the vulnerability type.
spanish) and Central Warehouses (AC, “Almacén
Central”, in spanish); both located in Lima and Socio-economic Night Day
pre-defined by INDECI. We follow a heuristic vulnerability accessibility accesibility
called “cluster-first route-second”, which deter- Very low (1) Very good (1) Very good (1)
mines clusters of customers compatible with vehi- Low (2) Good (2) Good (2)
Average (3) Regular (3) Regular (3)
cle capacity and solves a traveling salesman prob-
High (4) Bad (4) Bad (4)
lem for each cluster (Prins et al., 2014). Thus, for Very high (5) Very bad (5) Very bad (5)
this proposal we apply the Hierarchical Ascending
Classification, forming clusters using the total ad- Hazards Seismic
justed travel time for each route instead of the Eu- exposition vulnerability
clidean distance as a proximity measure. In order Low impact (1) Low (1)
to correct this time, we use as criterion “how crit- Average impact (2) Relativity high (2)
ical is the condition of the affected region”, which High impact (3) High (3)
Very high impact (4) Very high (4)
is based on measures of vulnerability, accessibil-
ity, exposure and proximity for each district of
Lima, where each AM is located. Table 2: Summary of vulnerabilities (SE:Socio
economic; DA:Day accessibility; NA:Night
3 Results and Discussion accessibility; HE:Hazard exposition; SZ:Seismic
Zoning) for each Supply Depot and its respective
The HAC analysis performed by using dendro- Delivery Point.
grams (Villardón, 2007), is as an efficient tool
Vulnerabilities
for the cluster identification task which combines Supply
Delivery Distance AC
depots SE DA NA HE SZ
many features. For instance, it is possible to sep- point to AM (Km)
arate the population into homogeneous clusters AC2 AM1 2 4 1 2 1 6.29
AC2 AM2 2 4 2 5 1 6.06
(low within-variability and high between variabil- AC1 AM3 2 4 3 5 2 2.06
ity). In this proposal, we have considered five fea- AC1 AM4 2 4 3 4 2 1.77
AC2 AM5 2 5 3 3 1 10.21
tures that describe vulnerabilities: (i) seismic lo- AC2 AM6 2 4 2 1 1 2.75
cation; (ii) socioeconomic state; (iii) access to AC2 AM7 2 3 1 2 2 12.54
delivery point; (iv) exposure to hazards and; (v) AC2 AM8 2 5 3 2 1 8.48
AC2 AM9 1 5 4 4 1 28.32
proximity to the central depot (AC). AC2 AM10 2 5 3 1 1 9.93
AC2 AM11 2 3 2 4 2 2.44
Step 1: we use an advanced statistical analysis AC2 AM12 2 4 3 3 1 1.92
tool (XLSTAT 2013.6.03) and the vulnerability AC2 AM13 2 4 1 3 1 6.43
AC1 AM14 2 4 3 5 2 1.04
scales were obtained from the INDECI categoriza- AC1 AM15 1 4 4 3 1 19.78
tion criteria (see Table 1). Then, based on this cri- AC1 AM16 1 4 4 3 1 19.71
AC1 AM17 1 4 2 3 1 17.44
teria, we obtained a summary of the value associ- AC1 AM18 1 4 4 3 2 21.58
ated with each type of vulnerability and the district AC1 AM19 1 4 4 3 2 24.37
where they belong to, as can be seen in Table 2. AC1 AM20 1 4 4 3 2 24.87
AC1 AM21 1 4 4 3 2 22.87
However, in order to apply the HAC approach, it is AC1 AM22 1 3 2 4 2 5.87
necessary to standardize our values, so there is an AC2 AM23 2 3 2 4 2 4.60
AC1 AM24 2 3 2 4 2 3.07
existent correlation (see Table 3). For this purpose, AC1 AM25 2 4 2 4 2 1.13
we used the method of the “maximum magnitude AC2 AM26 2 4 3 4 1 0.76
of 1” (Justel, 2008). This means, the division of AC2 AM27 2 4 1 2 1 4.96
Maximal value 2 5 4 5 2 28.32
the value of each variable by its maximum value,
obtaining values between 0 and 1.
instance, if the distance between AC1 and AM1 is
Step 2: we apply the HAC method on the new less than the distance between AC2 and AM1, then
standardized data, choosing which Central Ware- it will supply AC1. The result can be observed in
houses (ACs) will supply store whose Medical the dendrograms shown in Fig 1, where the hori-
Supplies Warehouses (AMs). This choice was zontal dotted line divides the collection of points
based on the shortest distance from AC to AM; for in three clusters set by AMs.
124
Figure 1: Dendrograms - Clusters supplied by AC1 and AC2.
Step 3: then, we apply the algorithm proposed responding to 50% of the average transport time).
by Clarke and Wright (1964), looking for routes
with lower cost, linking each AM to clusters. The
final result shows each AM supplied by each AC,
Also, reviewing historical events recorded by
as can be seen in Table 4.
INDECI, it realizes that poor accessibility in af-
fected areas increases between 25% to 100%, due
3.1 Distances Evaluation
to collapsed infrastructure or debris. For instance,
Here, we present an analysis about post disaster to evaluate AM1 distance, due to correction fac-
distances to be covered by routes. At the begin- tors, it will be increased in 65% (correction fac-
ning, Euclidean ideal distances have been consid- tor 165% or 1.65). Because its location has a 4
ered however they must be corrected by a “Correc- level accessibility then, corresponds to 25% and
tion Factor” in order to represent realistic post dis- its seismic zoning characteristics corresponds to
aster conditions; for example streets with debris, 40% (according to INDECI), hence 25% + 40% =
transport infrastructures collapsed like bridges. 65%. Whether it is applied this criterion in Ta-
According to the Peruvian Ministry of Transport ble 6, the corrected and covered distance (based
and Communications, the poor accessibility post on Table 5 percentages) for this application case is
disaster can cause variations up to 30 minutes (cor- 250.32 Km.
125
Table 4: Summary routes and distances with HAC
Ideal Distance
Clusters HAC Routes
(Km)
Cluster 1 AC1 AM17 AM21 AM20 AM19 AM18 AM16 AM15 AC1 52.15
Cluster 2 AC1 AM22 AM24 AC1 12.83
Cluster 3 AC1 AM4 AM25 AM3 AM14 AC1 7.63
Cluster 4 AC2 AM9 AM7 AM11 AM23 AC2 68.93
Cluster 5 AC2 AM5 AM8 AM10 AC2 37.35
Cluster 6 AC2 AM12 AM27 AM1 AM13 AM2 AM6 AM26 AC2 21.59
200.48
Table 3: Summary of standardized vulnerabilities Table 6: “Correction Factors” for each type of
(SE:Socio economic; DA:Day accessibility; vulnerability and supply depot.
NA:Night accessibility; HE:Hazard exposition;
Bad
SZ:Seismic Zoning) for each Supply Depot and Supply Seismic Correction
Accessibility
its respective Delivery Point. Depot Vulnerability Factor
(Day and night)
AM1 40% 25% 165%
Vulnerabilities
Supply AM2 40% 25% 165%
Delivery Distance AC
depots SE DA NA HE SZ AM3 40% 50% 190%
point to AM (Km)
AC1 AM3 1 0.8 0.75 1 1 0.08 AM4 40% 50% 190%
AC1 AM4 1 0.8 0.75 0.8 1 0.06 AM5 50% 25% 175%
AC1 AM14 1 0.8 0.75 1 1 0.04 AM6 40% 25% 165%
AC1 AM15 0.5 0.8 1 0.6 0.5 0.70 AM7 30% 50% 180%
AC1 AM16 0.5 0.8 1 0.6 0.5 0.70 AM8 50% 25% 175%
AC1 AM17 0.5 0.8 0.5 0.6 0.5 0.62
AM9 50% 25% 175%
AC1 AM18 0.5 0.8 1 0.6 1 0.76
AM10 50% 25% 175%
AC1 AM19 0.5 0.8 1 0.6 1 0.86
AC1 AM20 0.5 0.8 1 0.6 1 0.88 AM11 30% 50% 180%
AC1 AM21 0.5 0.8 1 0.6 1 0.81 AM12 40% 25% 165%
AC1 AM22 0.5 0.6 0.5 0.8 1 0.21 AM13 40% 25% 165%
AC1 AM24 1 0.6 0.5 0.8 1 0.11 AM14 40% 50% 190%
AC1 AM25 1 0.8 0.5 0.8 1 0.04 AM15 40% 25% 165%
AC2 AM1 1 0.8 0.25 0.4 0.5 0.22 AM16 40% 25% 165%
AC2 AM2 1 0.8 0.5 1 0.5 0.21
AM17 40% 25% 165%
AC2 AM5 1 1 0.75 0.6 0.5 0.36
AM18 40% 50% 190%
AC2 AM6 1 0.8 0.5 0.2 0.5 0.10
AC2 AM7 1 0.6 0.25 0.4 1 0.44 AM19 40% 50% 190%
AC2 AM8 1 1 0.75 0.4 0.5 0.30 AM20 40% 50% 190%
AC2 AM9 0.5 1 1 0.8 0.5 1.00 AM21 40% 50% 190%
AC2 AM10 1 1 0.75 0.2 0.5 0.35 AM22 30% 50% 180%
AC2 AM11 1 0.6 0.5 0.8 1 0.09 AM23 30% 50% 180%
AC2 AM12 1 0.8 0.75 0.6 0.5 0.07 AM24 30% 50% 180%
AC2 AM13 1 0.8 0.25 0.6 0.5 0.23
AM25 40% 50% 190%
AC2 AM23 1 0.6 0.5 0.8 1 0.16
AM26 40% 25% 165%
AC2 AM26 1 0.8 0.75 0.8 0.5 0.03
AC2 AM27 1 0.8 0.25 0.4 0.5 0.18 AM27 40% 25% 165%
AC1 30% 50% 180%
AC2 40% 25% 165%
Table 5: Percentage increased in distances consi-
dering each type of vulnerability.
3.2 Distribution Expenses Evaluation
Bad Accessibility
Level Seismic Vulnerability Once we already have obtained the routes and its
(Day and night)
1 10% 25% associated distance, it is necessary to know the
2 20% 50% type of transportation that will be used, in or-
3 30% 75% der to estimate the required resources. According
4 40% 100%
to (Martinez et al., 2011), the best vehicles to be
5 50% –
used in the humanitarian distribution due to its ca-
pacity and potency are the pick-up (4 ⇥ 4), whose
main characteristics are shown in Table 7.
126
Table 7: Vehicle features. Source: Nissan/Toyota; Table 8: Estimated affected population in the
UN Refugee Agency and International Federation largest Lima’s districts in case a major earthquake
of Red Cross and Crescent Societies. according to (Serpa Oshiro, 2014).
Feature Description Affected
District Sector
Engine power 2500 cc population
Number of cylinders 4 Ate 69954 East-Lima
Average performance 45 km/gal Callao 195954 Callao
Fuel Diesel Carabayllo 127612 North-Lima
Loading capacity 1 TM cc Chorrillos 51918 South-Lima
Comas 242235 North-Lima
Volume occupied by drugs 3m3
Lima 18674 Lima-Center
Drug packaging unit 20L - 40L
Lurigancho 74186 East-Lima
Lurin 36312 South-Lima
Pachacamac 15260 South-Lima
According to INDECI, each medicine packag- Puente Piedra 144323 North-Lima
ing unit (emergency backpack) should be able to S. J. de Lurigancho 314549 East-Lima
supply at least two people. It is recommended an S. J. de Miraflores 128435 South-Lima
average weight of 8 Kg, corresponding to a back- Ventanilla 14435 Callao
Villa el Salvador 113993 South-Lima
pack with a capacity of 20 to 40L. Thus, for practi-
Villa Maria del Triunfo 133171 South-Lima
cal calculations, we consider an intermediate value
of 30L. Then, considering 1 vehicle, we can cal-
culate the number of backpacks to carry and how
tering became to one route), considering the cor-
many people they would help. For instance, ev-
rected distance according to the correction factor.
ery trip that makes one transport, will attend 200
Moreover, we describe the cost of fuel used to sup-
people.
port all the victims considering the least distance
Backpacks = volume occupied by medicines in covered; which is S /.160, 520.62 approximately.
one vehicle; 3m3 = 3000L. We can also provide valuable additional informa-
tion, for instance, the amount of trips required to
1Backpack support all the victims considering the number of
3000L ⇥ = 100Backpacks
30L vehicles used.
People = attention capacity for backpack ⇥ For instance, in Table 11, we obtained the num-
quantity of backpacks in one pick up ber of vehicles needed to complete the route in an
acceptable number of days (8.26 days), using 600
2 people
⇥ 100 Backpacks = 200 people vehicles. It would support 120 000 people with 18
Backpack trips (number of trips is needed in each identified
route until complete the requested demand). Fi-
nally, as an expected result, we can see in Fig 2,
Furthermore, we proceeded to group the that the number of supported people will increase
provinces of Lima and Callao in four main with more assigned vehicles.
sectors: North-Lima, South-Lima, Lima-Center,
East-Lima and Callao; it will allow us to estimate 4 Conclusions and Future works
the amount of affected people to assist (see Ta-
ble 8). Lima and Callao have 49 districts, and In this study, we propose an approach to opti-
some of them do not have points of medical sup- mize aid distribution kits in an eventual disaster
plies depots, meanwhile other ones have more than in Lima. Previous research works consider the ex-
one depot. For this reason, we consider that each istence of infrastructure, transport, capacity, avail-
depot will support the victims by the sector where ability of public services, among others; as a post-
they belong to (see Table 9); regardless districts disaster state. However, a solution should be suit-
which are part of it. The support must be done able to manage an uncertain lack of resources,
proportionally to victims’ amount in each district. lost of capacity and infrastructure. Thus, our ap-
In Table 10, we indicate the total amount of proach using the corrected distances representing
victims to be supported for each route (each clus- the vulnerability of a location, uses minimal re-
127
Table 9: Number of victims to support for each depot. Source: INEI, SIRAD.
Victims to aid
Sector Total victims Depots Total
for each depot
North-Lima 540 254 AM8 , AM2 2 270 127
South-Lima 483 274 AM7 1 483 274
Center-Lima 64 280 AM1, AM6, AM13 , AM27 4 16 070
East-Lima 490 985 AM5, AM9 , AM10 3 163 662
AM3, AM4, AM11, AM12, AM14, AM15,
Callao 216 942 AM16, AM17, AM18, AM19, AM20, AM21, 17 12 762
AM22, AM23, AM24, AM25, AM26
1 795 735
Table 10: Total amount of victims to be supported for each route, considering corrected distance and the
cost of fuel.
Ideal Distance Corrected Distance Fuel cost
Clusters Trips Routes Victims treated
(Km) (Km) (S/.)
Cluster 1 52.15 58.54 447 Route 1 89 334 8010.36
Cluster 2 12.83 16.56 128 Route 2 25 524 656.25
Cluster 3 7.63 11.62 256 Route 3 51 048 920.97
Cluster 4 68.93 87.37 3363 Route 4 672 460 9 0967.59
Cluster 5 37.35 47.29 2988 Route 5 597 451 43 746.91
Cluster 6 21.59 28.94 1800 Route 6 359 931 16 127.55
200.48 250.32 1 795 748 160 520.62
Table 11: Number of day trips and days to support victims (mean speed 40 kph).
Quantity Quantity of Total of Covered Mean
Time Corrected
of supported trips distance correction Days
(HRS) time
vehicles people (Km) by trip factor
10 2000 899 225037.7 135022 : 36 : 29 1.76 237639 : 47 : 24 412.56
20 4000 450 112644 67586 : 24 : 00 1.76 118952 : 03 : 50 206.51
50 10 000 180 45057.6 27034 : 33 : 36 1.76 47580 : 49 : 32 82.60
100 20 000 90 22528.8 13517 : 16 : 48 1.76 23790 : 24 : 46 41.30
200 40 000 45 11264.4 6758 : 38 : 24 1.76 11895 : 12 : 23 20.65
600 120 000 18 4505.76 2703 : 27 : 22 1.76 4758 : 04 : 57 8.260
Figure 2: Number of Vehicles vs Humanitarian Operation Days and Victims Treated
128
sources (time to complete routes) and it is reliable Michel Leseure, Mel Hudson-Smith, Jérôme Chandes,
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