During the last decade, funds to face humanitarian operations have increased approximately ten times. According to the Global Humanitarian Assistance Report, in 2013 the humanitarian funding requirement was by US$ 22 billion, which represents 27.2% more than the requested in 2012. Furthermore, the transportation cost represents between one third to twothirds from the total logistics cost. Therefore, a frequent problem in a disaster relief is to reduce the transportation cost by keeping an acceptable distribution service. The latter depends on a reliable delivery route design, which is not evident considering a post-disaster environment. In this case, the infrastructures and sources could be inexistent, unavailable or inoperative. This paper tackles this problem, regarding the constraints, to relief delivery in a post-disaster environment (like an eight degree earthquake) in the capital of Peru´. The routes found by the hierarchical ascending clustering approach, which has been solved with a heuristic model, achieved the best result.
1 Introduction
Humanitarian response recognizes two phases
after a disaster: the life-saving and the
lifesustaining actions
Moreover, Martinez et al. (2011) confirms
that transport is the second largest general
budget of humanitarian organizations, after staff.
Thus, planning transportation routes (VRP,
Vehicle Routing Problem) is one of the most
important problems of combinatorial optimization
and it is widely studied with many applications
in the real world, like distribution logistics and
transport
In literature, numerous works have been
proposed to deal with the problem of spatial
clustering on data associated to natural disasters. Early
papers attacked the problem of emergency
evacuation, for exa
Later, Tai et al. (2010) described a method to
evacuate Shin-Hua city, Taiwan, after an
earthquake. They analyze the spatial correlation
between objects taking into account six indexes
associated to route characteristics. Moreover,
O¨ zdamar and Demir (2012), proposed a
hierarchical cluster and route procedure (HOGCR) for
coordinating vehicle routing in large-scale
postdisaster distribution and evacuation activities.
Recently, M
In Peru´, from 1582 to 2007, occurred 47 earthquakes with magnitudes between 6.0 to 8.6 on the Richter scale. At least 10 were greater than 8.0 and 100% of them occurred between the center and the south coast area of Peru´; where Lima is located. Leseure et al. (2010), presented the 7.9 earthquake in Pisco-Peru´ in 2007, which killed more than 500 people and affected more than 655 thousand people; who demanded water, food, shelter, clothes, etc. The assistance for victims was distributed through multiple civil defense committees, leaded by the Instituto de Defensa Civil (INDECI).
Despite the efforts, they could not manage a proper relief delivery, however the authors stand out the following conclusions: (i) humanitarian donations reception and transport were improvised; (ii) humanitarian aid was distributed haphazardly; (iii) duplication of supplies in some closer areas, while the more isolated ones, received partial support and; (vi) distribution of inappropriate aid relief and unfit food for consumption (rotten food, expired date drugs, etc.).
From these statements, three points can be highlighted: (1) the high risk that would suffer the Peruvian capital in a potential major earthquake due to its sociodemographic and seismic location; (2) the failed National delivery relief case described before and; (3) the importance of supplies transportation to humanitarian operations. Therefore, it is necessary to provide an optimal, efficient and resilient route design regarding the constraints of a post-disaster environment. For this purpose, we propose an approach based on the hierarchical ascending classification that seems the best option considering the expected bad conditions of the roads in a post disaster environment.
Following this brief introduction and review, the paper is organized as follows: Section 2, describes the followed methodology. Then, Section 3, exposes the medical aid relief delivery to Lima and Callao in an eventual earthquake, analyzing the Hierarchical Ascending Classification approach for humanitarian distribution. At the end, we conclude with an analysis of the solution with the lowest travel time and also some future research works are described. 2
Methodology In order to find an approximate solution to the process of delivery humanitarian relief in Lima, we propose an efficient and resilient approach. The efficiency is related to the ability to provide the service with fewer resources, while resilience condition is related to the ability to retain the operation in time, even whether infrastructures and sources are inexistent. Our methodology is composed by the following stages: 1. Obtain the information about the actual Peruvian humanitarian system from government entities (i.e. INDECI). 2. Perform an analysis about cartography in the territory of study, to identify the most vulnerable, exposed and threatened areas. 3. Carry out a study about available models to solve the vehicle routing problem. 4. Identify the costs following a clustering approach (Hierarchical Ascending Classification-HAC).
Our goal is to identify the routes to be used
for the distribution of humanitarian aid. Whereas
these routes be comprised by pre-positioned by
INDECI warehouses which are: the Medical
Supplies (AM, “Almace´n de Insumos Me´dicos”, in
spanish) and Central Warehouses (AC, “Almace´n
Central”, in spanish); both located in Lima and
pre-defined by INDECI. We follow a heuristic
called “cluster-first route-second”, which
determines clusters of customers compatible with
vehicle capacity and solves a traveling salesman
problem for each cluster
Results and Discussion
The HAC analysis performed by using
dendrograms
Step 1: we use an advanced statistical analysis
tool (XLSTAT 2013.6.03) and the vulnerability
scales were obtained from the INDECI
categorization criteria (see Table 1). Then, based on this
criteria, we obtained a summary of the value
associated with each type of vulnerability and the district
where they belong to, as can be seen in Table 2.
However, in order to apply the HAC approach, it is
necessary to standardize our values, so there is an
existent correlation (see Table 3). For this purpose,
we used the method of the “maximum magnitude
of 1”
Step 2: we apply the HAC method on the new standardized data, choosing which Central Warehouses (ACs) will supply store whose Medical Supplies Warehouses (AMs). This choice was based on the shortest distance from AC to AM; for instance, if the distance between AC1 and AM1 is less than the distance between AC2 and AM1, then it will supply AC1. The result can be observed in the dendrograms shown in Fig 1, where the horizontal dotted line divides the collection of points in three clusters set by AMs. Step 3: then, we apply the algorithm proposed 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, as can be seen in Table 4. 3.1
Distances Evaluation Here, we present an analysis about post disaster distances to be covered by routes. At the beginning, Euclidean ideal distances have been considered however they must be corrected by a “Correction Factor” in order to represent realistic post disaster conditions; for example streets with debris, transport infrastructures collapsed like bridges. According to the Peruvian Ministry of Transport and Communications, the poor accessibility post disaster can cause variations up to 30 minutes (corresponding to 50% of the average transport time).
Also, reviewing historical events recorded by INDECI, it realizes that poor accessibility in affected areas increases between 25% to 100%, due to collapsed infrastructure or debris. For instance, to evaluate AM1 distance, due to correction factors, it will be increased in 65% (correction factor 165% or 1.65). Because its location has a 4 level accessibility then, corresponds to 25% and its seismic zoning characteristics corresponds to 40% (according to INDECI), hence 25% + 40% = 65%. Whether it is applied this criterion in Table 6, the corrected and covered distance (based on Table 5 percentages) for this application case is 250.32 Km.
Distribution Expenses Evaluation
Once we already have obtained the routes and its
associated distance, it is necessary to know the
type of transportation that will be used, in
order to estimate the required resources. According
to
According to INDECI, each medicine packaging unit (emergency backpack) should be able to supply at least two people. It is recommended an average weight of 8 Kg, corresponding to a backpack with a capacity of 20 to 40L. Thus, for practical calculations, we consider an intermediate value of 30L. Then, considering 1 vehicle, we can calculate the number of backpacks to carry and how many people they would help. For instance, every trip that makes one transport, will attend 200 people.
Backpacks = volume occupied by medicines in one vehicle; 3m3 = 3000L.
3000L ⇥ = 100Backpacks 30L People = attention capacity for backpack ⇥ quantity of backpacks in one pick up
Backpack ⇥ 100 Backpacks = 200 people Furthermore, we proceeded to group the provinces of Lima and Callao in four main sectors: North-Lima, South-Lima, Lima-Center, East-Lima and Callao; it will allow us to estimate the amount of affected people to assist (see Table 8). Lima and Callao have 49 districts, and some of them do not have points of medical supplies depots, meanwhile other ones have more than one depot. For this reason, we consider that each depot will support the victims by the sector where they belong to (see Table 9); regardless districts which are part of it. The support must be done proportionally to victims’ amount in each district.
In Table 10, we indicate the total amount of victims to be supported for each route (each clusDistrict Ate Callao Carabayllo Chorrillos Comas Lima Lurigancho Lurin Pachacamac Puente Piedra S. J. de Lurigancho S. J. de Miraflores Ventanilla Villa el Salvador Villa Maria del Triunfo tering became to one route), considering the corrected distance according to the correction factor. Moreover, we describe the cost of fuel used to support all the victims considering the least distance covered; which is S /.160, 520.62 approximately. We can also provide valuable additional information, for instance, the amount of trips required to support all the victims considering the number of vehicles used.
For instance, in Table 11, we obtained the number of vehicles needed to complete the route in an acceptable number of days (8.26 days), using 600 vehicles. It would support 120 000 people with 18 trips (number of trips is needed in each identified route until complete the requested demand). Finally, as an expected result, we can see in Fig 2, that the number of supported people will increase with more assigned vehicles. 4
Conclusions and Future works In this study, we propose an approach to optimize aid distribution kits in an eventual disaster in Lima. Previous research works consider the existence of infrastructure, transport, capacity, availability of public services, among others; as a postdisaster state. However, a solution should be suitable to manage an uncertain lack of resources, lost of capacity and infrastructure. Thus, our approach using the corrected distances representing the vulnerability of a location, uses minimal reNorth-Lima South-Lima Center-Lima East-Lima
Callao sources (time to complete routes) and it is reliable (routes made under post-disaster conditions). Our results, suggests that the method of Hierarchical Ascendant Classification (HAC), allow us to find an approximate route solution, considering a postdisaster environment.
We found a sufficient and satisfactory humanitarian relief distribution, the searching solution criterion was the shortest time route with the lowest cost, under a spatial configuration which represents a post-disaster state, considering a Correction Factor (CF) to nominal times. This CF was calculated considering a previous HAC analysis, based on vulnerabilities assessment expressed by urbanistic layouts, forecast victims, seismic hazard maps, in Lima and Callao districts. For future research activities we consider to perform an evaluation adding a correction factor which use resilience assessment and; to evaluate the impact of non-considered costs as man power, maintenance, resources loading/downloading and security. In addition, to carry out a sensitivity analysis to choose particulars trucks, timetables and outsourcing service.