präsentiert von
2
Biographies
Ardavan Babaei received his bachelor's and master's Degree in Industrial Engineering from Iran University
of Science &Technology, Tehran, Iran (2015 and 2017). Now, he is a PhD student.
3
Preface
When a disaster occurs, it will cause serious human life and financial losses. Therefore, in order to contain
this issue, relief services and aids should be provided in the shortest possible time with the maximum
coverage, so that in the early moments of the disaster the decision can be made and in order to react quickly
to the extent that injuries and damages will be reduced and the probability of survival and non-destructions
will be maximized. Therefore, the distance to which the relief owners must go to reach the injured person
and, from there, bring him back to the place where he needs to be rehabilitated and return to his original
location for providing further service, is an important factor to be taken into consideration. In this way, time
is one factor that can be considered as a complementary factor of distance, especially in busy areas. In this
regard, depending on the coverage level, it is possible to maintain the survival probability of human life and
property in unforeseen events.
4
Table of contents
Chapter 1:
Humanitarian Relief Logistics ... 7
1. Introduction ... 7
2. Facility Location ... 11
3. Distribution ... 12
4. Discharge ... 14
5. Conclusion... 16
References ... 16
Chapter 2: A Supportive Human-Based Robust Humanitarian Logistics Model
Especially Considering to Disaster Management (Case Study: Kashan, Iran)
... 21
1. Introduction ... 22
2. Problem definition and mathematical model ... 26
3. -Constraint Method ... 39
4. Metaheuristic approach ... 41
4.1. Elements of Genetic algorithm ... 41
4.2. Parameter adjustment ... 43
4.3. Problem design ... 44
4.4. Validation ... 47
4.5. Solving Large Scale samples ... 50
5. Result Analysis ... 51
6. Conclusion... 53
References ... 54
Chapter 3: A Modern Humanitarian Logistics Model under Factual Conditions
of Urban Public Health Specially Considering to Environmental Issues ... 60
1. Introduction ... 61
2. Literature Review ... 62
3. Problem definition ... 66
4. Solution method ... 73
4.1. Solution Representation ... 73
4.2. Simulated Annealing Algorithm ... 74
5
5. Computational Results ... 77
6. Conclusion... 84
References ... 85
6
7
C
HAPTER
1
H
UMANITARIAN
R
ELIEF
L
OGISTICS
1. I
NTRODUCTION
Numerous human lives are debilitated and debased every year because of human
disasters and cataclysmic events. Hurtful and real wounds will happen in human lives
in light of these calamities yielding recoverable and unrecoverable results. War,
mischances, ailment, annihilation of unnecessary structures, absence of security amid
missions and obligations and occurrences of this kind beginning needed and
undesirable by individuals are surges, tremors, tropical storms et cetera.
Consequently, the significance of adapting and controlling such calamities and
occurrences is uncovered.
The components influencing the lives of people, the common and counterfeit
property, can be named as administration time and administration remove. Along
these lines, once a debacle or a disaster happens, it will cause genuine monetary and
life misfortunes. Along these lines, to contain this issue, the most limited conceivable
time with the greatest scope must be made keeping in mind the end goal to have a
right choice in the early snapshots of the episode, and with a fast reaction, in which
case the fiasco and occurrence will be decreased, all things considered, and the
probability of survival and non-decimation will be boosted. Consequently, the
separation which the rescuer must cross to contact the harmed individual and, the
extra separation required for exchanging the harmed to the restoration site and
coming back to his unique area for additionally benefit is a critical factor to be
thought about. Along these lines, time is one factor that can be considered as a factor
supplementing separation, particularly in occupied territories. In such manner,
contingent upon the scope level, it is conceivable to keep up the probability of
survival and property in anticipated and unanticipated occasions.
A considerable lot of the things that are considered when arranging disaster
circumstances are looked with genuine confinements. In all actuality, asset
8
imperatives underlie many arranging and feature the best choices to be made with
accessible assets. The deficiency of disaster vehicles, absence of subsidizing, talented
labor and street and vehicle disappointments are among these. In this manner, for
legitimate arranging and more accuracy in basic leadership, we should consider the
determined imperatives keeping in mind the end goal to manage debacle and
inevitable misfortunes betterly. Meanwhile, we should take a gander at unusual
confinements, so startling components can't beat the general consistency of reaction
to the point of wastefulness.
In this manner, an approach must be taken to gauge going before and succeeding
elements of the fiascos outcomes and lessen/evacuate them proficiently.
Compassionate coordinations includes a procedure of arranging, characterizing,
actualizing, and controlling effectiveness so as to make a financially savvy material
and non-material spill out of source to goal with an extraordinary regard for the
partner necessities, an answer that tends to the issues characterized in many
examines.
This issue can be explored and controlled in four principle ways. In the principal
stage, decreasing the ruinous occasions is assessed, so steps must be intended to
diminish wounds and harm. In the second stage, instruction and preparing are
essential concerning the selection of preventive choices in accordance with the
occasion of hopeless results of occurrences. The third stage tends to adapting to and
reacting to the results of occurrences and in the last stage, repairing and
reestablishing the different properties and soundness of people are critical. The initial
two stages have a place with the episode and the following two stages have a place
with the occasions after the debacle.
The previously mentioned issue is characterized basically through two
unmistakable and non-deterministic courses by calculated and scientific models in
three levels of key, strategic and operational by these methodologies: disaster focus
area, alleviation conveyance, for example, stock administration and bolster
administration.
9
Help is investigated and characterized as far as appropriate steering with different
partners, including the administration, group gatherings and different ventures
(Wassenhove, 2006; Altay and Green, 2006; Akhtar et al, 2012).
The accompanying figure demonstrates the arrangement of the issues
contemplated in this field:
Fig. 1. Categorization of humanitarian logistics issues
With respect to the above arrangement, the space considered for issues is
deterministic or stochastic. At the end of the day, if no vulnerability is considered in a
given issue, the issue is deterministic, else it is stochastic. Then again, if the models
exhibited consider time skyline arranging, the proposed show is dynamic and
generally is static.
As indicated by the figure underneath, the issues are equivalent to the survey
space:
Catagorizaton of
Humanitarian
Logistic
Problems
Deterministic
Static Models
Stochastic
Dynamic
Models
Stochastic
Deterministic
Models
Deterministic
DynamicModels
10
Fig. 2. Review Space
The following figure shows the study of the research phases according to the types
of decisions in the reviewed papers:
Fig. 3. Problem phases
The objectives sought after in the proposed models are mostly gone for
diminishing costs, expanding the scope of harmed and harmed individuals keeping in
mind the end goal to give better administrations, minimizing the voyaging time and
separation between help focuses and harmed with a specific end goal to assist
lifesaving and increment the likelihood of survival, and diminishing the harm caused
by episodes and debacles.
Uncertainty
Location
Inventory
Management
Routing
Certainty
Location
Inventory
Management
Routing
Strategic
Tactical
Operational
· In each 4
phases
· Mostly in
phases 2
and 3
· Mostly in
phase 3
11
A few analysts have considered research, for example, the accompanying: cases
are separated into the accompanying classes, which speak to a basic leadership
condition for adapting to a disaster:
A) Facility Location
B) Distribution
C) Discharge
2. F
ACILITY
L
OCATION
Dekle et al. (2005) developed a model for the establishment of recovery centers in
the pre-disaster phase and the coverage of injuries by distributing relief supplies in
the target area. Chang et al. (2007) developed a model for distributing relief supplies
during urban flood events. Warehouse location, prioritization of the allocation of
vehicles, shortage and fines are applied in the model by the objective function
through minimizing the transportation cost, the establishment cost of the facilities,
and the cost of sending the relief equipment. Beamon and Balcik (2008) proposed a
Facility Location Problem (FLP) for the post-disaster phase. The problem is
formulated as a maximum coverage model with limited budget and capacity of
resources. They consider a number of locations as distribution centers and quantity of
relief supplies at each facility to cover all demand. Bozorgi-Amiri et al. (2012)
developed a stochastic model for the relief distribution, followed by relief supplies
allocated to the affected area with the objective function of minimizing the cost for
pre-disaster planning, including logistics costs, transportation, and maintenance and
shortage costs. Horner and Downs (2010) proposed a model for determining the
location of the warehouse in which the warehouses were established for allocating
relief goods to affected areas. Zhang et al. (2012) developed a resource allocation
model, with and multi-resource and multi-location constraints, with the goal of
minimizing total time for emergency resources allocation. Ahmadi et al. (2015)
proposed a multi-depot Location-Routing problem model. They formulated the
problem in order to determine the location of emergency warehouses and construct
the optimal routes for delivering relief goods from these warehouses to injured
people. They considered some effective factors such as failure in the network, such as
road failures and the penalty cost for uncovered demands, and developed a local
search algorithm to solve the problem. Wohlgemuth et al. (2012) introduced an
12
improved and applicable problem in which candidate emergency facilities can both
receive and send goods in a disaster. They considered vehicle routing and planning
for transportation and existence of the relief agencies with the aim of avoiding delays
in delivering and maximizing required equipment for service. Shen et al. (2009)
considered the problem of vehicle routing in the context of an emergency
bioterrorism. They provided a two-stage model for a disaster. In the first stage, which
is called the planning stage, the optimal routes are determined. In the second stage,
when some information is available, the planning is modified according to the
updated information. By formulating the problem, they used a mixed-integer
programming and provided an approximate method to solve the problem. Bozorgi-
Amiri et al. (2013) proposed a robust model for supplying and distributing relief in a
disaster. They considered the uncertainty factor in supply and purchase costs with the
goal of minimizing total cost in a relief supply chain and maximizing satisfaction
levels.
3. D
ISTRIBUTION
Some researchers developed models just for relief distribution operations. For
example, Tzeng et al. (2007) proposed a relief distribution model using a multi-
objective planning. Productivity has been designed with a goal to minimize travelling
time and travelling costs and fair has been considered with a goal to minimize the
level of maximum dissatisfaction. Sheu (2014) developed a new approach in a
concentrated relief distribution model that the post-incident psychological factors,
such as emotional cognition, considered the live person's attitude toward the injured
as an effective factor. They considered the objective function by maximizing the
level of psychological satisfaction of survivors during emergency logistics
operations. Afshar and Haqhani (2012) recommended an integrated mathematical
model that controlled a different flow of relief goods in large quantities during a
disaster. The model aims to send disaster relief goods to the maximum number of
people as quickly as possible to save time. The objective function is to maximize
survivors and minimize total cost. Lin et al. (2011) proposed a logistics model that
prioritized deliveries during a disaster with the aim of minimizing total response
time. They considered a soft-time window with multi-period routing and explained
the results to prioritize delivery during relief operations. Vitoriano et al. (2009)
proposed a model for logistics operations with the goal of minimizing total costs,
minimizing the maximum probability of road failures, and maximizing the minimum
13
reliability of the connections and solved using goal programming method. Chen et al.
(2011) developed a disaster distribution model for post-disaster planning based on
geographic information systems with the goal of minimizing relief and resource
allocation. Liberatore et al. (2014) considered a new point view for distributing
emergency products. They suggested that they would be unsafe by using
constructions, such as roads and bridges after a disaster occurred. They developed a
model to improve the damaged elements of the distribution network with the
objective function of maximizing demand satisfaction. All aids and reliefs are
presented to the affected country through their berths and airports, then, they are
transferred to a large warehouse. They are classified in their large warehouse and
transported to the central warehouse. In the central warehouse, requests are collected
from regional distribution centers and relief supplies are accordingly dispatched.
Relief supplies are delivered to the affected people from regional distribution centers.
As the situation in the affected region is undesirable, distribution management from
the regional distribution center to the affected people plays an important role in
satisfying the demand.
Dean and Nair (2014) developed a model aimed at the effective evacuation of
victims and transported them to various hospitals with the objective function of
maximizing the number of remnants of the disaster. Wang et al. (2012) developed a
zone-based simulation model for a city and emergency response simulation in a
massive disaster using the GIS. Wilson et al. (2013) developed a hybrid model for
processing casualties with the goal of minimizing losses and suffering and
maximizing productivity. They used a meta-heuristic algorithm to solve the model.
Salman and Gül (2014) developed a mixed-integer programming model in order to
allocate the capacity and transfer losses with the goals of minimizing waiting times
and the cost of establishing a new vehicle. Apte et al. (2014) conduct a study in
Columbia in order to develop a tool to help planners to locate the point of collecting
casualties in a affected area with the aims of maximizing the loss control and
minimizing the traveling time for transferring the injured people to a shelter.
Hu and Sheu (2013) developed a model includes reverse logistics costs and
psychic costs, with the aim of minimizing the procurement cost of logistics,
environmental and operational costs and psychic costs. When a disaster occurs, help
from donor countries and international organizations are sent to the affected country.
14
To manage these relief supplies, Adivar and Mert (2010) and Camacho-Vallejo et al.
(2015) proposed models that aimed to minimize reaction time and procurement cost.
4. D
ISCHARGE
Many models have been developed to evacuate public transportation. Sheu and
Pan (2014) considered public evacuation as a part of an integrated emergency
network model. In this model, they aimed to minimize travelled distance, operational
costs, and psychic costs. They transformed sheltered networks, medical networks and
integrated distribution networks into an integrated concentrated emergency network.
Whenever there is a disaster like a flood, governments tries moving people away
from high-risk areas. In such a situation, the most common issue is the availability of
a sufficient number of bus drivers. By observing this issue, Morgul et al. (2013)
proposed two stochastic models to determine the additional drivers required during
an emergency evacuation operation, with the aim of minimizing the cost of
unsatisfied demand and the cost of additional personnel for recruitment. Naghawi and
Wolshon (2012), also developed a bus-based evacuation model during a disaster, in
which the impact of bus deployment on the operation in the road network for a
special region was studied.
With regard to private evacuation research, Chiu and Zheng's study (2007)
describes a cell transfer model in which a particular group, for example, physicians
have a higher priority during the evacuation process with the goal of minimizing the
total priority of travelling time from all other groups. Hsu and Peeta (2014)
developed a model based on important information for successful private evacuation
operations. By using behavioral strategies and classified information, they have
determined the supply-demand interaction with the aim of minimizing the difference
between the desired and the forecasted ratios and of the evacuation. In the other
research, Hsu and Pita (2014) proposed an evacuation operation based on a hazardous
zone. They design the hazard zone based on disaster characteristics, traffic pattern
and network supply conditions.
Most of these issues are investigated in various studies with respect to
complicated planning, which are subdivisions of issues with mathematical models.
According to the literature review, most studies are related to the reduction (the
effects of a disaster) and handling phases.
15
Essential actions and reactions are always considered in a pre-disaster and post-
disaster phases such conservation of life and human health, material and immaterial
factors. From this point of view, the examined area is divided into areas for relief
from the perspective of the disaster, and there are potential health-care centers for
relief and rehabilitation operations.
As outlined above, the following figure illustrates the whole issue under
consideration:
Fig. 4. A schematic scheme of the problem
The symbols in Fig. 4 are in accordance with Table 1:
Table 1. The definitions of the symbols
Symbols
Descriptions
Potential demand point
Potential health
rehabilitation center
Potential emergency
station
Route
16
5. C
ONCLUSION
In this book, the establishment of emergency centers with consideration of
demand satisfaction by the appropriate distribution of ambulances and the choice of
the direction of movement of ambulances is examined. The establishment of
emergency centers, the allocation of ambulances and the selection of their route of
movement are also under consideration in the preparation phase for the disaster. Due
to the uncertainty about some values of the disaster logistics issue, it has also been
considered in formulating issues of this importance.
The models available for such an issue often focus on the allocation, location, and
selection of paths. So far, considering the real conditions, such as problem stability,
the phases of solution, the type of demand satisfaction, and integration in less
research, have been observed. Today, researchers are looking to develop models that
are more in line with the real world and therefore have more efficiency and
conformity. Therefore, the above mentioned problem is considered algorithmically in
this book. In other words, it is designed to solve the algorithmic disaster problem in
order to identify and solve the problem step by step. In the proposed algorithm, the
stability, control, and math model are investigated according to the context of the
urban disaster. Finally, depending on the assumptions of the problem, it is formulated
and attempts to achieve optimal or near optimal values. Finally, the problem analysis
is tailored to the type of solution.
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18
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20
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21
C
HAPTER
2
A
S
UPPORTIVE
H
UMAN
-B
ASED
R
OBUST
H
UMANITARIAN
L
OGISTICS
M
ODEL
E
SPECIALLY
C
ONSIDERING TO
D
ISASTER
M
ANAGEMENT
(C
ASE
S
TUDY
:
K
ASHAN
,
I
RAN
)
Abstract
Natural and unnatural events such as accidents, diseases, and disasters may be
occurred with a human or inhuman origin and threatening to the lives of many
people. There should be pre-planned actions for urban relief logistics to protect
people life that is a nonrenewable valuable asset. In this chapter, a multi-objective
multi-level robust model based on fair competitive disaster management is presented
to locate emergency stations, determine the quantity of manpower and ambulances in
each station in order to cover the total demand of the affected areas after occurring an
event. Also, this model is integrated because of considering employment, deposal and
the insurance of manpower, route destructions, supporting the stations from each
other with the aims of maximizing demand covering and emergency station
supporting, minimizing total cost, and minimizing total time of service with a
dynamic approach to protect people. By considering some real assumptions such as
supporting of demand point, route destructions and special emergency routes make
the model more responsive and more applicable. To solve the problem and do the
sensitivity analysis, we present an NSGA-II algorithm to deal with multi-
objectiveness of the problem. A -Constraint method is proposed to evaluate the
performance of the proposed algorithm. Finally, a case study in Kashan is analyzed to
show the applicability of the model.
22
1. I
NTRODUCTION
Response planning to meet the needs of people during natural disasters such as
hurricanes, floods, and earthquakes is challenging because resources of more than
one type have to be delivered to the demand areas in a timely manner and in right
quantities. It also requires a carefully planned process of acquiring and distributing
the resources. This poses the further challenge as the demand in such disasters may
vary over time in terms of the type of materials (or service) or in terms of quantity.
Disasters are characterized by uncertainty and unpredictability; and therefore,
demand may 25 change rapidly in such an environment (Swiss, 2015). Additionally,
demand for resources in one location at a period may not exist in the next period; or,
a particular location may have a very high demand in the subsequent period. The
performance of emergency services is measured in terms of the response time and the
total logistics cost (Shafia et al, 2013). Therefore, if demand is not met on time, the
performance of service will degrade. In order to address such a situation, a flexible
and efficient emergency response system should be developed so that both social and
economic losses due to the aftermath of disasters could be minimized (Balcik et al,
2008). Therefore, location and allocation of relief distribution facilities become
critical for an effective emergency response planning besides ambulance and
helicopter routing and assignment problem (Danya et al, 2015).
The researches in the humanitarian logistics operation have different levels
including one-level (Overstreet et al, 2011), two-level (Tzeng et al, 2007) and multi-
level (Balcik et al, 2008). The number of facilities in this category of problems
includes single-facility and multi-facilities (Jotshi et al, 2009). The scale of transport
fleet is investigated for one vehicle and several vehicles (Tzeng et al, 2007).
Ratick et al, (2009) declare that the emergency request is probable and fuzzy in
the certain humanitarian logistics operation. The duration of travel for satisfying the
certain/stochastic request has been investigated by them. Mete and Zabinsky (2010)
showed that accessibility of facilities and paths is studied by two criteria of certain
and stochastic. The limitation of facilities capacity in all types of models is active and
sometimes passive. The emergency vehicles are considered in two types of with
capacity and without capacity. The time window in considered in three categories of
unlimited time (Mete and Zabinsky, 2010), soft time window (Balcick and Neamon,
23
2008) and hard time window (ozdamar, et al., 2004). The humanitarian logistics
model can perform the delivery operation (Mete and Zabinsky, 2010, Babaei. 2017),
loading (Batta, 2009) and simultaneous delivery and loading (Campbell et al., 2008)
in the stations. The type of path is defined in two types of open (Jotshi et al, 2009)
and closed (Hale and Moberg, 2005). The location of customers in the network needs
routing of nodes (Mete and Zabinsky, 2010; Sheu, 2007; Alinaghian et al, 2014;
Mirmohammadi et al, 2017; Tirkolaee and Goli, 2016) or edges (Campbell et al,
2008; Tirkolaee et al, 2016; Tirkolaee and Goli, 2016). The type of objective
functions is cost (Rawls et al, 2010), humanitarian (Jotshi, et al, 2009) or the
combination of the two which is single-objective (Ozdamar et al, 2004; Mete and
Zabinsky, 2010), two or multiple objective (Mete and Zabinsky, 2010). These models
can be employed in the disaster such as an earthquake (ozdamar et al, 2004; Mete and
Zabinsky, 2010), flood (Doerner et al, 2008) and others. The method of solving these
models are precise (Balcick and Neamon, 2008), meta-heuristic (Paul and Batta,
2008) of heuristic (Doerner et al, 2008). The decision-making levels in these
problems are strategic (Doerner et al, 2008), tactical (Mete and Zabinsky, 2010) or
operational (Mete and Zabinsky, 2010; Ozdamar, et al., 2004). The time horizon in
these issues is static (Doerner et al, 2008; Mete and Zabinsky, 2010) or dynamic
(ozdamar, et al., 2004). The type of consignment in the humanitarian logistics
problems can be goods (Ozdamar et al, 2004; Mete and Zabinsky, 2010), human
beings (Drezner, 2007) or a combination of these two. In some other logistics papers,
the investigation is conducted based on Markov and semi-Markov chain and
investigation the air emergency and considering that the problem is dynamic in order
to control the fluctuations (Cheng, 2015).
The emergency facility location issues are employed in the below papers:
Modeling of the location problems of emergency facilities with the world war two
has emerged in the scientific discussions and the researchers pay special attention to
the research in this field. The 1970s decade can be considered the commencement of
modeling of emergency facility location. In this decade, in the beginning, the primary
models of LSCP and MCLP (Moeini et al, 2015) has been created which the most of
the emergency facility location models refer to them. The first model used
minimizing the response time instead of objective envelopment function (Swoveland
et al, 1973). Berlin and Liebman (1974) presented the first dynamic model simply in
24
1974. Also, Schilling et al (1979) represented the FLEET (Facility Location
Equipment Emplacement Technique) and TEAM (Tandem Equipment Allocation
Model) model with several types of servers.
In the years between 1970 until 1980 most of the models have been considered as
certain and uncertainty was less considered in the parameters. The first probable
model has been created in 1978 (Aly and White, 1978) and in the 1980s decade most
of the researchers considered the models to be probable and parameters to be random.
Also in this period the models with supportive cover (Hogan and Revelle, 1986) were
most in attention. One of the most important probable with envelopment objective
function which provides a field for using of probable models was presented by
Daskin (1983). Moreover, in this period, location-assignment (Pirkul, 1988) models
were considered. The first review model which categorized the emergency facilities
models was presented by ReVelle (1989). Also, Matsutomi and Ishii (1992) for the
first time employed the fuzzy concept in the modeling and solving of emergency
facility location problems. The first model with considering the reliability was
presented by Ball and Lin (1993). Also, Marianov and Serra (1996) used the queue
theory in their model.
Between the years 1990 until 2000 the researchers developed the existing models
by focusing on these models. From the year 2000 onward there was great attention to
the solving method and in these years the multiple objective models were in attention.
In the year 2004, the partial cover model was presented by Karasakal brothers (2004)
which solve the main problem of MCLP model. Erkut et al, (2009) evaluated and
developed the MCLP in 4 different states. Berman et al, (2007) used the transfer
point concept in their paper for the first time. Also, Erkut et al, (2007) presented the
significant model of MSLP with the development and troubleshooting. Also
according to the solution method caused the using of heuristic and meta-heuristic
models in the papers in recent years. For instance, Rajagopalan et al, (2007)
compared 4 meta-heuristic models for solving the MEXCLP problem which was
presented by Daskin (1983).
For example, the distribution and emergency transport issues are used in below
papers.
25
Different models in the fields of disaster based on the transport and distribution on
the humanitarian logistics have been investigated which are explained in the
following. In the files of transportation, the models are based on cost, time and
number.
The models based on the cost include the cost of travel which is comprised of
maintenance and repair and distance and choosing the source with regards to the
capacity and the supported area and the extent of flow under evaluation (Ben-Tal,
2011).
Based on the purpose we should minimize the time of travel and the loading time
with regards to the path and extent of transportation and traffic flow should be
evaluated to introduce effective factors in the decision-making (Campos, 2012).
In terms of shortening the distance with the request and travel time constraints and
the road damages the third model is investigated (Shen et al, 2008) with regards to
the fourth basis which is the number of cases that the request is not satisfied, the
number of needed emergency units, the total number of covered requests, minimizing
the risk and increasing the survival of people, decreasing the waiting time of injured
people for help, the volume of traffic and capacity of havens based on the number of
vehicle, request, the covered area, cost and time of travel has been created (Campos,
2012).
The locating and assigning in the transport of humanitarian logistics is with the
purpose of minimizing the transportation time with regards to the series presenting,
emergency requests and the budget and resource constraints to increase the lifetime
of the patients (Edrissi, 2013).
But based on the distribution, humanitarian logistics models have objectives such
as cost which includes minimizing the travel costs, the distribution cost and distance
which their space is proportional to the extent of supply (Liberatore et al, 2014).
With the purpose of minimizing the transportation time and the distribution time
of necessary goods and the service time some papers have been researched (Vitoriano
et al, 2011) Satisfying the demand and the number of emergency units needed with
26
regards to the number of vehicles, type of vehicles and the balance flow provided a
basis for the distribution of the logistics models (Vitoriano et al, 2011).
Locating and assigning can be investigated based on the cost, time and number
factors. With the purpose of decreasing the travel cost, the distribution cost and
shortening the distance for the factor of cost a factor of time, decreasing the
transportation and distribution cost, the demand factor has been investigated.
The capacity of facilities is one of the main items in these problems with regards
to the satisfaction of demand. Therefore issues such as the extent of stock and the
resource flow and the number of injured are from this category (Davis, 2013).
Considering the supportive functions for emergency stations from each other,
construction of special emergency routes in order to have better service, route
destructions, ambulance availability, employment-deposal and insurance of
manpower, preventive actions for too many changes in employing-deposing of
manpower.
2. P
ROBLEM DEFINITION AND MATHEMATICAL MODEL
As it was mentioned in the previous section, an integrated dynamic multi-
objective multi-level robust model is developed considering scenario-based policies.
The scenarios are generated by the intensity of the disaster. As much as the index s
becomes bigger, the intensity of the disaster gets a higher value. This model is to
locating temporary and permanent emergency stations, assigning ambulances to
them, determining optimal routes between emergency stations, demand points and
hospitals. Temporary and permanent emergency stations are different in the amount
of capacity. By locating these stations, some stations will have supportive functions
beside their services for covering demand points. On the other hand, the locations for
establishing emergency stations should be determined according to the shortest path
in terms of time considering for transferring the injured to the hospital, and also
should precede other unestablished stations in terms of time distance from the
established stations to provide services in emergency conditions. The proposed model
is studied with a dynamic approach, multi-period time horizon, and it is a scenario-
based robust model that considers uncertainty on the number of established
27
emergency stations. The target is to cover the demand of a period just in the same
period, and if it is not possible, it can be covered in the next periods by incurring
penalty costs and losing some demand points. Moreover, if temporary stations are
established in the specific periods, they can be transformed to the permanent stations
by considering maximization of the reliability and the capacity of response.
Employment, deposal, and insurance of the manpower and their relative costs are
added to the model. Also, route destructions and ambulance breakdowns are
considered. If determined optimal routes are not able to provide service within a
given standard time, other routes namely emergency routes are constructed (on the
normal routes) to transfer the injured to the hospitals within a certain time that is less
than or equal to the standard time.
In this paper, disaster management is studied by considering seven main
components of management principles including 1) Planning 2) Organization 3)
Employees 4) Employer (Leader) 5) Coordination 6) Reporting and 7) Budgeting.
Planning in disaster, an organization of disaster for decreasing and coping with
injuries and incidents, employees, training, employers, coordination of components to
be integrated into coping with disaster, appropriate reporting and establishing an
optimal pattern for budgeting are such indicators of disaster management for each
emergency station. In each station, resource assignment to the indicators of disaster
management depends on establishing cost and effectiveness of each indicator. Thus,
all indicators are in a competition with each other in order to achieve more resource
to make more responsible service in each emergency station. However, two main
topics have been considered critical according to the model namely fairness and
competition in line with emergency stations. According to this model, the difference
between resources assigned to disaster management should not be out of minimum
and maximum ranges in order to observe minimum standard and maximum facilities
for each emergency station that leads to being fair with other stations. On the other
hand, maximizing the difference between the assigned resources for developing
emergency stations is considered in order to create a competition between these
stations. Therefore, fairness and competition are implemented in the model
simultaneously to have more optimal emergency service system.
Briefly, the objectives can be classified into three categories: 1) Maximizing
demand covering and the relative supporting demand points. 2) Minimizing total
28
cost. 3) Maximizing the efficiency of disaster management and 4) Minimizing total
time of the system.
Motivation problem in disaster management is a critical problem. Sometimes
there are no appropriate consequences despite owning adequate resources, and
sometimes there are significant consequences by possessing lower resources and
higher motivation. This fact has been implemented to the model, thus disaster
management has been merged with motivation level to deal with disaster and sense of
empowerment. This sense of empowerment and motivation is considered as chance
feeling in order to cope with disaster. Since the amount of chance feeling is unknown
and uncertain, robust optimization is applied according to the (Ben-Tal, 1998), and a
changing radius has been considered to show uncertainty in the amount of this
feeling.
As far as the proposed model is scenario-based, Mulvey approach is applied to
have a robust model (Mulvey, 1995). To deal with this impreciseness, the robust
optimization approach is employed to design a system which is immunized against all
or most realizations of the uncertain values. A solution to an optimization model is
defined as: solution robust if it remains "close" to optimal for all scenarios of the
input data, and model robust if it remains "almost" feasible for all data scenarios. We
then develop a general model formulation, called robust optimization (RO), that
explicitly incorporates the conflicting objectives of solution and model robustness
(Mulvey, 1995).The robust models are used in conjunction with a deterministic
model which selects the core variables. Additional constraints are imposed on total
costs during solving the model.
A complete list of sets, parameters, variables, and other assumptions used for
modeling are briefly listed below.
Indices
Set of candidate points for establishing shelter facilities
Set of demand zones
Set of health recovery centers
Set of scenarios
k
Set of supporter
t
Set of time periods
29
Parameters
Occurrence probability of scenario s.
Demand of ith point from emergency station j in sth scenario and tth
period.
The establishment cost of the route from emergency station j to
demand point i and hospital h.
The establishment cost of the emergency route from emergency
stationj to demand point i and hospital h.
Assigning cost of the ambulances to the stationj.
The establishment cost of the permanent emergency stationj.
The establishment cost of the temporary emergency stationj in tth
period.
The establishment cost of the hospital h.
The employment cost of manpower for jth emergency station in tth
period.
Penalty cost for employing and deposing of the manpower in tth
period.
The cost of considering supporter k for demand point i.
Route destruction cost between emergency stationj to demand point i
and hospital hin tth period.
The insurance covering cost for manpower of stationj in tth period.
Penalty cost of being uncovered of demand point i by stationj in sth
scenario and tth period.
Penalty cost of not established permanent emergency station.
Penalty cost of delay in covering demand point i.
BUDG
Total available budget.
Profit gained by in time demand covering for point i.
Route traversing time between ith demand point, hospital hand station
j in tth period.
Standard time.
A binary matrix, it equals to 1 when demand point i is covered by
station j in sth scenario, otherwise, it is 0.
Total number of permanent emergency stations.
Total number of temporary emergency stations.
E
Total number of emergency routes.
The proportion of demand covered by permanent emergency stations.
The required covering percent of demand point i in sth scenario and
30
tth period.
A binary matrix, it equals to 1 when hospital h is established,
otherwise, it is 0.
Accessibility time of emergency stations to each other.
Equivalent rate of station demand to manpower.
Minimum proportion of covered demand.
The proportion of demand covered by temporary emergency stations.
The probability of route destruction equals to that demand percent of
ith demand point covered by station j to transfer to hospital h in tth
period.
The probability of accessibility to the ambulances of station j in sth
scenario and tth period.
The probability of surviving in each scenario.
Weight of scenario effects on each other.
Weight of deviation from feasible space.
An optional large number
Planning cost in disaster
Organization cost in disaster
Employee preparation cost in disaster
Employer preparation cost in disaster
Coordination cost in disaster
Reporting cost in disaster
Establishment cost of an appropriate pattern for budgeting
Conversion ratio of manpower to components of disaster management
Effectiveness of planning in disaster
Effectiveness of organization in disaster
Effectiveness of employee preparation in disaster
Effectiveness of employer preparation in disaster
Effectiveness of coordination in disaster
Effectiveness of reporting in disaster
Effectiveness of establishing an appropriate pattern for budgeting in
disaster
Tolerance of deviation from disaster management principles in each
station against other stations
Importance weight of uncertainty component in chance feeling
Uncertainty value in occurrence probability of chance feeling
Chance feeling in emergency station j in period t under scenario s
31
Variables
A binary variable, it equals to 1 when demand point i is covered in sth
scenario and tth period, otherwise, it is 0.
A binary variable, it equals to 1 when demand point i is covered by
station j in sth scenario and tth period, otherwise, it is 0.
A binary variable, it equals to 1 when demand point i is not covered
by station j in sth scenario and tth period, otherwise, it is 0.
A binary variable, it equals to 1 when emergency station j is
established, otherwise, it is 0.
A binary variable, it equals to 1 when temporary emergency station j
is established in tth period, otherwise, it is 0.
A binary variable, it equals to 1 when a route between demand point
i,and jth station and the hospital h in tth period is constructed,
otherwise, it is 0.
A binary variable, it equals to 1 when an emergency route between
demand point i,and jth station and the hospital h in tth period is
constructed, otherwise, it is 0.
A binary variable, it equals to 1 when hospital h is established,
otherwise, it is 0.
A binary variable, it equals to 1 when demand point I is supported by
supporter k in tth period, otherwise, it is 0.
The number of the assigned ambulances to the jth emergency station
in sth scenario and tth period.
The number of the employed manpower to the jth emergency station
in sth scenario and tth period.
The difference between the number of the employed and deposed
manpower in the jth emergency station in sth scenario and tth period.
The number of destroyed routes between demand point i,jth station
and the hospital h in tth period and sth scenario.
A binary variable, it equals to 1 when manpower of station j is under
insurance covering in tth period, otherwise, it is 0.
The number of in time demand covering.
The number of postponed demand covering.
Minimum required periods for transforming a temporary station to an
emergency station.
Required time for supporting other stations by emergency station j in
tth period.
Deviation variable from feasible space.
32
Robust linearizer variable.
Amount of resource assignment for planning in disaster in station j
and period t under scenario s
Amount of resource assignment for organizing in disaster in station j
and period t under scenario s
Amount of resource assignment for training of employees in disaster
in station j and period t under scenario s
Amount of resource assignment for preparing of employer in disaster
in station j and period t under scenario s
Amount of resource assignment for coordinating in disaster in station
j and period t under scenario s
Amount of resource assignment for constituting an appropriate
reporting system in disaster in station j and period t under scenario s
Amount of resource assignment for establishing an appropriate
budgeting pattern in disaster in station j and period t under scenario s
Amount of resource assignment for establishing disaster management
system in disaster in station j and period t under scenario s
Competition capability of station j and period t under scenario s
Free variables indicating chance feeling value
Our model and constraints under the proposed consumptions are as below:
Max
+
(1)
33
Min
+
+
+
+
+
(
-
,
+ 2
) +
+
+
+
+
+
+
+
+
+
,-1
+
-
+ (
+
+
+
+
+
+
)
(2)
Min
+
(3)
+
=
+
, , ,
(4)
+
+ (
(
-1
-1
-
-1
))
, ,
(5)
+
= 1
, , ,
(6)
(7)
(8)
- 0
(9)
34
,-1
(10)
(11)
+
= 1
, , ,
(12)
(13)
(14)
, ,
(15)
+
,
,
(16)
,
,
(17)
+
, ,
,
(18)
, ,
, ,
(19)
+
, ,
,
(20)
+
1
(21)
,
+
,
,
(22)
-
, ,
,
(23)
E
(24)
(
+
)
, ,
(25)
+
+
+
+
+
+
, ,
(26)
,
,
,
,
,
,
> 0
, ,
(27)
=
+
+
+
+
+
+
, ,
(28)
-
, , ,
(29)
-
-
, , ,
(30)
-
=
, , ,
(31)
- (
)
(32)
,
(33)
-
-1
,
(34)
-1
-
,
(35)
35
+
,
(36)
1
,
(37)
+
+
+
+
+
(
-
,
+ 2
)
+
+
+
+
+
+
+
+
+
+
(1 + )
,-1
+
-
(38)
-
,
+
0
(39)
36
,
,
,
,
,
,
,
,
,
{0,1}
, ,
, , , (40)
,
,
,
,
,
,
,
,
,
,
,
,
0
, ,
(41)
0 ,
, , , ,
(42)
, , ,
, ;
, , ,
(43)
1) The first objective consists of two parts. In the first part, it wants to have a
maximum demand covering (demand points are those population requiring
emergency services). In the second part, it is to maximize the number of covering
emergency stations as supporting centers.
2) The second objective consists of eighteenth parts. The first part is related to the
determination of the minimal-cost routes. The second part is to minimize assignment
costs of the ambulances to the stations. The third part is to minimize the
establishment costs of the permanent stations. The fourth part is to minimize the
establishment costs of the temporary stations. Parts 5, 6, and 7 are related to the
robustness costs of the model. In these parts, the assignment probability of the
demand points that leads to establishing the station, the effect of different scenarios
on each other, and overall changes made in feasible space are minimized
respectively. Eights part is related to minimizing the establishment costs of the
hospitals. Ninth part considers total employment cost of manpower. Tenth part
minimizes the total change of employment and deposal of manpower in each period.
Eleventh part minimizes supporting cost for demand points. Twelfth part minimizes
construction costs of emergency routes. Thirteenth part minimizes incurring costs for
route destructions. Fourteenth part is to minimize penalty costs of non-assigned
demand to the emergency stations in each period. In the fifteenth part, penalty costs
of non-established permanent emergency stations will be minimized due to
establishing more permanent stations to be more responsive. Sixteenth part is
associated with the penalty cost of late demand covering that shall be minimized. In
the seventeenth part, profit values should be considered because of in time demand
covering. And in the last constituting part of the second objective, establishment cost
of disaster management shall be minimized.
3) In the third objective, two issues would be followed. Firs, routes which make
lower service time will be determined in order to transfer the injured to the hospitals.
Second, emergency stations have higher priority to be established because of
37
providing better supporting service to the other stations in emergency conditions
besides fast transferring of the injured to the hospitals.
4) This constraint determines which permanent /temporary emergency stations
should be established. This constraint considers more established stations using the
deviation from feasible space in order to have a better response to demand points.
5) Covering amount of each demand point is determined based on demand value
of current period and previous periods in which demand points are uncovered. If
there is a demand point uncovered in a period, it will be covered in the next period
according to the remaining demand value.
6) Each demand point is covered in each related period, or it will be covered in
the next periods if it exits.
7) Covering amount in a period with positive demand value is determined.
8) Covering amount with the delay in service is determined.
9) In time covering amount should be higher than covering amount with the
delay in service.
10) It demonstrates maximum period numbers that temporary station will be
established.
11) In lieu of establishing the temporary emergency station in periods, that station
would be transformed to a permanent one.
12) Temporary or permanent emergency stations have a chance to be established
at each point.
13) It determines the number of the potential emergency stations be established as
permanent stations.
14) It determines the number of the potential emergency stations be established as
temporary stations.
15) All demand points should be covered at least by an emergency station.
16) The number of available ambulances in each station is a proportion of the
asked demand from the established station.
17) It determines the minimum needed ambulances to provide service to each
demand point in each period.
18) There should be some constructed routes in order to transfer the destruction
probability of the routes.
19) The number of destroyed routes will be determined according to a given
percentage of demand.
38
20) In order to determine optimal routes, there should be a pre-established
hospital, otherwise required hospital(s) should be established.
21) Defined nodes on the network are allowed to have one established emergency
stations, max.
22) This is an important advantage for emergency stations to have a short time
access to the other emergency stations in order to provide fast service. Thus, the
length of service of service time is determined by this constraint for each station. Tjk
can be assumed inconsiderable to have more supple and simplified model.
23) Constructed routes should be able to take the injured to the hospital within a
given standard time, otherwise, emergency routes will be constructed to observe this
allowable time.
24) There are a limited number of emergency routes considered to be constructed
in the planning time horizon.
25) The number of manpower working in each emergency station is determined
by this constraint in each period.
26) Resource assigned to the components of disaster management is determined
according to manpower conversion coefficient in each station in each period and in
each scenario.
27) All components of disaster management shall have the lowest value for
activities.
28) The amount of investment in each station in each period and in each scenario
is determined.
29) The maximum allowable difference in the amount of investment for disaster
management of emergency stations is determined.
30) The minimum allowable difference in an amount of investment is determined
by disaster management of emergency stations. Equation (30) and Equation (31) are
related to the fairness. In other words, an amount of assigned resources to the stations
are fair.
31) Difference between resource assigned to the stations in each period and in
each scenario is determined. This difference will be maximized in objective function
in order to have development in each station by considering fairness and competition.
32) Chance feeling and motivation are determined with respect to the uncertain
nature of these parameters.
33) All manpower working in emergency stations should be under insurance
cover.
39
34) The number of employed manpower is determined in each period by this
constraint.
35) The number of deposed manpower is determined in each period by this
constraint.
36) The number of demand point supporter is determined by this constraint.
37) Demand point is covered only by a limited number of emergency stations.
38) It shows the total available budget limitation.
39) It is related to the robust linearization constraint according to the Mulvey's
approach (Mulvey et al, 1995).
41 to 44) They show the type of different variables.
3.
-C
ONSTRAINT
M
ETHOD
This Method can transform a multi-objective problem into a single-objective one
with additional constraints, where the objective with the highest priority is
maintained as the main objective function (MOF) and the others are transformed into
the constraints (Mavrotas and George, 2009). In fact, a multi-objective problem is
solved in the form of a single one with the use of GAMs software. For instance,
application of the -Constraint Method can be written through Equation (44), as
follows, for the given problem.
(44)
Min f
1
(X)
f
2
(X)
2
...
f
n
(X)
n
In the proposed problem, we have:
(45)
Maxf=f
1
f
2
(X)
2
f
3
(X)
3
As can be seen, f1 has been remained in the MOF, representing maximal covering,
and f2 and f3 have been transformed into the constraints.
Briefly, the procedure of the mentioned -Constraint Method is as below:
40
1) Choose one of the objective functions as MOF. In this research, the first
objective function is chosen as MOF because, in a disaster situation, the highest
priority is to cure the injuries or provide the emergency services.
2) Consider three break points for the objectives f2 and f3, so that nine Pareto
points can be generated for each problem.
3) The distance between two optimal values of objectives f2 and f3 are divided
into a number of pre-determined parts based on the break points.
4) Solve the problem with its MOF, and report the objective function values to
determine Pareto front (see Table 1).
Also, by changing the value of epsilon, different Pareto solutions can be
generated. In this research, to avoid redundancy and unnecessary data, nine non-
dominated Pareto solutions are created and presented. In other words, there were a
large number of Pareto solutions to be created and by increasing the problem size,
this number increases exponentially. In this research, due to the fact that the Pareto
solutions are following the same trend and there is no unpredictable point or trend in
the Pareto front, it has relied on just a set of Pareto solutions which show the
uniformity and coverage of the Pareto front.
Table 1. Different vector choice in each break point.
Break Point
Constraint vector choice
2
3
1
1988628.834*
3272.635*
2
2386354.601
3665.3512
3
2406240.889
3894.43565
*Obtained by solving single-objective problem
Break points determine the number of different . If we consider 3 breakpoints for
objective 2, we consider three different values for 2 for f2. Analogously, we have
this rule for the third objective
It is worthy to say the model was solved through GAMS software with the use of
Baron Solver in 3600 seconds. The specifications of the system which was used to
solve the problem, are shown in Table 2.
41
Table 2. Hardware specification.
Intel® CoreTM i7-2600 CPU @ 3.40 GHz
Processor
4.00 GB(3.24 GB usable)
Installed memory(RAM)
32-bit Operating System
System type
4. M
ETAHEURISTIC APPROACH
The proposed exact method is not capable of solving large scale problem in a
reasonable time. Thus, in order to solve the problem in the least time possible a Non-
dominated sorting Genetic Algorithm is used.
The objective of the NSGA-II algorithm is to improve the adaptive fit of a
population of candidate solutions to a Pareto front constrained by a set of objective
functions (Deb et al, 2002). The algorithm uses an evolutionary process with
surrogates for evolutionary operators including selection, genetic crossover, and
genetic mutation. The population is sorted into a hierarchy of sub-populations based
on the ordering of Pareto dominance. The similarity between members of each sub-
group is evaluated on the Pareto front, and the resulting groups and similarity
measures are used to promote a diverse front of non-dominated solutions.
By the way, in this section, the proposed NSGA-II algorithm is introduced and its
elements are described. Then, the performance of the proposed algorithm is
compared with the results of -Constraint and it is validated to examine whether the
proposed metaheuristic approach is efficient. Finally, a large-scale sample (a case
study in Kashan) is solved and the corresponding results and Pareto fronts are
presented. The proposed NSGA-II algorithm was coded and implemented in Matlab
Software (Matlab R2010a).
4.1. E
LEMENTS OF
G
ENETIC ALGORITHM
Chromosome: here, two chromosomes are defined to form the solution space.
A binary chromosome is used with J*T cells where J and T are the potential locations
of emergency stations and time periods, respectively. Obviously, if temporary station j
is established = in period t, the corresponding cell in the chromosome will be one,
otherwise zero. In addition, a second binary chromosome is also defined with I*S*T
42
cells. So, if demand i is covered in scenario s and time period t, the related cell in
chromosome will be one, otherwise zero. Fig. 1 represents the applied chromosome
for NSGA-II algorithm.
t
1
t
2
t
T
m
M
...
...
...
...
j
1
j
2
j
J
t
1
t
1
t
2
t
2
t
T
t
T
t
1
t
1
t
1
t
1
t
1
t
1
t
2
t
2
t
2
t
2
t
2
t
2
t
T
t
T
t
T
t
T
t
T
...
...
...
...
...
...
...
...
...
...
s
1
s
1
s
1
s
S
s
S
s
S
i
1
i
2
i
I
Fig. 1. Applied chromosome for NSGA-II algorithm.
Initial population: A group of chromosome generates the initial population. In
this research, the initial population is considered equal to 400 and they are generated
randomly.
Fitness function: the objective functions of the mathematical model are
considered as the fitness function for NSGA-II algorithm.
Crossover operator: One-point crossover is used. A cell is selected randomly
and the first part of the first parent and the second part of the second parent form a
new chromosome as an offspring. Fig. 2 and Fig. 3 represent the Crossover operator.
1
0
1
0
1
0
0
m
M
0
1
0
1
1
Parent 1
0
1
0
0
0
0
0
m
M
1
1
0
0
1
Parent 2
Offspring
1
0
0
0
0
0
0
0
0
0
1
1
Fig. 2. Crossover operator.
43
Mutation operator: A cell is selected randomly and the value of the cell is
reversed. For example, In Fig. 3, the last cell of the chromosome was selected
randomly. After the selection, the value of the cell was turned into 1.
1
0
1
0
1
0
0
m
M
0
1
0
1
1
1
0
1
0
1
0
0
m
M
0
1
0
1
0
Fig. 3. Mutation operator.
Stopping criterion: if the solution quality does not improve in last 60 iterations
the algorithm stops and the best obtain solution is reported.
4.2. P
ARAMETER ADJUSTMENT
To obtain the best performance of proposed NSGA-II, some of its necessary
parameters are needed to be adjusted. There are two methods to adjust the
parameters: (1) standard analysis of variance method (ANOVA), and (2) signal to
noise ratio method (S/N). The value of S/N represents the dispersion around a certain
value. In other words, it implies how our solutions have changed among the several
experiments.
In this research, in order to minimize the dispersion of objective functions, signal
to noise ratio of Taguchi method is used. S/N ratios describe noise factors that
accompanying controllable parameters (Yang et al, 1998).
To do this, three values are considered for crossover rate, mutation rate, and initial
population. These values are shown in Table 3.
Table 3. Considered values for the parameters of NSGA-II.
Values
Parameters
0.7, 0.8, 0.9
Crossover rate
0.1, 0.2, 0.3
Mutation rate
200, 250, 300
Initial population
44
By searching in the different Taguchi tables by means of Minitab statistical
software, the table related to the L27 presentation is selected for our purpose. After
testing the data of Table 3, the average rate of S/N for 27 states of Taguchi and the
optimal value of parameters of NSGA-II algorithm are shown in Fig. 4 and Table 4.
3
2
1
-13
-14
-15
-16
3
2
1
3
2
1
-13
-14
-15
-16
A
M
e
a
n
o
f
S
N
r
a
ti
o
s
B
C
Main Effects Plot for SN ratios
Data Means
Signal-to-noise: Smaller is better
Fig. 4. Results of Taguchi analysis.
Table 4. Optimal values for the parameters of NSGA-II.
Stopping criteria
Initial population
Mutation rate
Crossover rate
50
250
0.3
0.7
Due to the initial tests, stopping criteria is decided to be considered as 50
sequential iterations of the algorithm without improvement in the solution quality.
Therefore, there is no need to adjust this parameter by Taguchi design.
4.3. P
ROBLEM DESIGN
To solve the problem with the proposed algorithms, it is needed to generate some
sample instances. Due to this, three samples problem are designed and presented in
Table 5. Small and medium size instances were generated randomly and they are
used to validate the propose NSGA-II. Therefore, the value of parameters is selected
according to the given data in Table 6. Some of the parameters have a definite value,
45
but for some others, an interval is defined. The parameter takes the value in their
specified defines randomly.
After validation of the algorithm, large size instance is solved by means of NSGA-
II and the results are shown. Because we consider the large size instance as a case
study, therefore the data to solve the parameters were extracted previously and there
is no requirement of creating values for the parameters.
Table 5. Model's data in small, medium and large size.
Points number and different facilities
Sets
Small size
instance
Medium size
instance
Large size Instance
(Case study data)
I
20
30
40
J
12
15
20
H
2
3
5
K
12
15
20
T
6
8
12
S
3
4
6
Table 6. Parameter value for small and medium size instance.
Parameter
Value
(0.5,0.4,0.1)
Uniform(10,15)
Uniform(3,8)
Uniform(7,12)
Uniform(11,13)
Uniform(40000,50000)
Uniform(20000,25000)
Uniform(80000,100000)
Uniform(1000,1200)
Uniform(100,130)
Uniform(50,75)
Uniform(100,120)
Uniform(5,6)
Uniform(140,200)
250
46
Parameter
Value
Uniform(40,45)
BUDG
6000000
Uniform(200,400)
Uniform(0.25,0.4)
3
8
12
E
10
0.7
Uniform(0.1,0,4)
(1,1)
Uniform(0.1,0.2)
0.4
0.7
0.3
Uniform(0.2,0.5)
Uniform(0.6,1)
(0.95,0.7,0.5)
0.2
0.3
100000
50000
10000
12000
20000
2000
7000
Uniform(0.4,0.7)
0.8
0.9
0.85
0.7
0.9
0.8
0.95
0.05
0.4
Uniform(0.2,0.5)
47
Parameter
Value
Uniform(0.5,0.8)
The schematic network for the case study is depicted in Fig. 5. As we can see in
Fig. 5, each demand zone is candidate for establishing a shelter.
2
4
3
5
2
1
4
5
6
7
3
1
1
0
8
9
Candidate points
Demand zones
Health recovery centers
16
17
18
19
20
12
13
14
15
11
5
6
2
4
1
3
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Supporter
Fig. 5. Schematic network for the case study.
4.4. V
ALIDATION
To evaluate the performance of the proposed algorithm, two sample instances are
solved and compared with the results of the sample which was solved by the exact
method. For this propose, two random instances in small and medium size (see Table
5) are generated and solved with both approaches and the results are presented.
48
As far as the problem is investigated with multi-objective function, to make a
comparison between exact and metaheuristic approaches and to examine if the
proposed metaheuristic algorithm is efficient or not, some criteria are needed. In this
research, criteria such as MID, SM and DM have been utilized (Zitzler, 2000). In
Table 7, these criteria have been calculated and shown. As it is clear in the Table,
proposed NSGA-II is performing very closely to the exact method. Although there
are some differences between two approaches in all three criteria, they are nominal
and negligible.
Note that if MID and SM is less or DM be more, the better they are. Therefore,
these criteria cannot be transformed to one single criterion (R) unless their direction
becomes the same.
Anyway, by weighing these three criteria equally and making their direction in the
same way, criteria R is calculated which shows an overall efficiency of the algorithm.
In details, R is calculated by following steps:
- Alignment of MID, SM and DM: Because some of the criteria are better when
they take a higher value and some other is better when they are smaller, then it is
needed to make their direction in the same way. Therefore, the values of MID and
SM are reversed.
- Weighted Average: After alignment of criteria, their average is calculated and
presented as R. In this research, it is assumed that the criteria have the same weight.
The more the R be, the more efficient the algorithm is.
In Table 7 and Table 8, the calculated criteria for each problem are presented.
According to Table 7 and Table 8, it is obvious that the value of R for NSGA-II is
very close to the value of R for the exact method. As a result, the proposed NSGA-II
algorithm is efficient and shows its capability to find near-optimal solutions.
Table 7. Validation of proposed NSGA-II for small size instance
Approach / Index
MID
SM
DM
R
E-constraint
0.76
0.44
1.54
1.70
NSGA-II
1.04
0.51
1.52
1.48
49
Table 8. Validation of proposed NSGA-II for medium size instance
Approach / Index
MID
SM
DM
R
E-constraint
0.78
0.91
1.11
1.16
NSGA-II
0.83
1.01
1.07
1.09
Also, the Pareto fronts for each pair of objective functions are presented in Fig. 6.
As it is evident, NSGA-II algorithms properly find the Pareto solution often as well
as the exact method.
Furthermore, the values of MID, SM, and DM show that the quality of proposed
set of Pareto solution for epsilon constraint method is high. Because all the criteria
show that the Pareto front created by this method is acting much more rigorously than
NSGA-II.
a) Pareto front derived from 1
st
and 2
nd
objectives
b) Pareto front derived from 1
st
and 3
rd
objectives
c) Pareto front derived from 3
rd
and 2
nd
objectives
1500000
2000000
2500000
3000000
3500000
4000000
44000
46000
48000
50000
52000
2nd
obj
ec
tiv
e
1st objective
NSGA II
EC
3000
3500
4000
4500
5000
5500
6000
44000
46000
48000
50000
52000
3rd
o
bjec
tiv
e
1st objective
EC
NSGA II
3000
3500
4000
4500
5000
5500
6000
0
1000000
2000000
3000000
4000000
5000000
3rd
o
bjec
tiv
e
2nd objective
EC
NSGA II
50
Fig. 6. Pareto front derived from objectives.
4.5. S
OLVING
L
ARGE
S
CALE SAMPLES
Since proposed NSGA-II has appropriate performance, therefore, it can be used to
solve large-scale problems which the exact method is not able to solve them in
normal time. So, a large-scale sample instance that is the case study of this paper (see
Table 5) is solved and the results are shown. By solving this sample, 19 Pareto
solutions have been reached. The value of the objective function for each of Pareto
solutions is presented in Fig. 7.
a) Pareto front for objective functions 1 and 2
b) Pareto front for objective functions 1 and 3
c) Pareto front for objective functions 2 and 3
Fig. 7. Pareto front for objective functions obtained by NSGA-II algorithm.
5000000
7000000
9000000
11000000
13000000
15000000
17000000
19000000
21000000
23000000
200000
250000
300000
350000
400000
1st
ob
jec
tiv
e
2nd objective
10000
15000
20000
25000
30000
35000
200000
250000
300000
350000
400000
3rd
o
bjec
tiv
e
1st objective
10000
15000
20000
25000
30000
35000
5000000
10000000
15000000
20000000
25000000
3rd
o
bjec
tiv
e
2nd objective
51
5. R
ESULT
A
NALYSIS
In A Sensitivity analysis was conducted on the presented model so that its
reliability could be assessed. Therefore, the sensitivity analysis is done one the case
study data defined in Table 5.
We solve all the problems using the proposed NSGA-II and report the best parent
solutions.
,
, and parameters in the problem are changed in a reduction and increase
the range of 20 percent so that the sensitivity level of a problem are studied according
to them. Fig. 8 represents the Sensitivity analysis of the problem. In case the
objective functions maintain different scales, we changed the scales to have
integrated graphs.
a) changes effects on the objectives
0
0.05
0.1
0.15
0.2
0.25
0.8
0.9
1
1.1
1.2
Normalized Objectives
Obj 1
Obj 2
Obj 3
52
b)
changes effects on the objectives
c)
changes effects on the objectives
0
0.05
0.1
0.15
0.2
0.25
0.8
0.9
1
1.1
1.2
Normalized Objectives
Obj 1
Obj 2
Obj 3
0
0.05
0.1
0.15
0.2
0.25
0.8
0.9
1
1.1
1.2
Normalized Objectives
Obj 1
Obj 2
Obj 3
53
d)
changes effects on the objectives
Fig. 8. Sensitivity analysis of the problem.
As it can be understood by the obtained results from the sensitivity analysis of the
case study, objectives have different behaviors in front of the parameter changes. It is
noticeable that first objective has shown no changes while parameters changed. The
root cause is that demand parameter possesses an important role in this objective and
it is analyzed by applying defined robust optimization method in the problem.
However, the other objectives (2nd and 3rd) have mainly shown noticeable changes
for increasing/decreasing of all specific parameters that these changes are in line with
parameter changes i.e. they increase if the parameters increase, or they decreased if
the parameters decreased. Except, by changing of parameter at the middle point of
change i.e. for 10% increase and decrease, second and third objectives have different
behaviors.
6. C
ONCLUSION
In this chapter, disaster management is studied by considering seven main
components of management principles including 1) Planning 2) Organization 3)
Employees 4) Employer (Leader) 5) Coordination 6) Reporting and 7) Budgeting.
Therefore, emergency stations are in a competition with each other and
simultaneously there is no distinction between them to have more or less resource
assignment. However, the level of assigned resources to these seven principles
0
0.05
0.1
0.15
0.2
0.25
0.8
0.9
1
1.1
1.2
Normalized Objectives
Obj 1
Obj 2
Obj 3
54
depends on the effectiveness of them. In addition, this model is integrated because of
considering employment, deposal and the insurance of manpower, route destructions,
supporting the stations from each other with the aims of maximizing demand
covering and emergency station supporting, minimizing total cost, and minimizing
total time of service with a dynamic approach to protect people. A case study at
Kashan is analyzed to investigate the validation of the proposed model. We used an
NSGA-II algorithm and -Constraint method to deal with multi-objectiveness of the
problem, solve the problem, and do the sensitivity analysis on the case study
problem. Our proposed algorithm showed an appropriate performance, and the
obtained results show the difficulty of management decision-makings. For the future
studies:
- The injured can be categorized according to the degree of the injuries.
- The ambulances can be categorized according to the type of the injuries.
- The health recovery centers can have different experts to relieve injured
people.
- The manpower work shifts can be considered and the possibility of the
supportive activity to the other shelters is considered.
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C
HAPTER
3
A
M
ODERN
H
UMANITARIAN
L
OGISTICS
M
ODEL UNDER
F
ACTUAL
C
ONDITIONS OF
U
RBAN
P
UBLIC
H
EALTH
S
PECIALLY
C
ONSIDERING TO
E
NVIRONMENTAL
I
SSUES
Abstract
Sudden incidents and diseases are often in need of quick relief as they influence
directly on people's lives, and the final result of relief delivery is reflected by adding
time span. With regards to the unpredictability of relief demand, uncertain conditions
should be investigated in a more appropriate way of the planning process. This paper
investigates a comprehensive and multi-level emergency Location-Allocation
Routing emergency problem under uncertain conditions with stable response to the
different situations. Also, environmental, behavioral safety and a green approach are
considered as regional pollution coefficient besides safety drive training for
ambulance drivers and emissions of ambulances. In the proposed model, demands
from emergency stations are considered in a fuzzy and probability condition, so that
it indicates real world conditions. In the presented model, assignment costs
according to the scenarios are minimized by considering fuzzy costs. A simulated
annealing (SA) algorithm is developed to solve the problem. The obtained results
show that the proposed algorithm has good performance. Finally, a sensitivity
analysis is done to consider the effect of different values and uncertainty taken by
parameters in the real world.
61
1. I
NTRODUCTION
The occurrence of unpredicted incidents and diseases always impacts the various
parts of the world, especially in the big cities. Usually, incidents and unexpected
diseases need quick relief regarding the financial and therapeutic limitations. The
process of planning, management, and control of the flow of relief resources for the
injured people and patients is called relief logistics. The relief logistics seeks to
present the best possible relief services to the people in need of relief with the
available resource (Overstreet, 2011, Danya et al. 2015). Disasters are characterized
by their uncertain and unpredictable natures; and therefore, demand may change
rapidly in such an environment (Swiss, 2015). The performance of emergency
services is measured in terms of the response time and the total logistics cost (Shafia,
eta al., 2013).
Iran is a western Asian country, located in the Central Asian and Caucasus region,
with an area of approximately 1,650,000 km2 and a population of more than 75
million people. According to the World Health Organization (WHO), cardiovascular
diseases are the most prevalent causes of mortality in Iran (Bahadori et al, 2010).
Unintentional accidents are the second cause of mortality. Iran with 28000 annual
deaths has the highest mortality rate from road traffic accidents in the world. The
road accidents rate in Iran is 20 times higher than the world average. According to the
Iranian data, one person loses his/her life every 19 minutes due to car accidents
(Bahadori et al, 2010). Iran also constantly exposed to natural disasters such as
earthquakes and floods.This situation further emphasizes the importance of an
integrated system of relief logistics in place throughout the nation, because such a
system benefits not only individual people but also serves the best interests of the
nation.
Limited financial power for implementing and managing of the ambulance
stations is the reason why planning is largely necessary for this field. In addition,
because of uncertain conditions in ambulance demand and the traversing time of the
ambulances through the path in the various times of the day, uncertain planning will
yield more real applications.
62
All in all, a notable missing of the aforementioned research is the lack of
considering the stability of the problem space initially. By obviating this gap, the
decisions will be accompanied by desirable and stable results through robust
programming. On the other hand, the integrated modeling of locating the emergency
stations, allocating the ambulance and routing can lead to the better and more precise
results
2. L
ITERATURE
R
EVIEW
The studies in the humanitarian logistics operation are categorized in different
levels including one-level, two-level and multi-level (Balcik, et al., 2008; Jotshi, et
al., 2009). The scale of transport fleet is investigated for one vehicle and several
vehicles (Tzeng, et al., 2007).
Ratick et al. (2009) declared that the emergency request is stochastic and fuzzy in
a certain humanitarian logistics operation. Mete and Zabinsky (2010) showed that
availability of facilities and paths is studied by two criteria of the certain and
uncertain condition. The capacity limitation of the facilities in all types of models is
considered and sometimes it is not considered. The emergency vehicles are
considered in two types of with capacity and without capacity. The time window is
considered in three categories of unlimited time, soft time window and hard time
window (Ozdamar et al., 2004). The humanitarian logistics model can perform the
delivery operation, loading and simultaneous delivery and loading in the stations
(Campbell et al., 2008). The type of path is defined in two types of open and closed
(Jotshi, et al., 2009). The location of customers in the network needs routing of nodes
(Mete and Zabinsky, 2010; Sheu, 2007; Alinaghian et al, 2014; Mirmohammadi et al,
2017; Tirkolaee and Goli, 2016) or edges (Campbell et al, 2008; Tirkolaee et al,
2016; Tirkolaee and Goli, 2016). The type of objective functions is cost,
humanitarian or the combination of the two which are single-objective, two or
multiple objectives (Mete and Zabinsky, 2010). These models can be employed in a
disaster such as an earthquake, flood and others (Ozdamar, et al., 2004; Mete and
Zabinsky, 2010).
Modeling of location problems of emergency facilities has emerged in scientific
discussions with the onset of World War II and the researchers pay special attention
to the research in this field. The 1970s can be considered as the commencement of
63
modeling of emergency facilities location. The first model was used to minimize the
response time instead of target envelopment function (Swoveland et al., 1973).
Between 1970 and 1980, most of the models have been considered in certain form
and uncertainty was less in the warmth of respect. The first stochastic model has been
created in 1978 (Aly and White, 1978) and in the 1980s, most of the researchers
considered the models to be stochastic and the parameters to be random. Meanwhile,
the models with supportive cover (ReVelle, 1989) were more attractive. One of the
most important stochastic models with envelopment target function which provides a
field for the application of stochastic models was presented by Daskin (1983).
Moreover, in this period, location allocation (Pirkul, 1988) models were considered.
The first review model which categorized the emergency facilities models was
presented by ReVelle (1989). Also, Matsutomi and Ishii (1992) utilized fuzzy
concept in modeling and solving the emergency location problems for the first time.
The first model with considering the reliability was presented by Ball and Lin (1993).
From 1990 to 2000, the researchers developed the existing models by focusing on
above models. From 2000 on, there was a great attention to the solution methods and
the multiple objective models were more popular during these years. In 2004, the
partial cover model was presented by Karasakal brothers (2004) which solve the main
problem of maximal covering location problem (MCLP) model. Furthermore,
receiving a lot of attention to solution methods caused that heuristic and meta-
heuristic approaches play a significant role in the papers published in recent years.
Based on the purpose we should minimize the time of travel and the loading time
with regards to the path and extent of transportation and traffic flow should be
evaluated to introduce effective factors in the decision-making (Campos, 2012).
In order to handle demand distribution, traveling time limitation and road
damages, the third model is investigated (Shen et al, 2008) with regards to the fourth
basis which is the number of cases that the request is not satisfied, the number of
needed emergency units, the total number of covered requests, minimizing the risk
and increasing the survival of people, decreasing the waiting time of injured people
for help, the volume of traffic and capacity of havens based on the number of
vehicles, request, the covered area, cost and time of travel has been created (Campos,
2012).
64
(Walter and Gutjahr, 2014) presented a location-routing model for offering relief
supports to affected people during a disaster. They declared that intermediate
emergency stations shall be built temporarily in order to respond to the needs of
people in the possible shortest time. They proposed a three-objective model for
minimizing short-term and mid-term costs. They used the epsilon-constraint method
to solve their model.
(Abounacer et al, 2014) tried to find the optimal number of relief centers and
humanitarian aid distributions. They also tried to find the best routes for delivering
aids to demand points. They considered three opposite objectives. The first objective
was to minimize the time of delivering aids to the affected areas. The second
objective was to minimize the number of centers. The third objective was to
minimize uncovered demands. Using epsilon constraint method and by balancing the
objectives, they found the optimal solutions for the problem.
(Barzinpour et al, 2014) developed a simulated annealing algorithm (SA) and a
genetic algorithm (GA) in order to solve a bi-objective Possibility Planning Model of
Location-Allocation in Disaster Relief Logistics. The aim of their study is to
simultaneously determine the location of relief distribution centers and the allocation
of affected areas to relief distribution centers.
(Jahangiri et al, 2011) presented a problem for optimizing signal timing and
increases the outbound capacity of the network for emergency evacuation, and
developed an SA algorithm for finding the optimal solution for the problem.
(Chen and Yu, 2016) studied a location-routing problem for providing medical
emergency services during a disaster for demands. The aim of this study was to
improve the efficiency of services during a disaster. This was done by mixed integer
linear programming and graph network in order to find the optimal locations for
facilities. They used a Lagrangian method to solve the problem. Finally, they have
done a case study and analyzed the obtained results to evaluate their model
applicability.
Location and Allocation in humanitarian logistics transportation aim to minimize
the transportation time with regards to the servicing, emergency demands and budget
and resource constraints to increase the lifespan of the patients (Edrissi, 2013;
65
Shahanaghi and Babaei, 2017). However, based on the distribution, humanitarian
logistics models have objectives such as cost which includes minimizing traveling
costs, distribution cost and distance which their feasible space is proportional to the
extent of supply (Liberatore et al, 2014). On the other hand, the capacity of facilities
is one of the main elements in these problems with regards to the demand
satisfaction. Therefore, issues such as the extent of stock, resource flow and the
number of injuries fall into this category (Davis, 2013).
(Camacho-Vallejo et al, 2014) presented a bi-level optimization model for aid
distribution after the occurrence of a disaster. They developed a linearized model to
obtain a mixed integer programming problem, then they considered a case study for
the earthquake in Chile in 2010 to validate their model.
By paying special attention to the uncertainty, (Haghi et al, 2017) Developed a
robust multi-objective model for pre/post disaster times under uncertainty in demand
and resource. They used MOGASA algorithm is proposed, and the results are
compared to those of the NSGAII algorithm.
However, considering environmental, behavioral safety and green approach as
regional pollution coefficient besides safety drive training for ambulance drivers and
emissions of ambulances, are the main necessity of this paper and the main gap
between studies that makes the proposed model more real and applicable.
According to this requirement, a comprehensive algorithm for the location of
emergency centers, allocation and routing of ambulance under the uncertain condition
is studied. In turn, a hybrid robust multi-step planning is used which relies on chance
due to the interaction with the decision maker.
The organization of this paper is as follows: The proposed model is presented in
Section 4. Solution method and numerical analysis are described in Section 5 and
Section 6 respectively. Finally, in Section 7, the concluding remarks are presented
and suggestions for further studies are recommended.
66
3. P
ROBLEM DEFINITION
Limited financial capability for activating ambulance in emergency stations
justifies the necessity of programming in this field and also because of the dominance
of uncertain conditions in the demand amounts for an ambulance in different
locations and the variable time of ambulance routes in different times of day, the
uncertain programming can present a more suitable solution. In the current research,
integration of planning of relief supply chain which includes the location of the
stations, assigning ambulances to them and also ambulances routing to relieve the
patients in a standard time and with the minimum cost is considered.
To model the problem, consider a city that needs to be relieved when a disaster
occurs. The problem can be shown as a graph network, therefore, some nodes of the
graph (in the considered city) are candidate locations for building and establishing the
stations for the ambulances and also, stations can be established with various costs in
these nodes. These centers are a depot of the ambulances which they begin their tour
from there to go to the required nodes and then, to the hospitals. So, different paths
can be chosen. The optimal routes of ambulances are in line with optimal objective
value.
Traffic load of these paths depends on the time and because of this, a single
approach cannot be chosen for all times. As a consequence, different scenarios should
be simulated. This traffic load has a direct impact on the traveling time. It is possible
that a long time would be necessary for a short path and vice versa. Therefore, it is
more appropriate to consider time instead of the path between two points. Finally, it
should be decided about the selection of destination hospitals. The possibility of
transferring the ambulances in order to have a better use of available resources is also
considered. On the other hand, due to the uncertainty of demand of ambulances in the
stations, demands are considered based on different scenarios.
The proposed model has multiple steps that in one step the assignment is based
on the scenarios for satisfying the demand of emergency stations. In next step, the
final assignment for establishing the ambulances in the stations based on the assigned
scenario is conducted and then based on the final assignment; the locations of the
needed emergencies are established. And finally, after locating the emergencies
centers, the routes proportional to them are constructed. Therefore, the proposed
model is a multi-step one. Furthermore, environmental issues are considered as air
67
pollution coefficient whereas more polluted regions have a bigger coefficient. Safety
behavioral issues for driver training are studied to observe safety points during
driving and emergency conditions. In addition, a green problem is one of the most
important real-world problems that are considered in this paper to estimate amounts
of emissions of the ambulances assigned to each emergency station.
It has been considered in the proposed model that emergency relief resource
distribution leading to the harmful gases emissions and requiring observing safety
and environmental training issues is following the defined standard and the difference
between each station and the other stations in the above-mentioned problems shall be
possibly kept at low in order to observe safety and environmental issues, and to
prevent air pollution. Therefore, we can control and prevent high density of air
pollution, unfair training, and unbalanced environmental by managing fair
distribution of emergency relief resources to the emergency stations.
A schematic example has been depicted in Fig. 1. Six applicants, one hospital
and two potential emergency stations are considered in a one section city with. The
constructed routes are shown using arrows toward demand nodes. Only one of two
potential emergency stations is established with respect to demands value.
In next section, the model is presented.
68
2
1
4
6
5
3
1
2
1
2
1
Established emergency station
Not established emergency station
Applicant (demand node)
Hospital
1
Fig. 1. The schematic example
After simulating the demand, the proposed models can be presented in the
following.
Indexes
i: Applicants
j: Emergency stations
k: Hospitals
S: Scenarios
Parameters
69
: The quantity of demand i in scenario S
T: The standard time
: Minimum cover percentage
t
ijks
: The traversing time from emergency station j to the demand i and from then, to the
hospital kin each scenario
M: A large number
f
j
: Establishing cost for emergency location j
g
j
: Cost of assigning the ambulance to the emergency station j
C
s
: Cost of required ambulance for demand i from the station j under the scenario S
A: Cost of establishing a path from i to j up to k
B: Cost of establishing a special path from i to j and to k
Bb: Budget
: Performance coefficient for assignment in each scenario
: Coefficient of feasible space
: Coefficient of scenario effects
M: A large number
dd: The difference between fuzzy central number with the lower bound
: Confidence percentage
: The average of demands
: Fuzzy allocation cost
:
Obtained efficiency value of demand point i under scenario s.
:
Emission amount of ambulances in station j.
:
Safety drive training cost for each ambulance in order to prevent accidents and
incidents.
:
Path compatibility with the environment.
:
Maximum undertaking cost for emission
:
Minimum cost to observe safety standards
:
Minimum cost to observe environmental standards
:
Deviation value in the gas emissions
:
Deviation value in the safety training
:
Deviation value in the environmental approaches
Decision variables
Xj: One, if location j is established as the emergency station, otherwise 0.
y
ijs
: The number of needed ambulance for demand point i in station j under scenario s.
z
j
: The number of assigned ambulances to the emergency station j.
x
ijk
: One if the ambulance goes from emergency j to the demand i and then to the hospital k,
otherwise 0.
70
x
ijk
´
: One if the ambulance goes from emergency j to the demand i and then to the hospital k
through a special path, otherwise 0.
,
: Converter variables.
1.1. Robust model
For retrofitting the model in order to do the final assignment of the ambulance
according to the number of required ambulances for each demand point, the deviation
from the feasible space is considered. On the other hand, the impact of other
scenarios on each scenario is considered as a retrofitting factor for the model and in
the objective function. This means in each scenario the number of the needed
ambulance in each demand point causes the differences with the other scenarios.
(
+ (
+
)
)
+
( +
`
)
i
+
+
(
-
`
`
+ 2
)
+
(
+ 2
)
(1-2)
- + 0
(3)
y
ijs
i
- b
s
z
j
+
s
= 0
j,s
(4)
(1 +
)
- y
ijs
s
0
j
i
i
(5)
- d
is
0
i,
j
(6)
-
`
- 0
,,,
(7)
-
0
(8)
- M
0
i,j,
(9)
71
-
s
-
+ p
s
`
s
`
0
s
i
(10)
-
s
-
s
0
s
(11)
(12)
(
)
j
(13)
(
)
j
(14)
k
j
i
( +
`
)
i
j
,
,
k
(15)
(
)
- (
-1
)
-1
-1
lj
(16)
-
(
)
- (
-1
)
-1
-1
lj
(17)
(
)
- (
-1
)
-1
-1
lj
(18)
-
(
)
- (
-1
)
-1
-1
lj
(19)
( +
`
)
i
-
-1
( - 1 +
`
-
-1
i
1)
lj
(20)
-
( +
`
)
i
-
-1
( - 1 +
`
- 1)
i
lj
(21)
y
ijs
0, Z
j
0 ,
,,
,
,
{0,1},
j
,
s
,
0
(22)
The objective function (1-2) includes five terms. The first term minimizes the
cost of establishing the emergency location and the cost of final assignment of an
ambulance to the emergency station considering emission and training cost
minimization. The second term tries to minimize the cost of establishing the path and
the special path considering path compatibility with the environment. The third term
aims to minimize the number of needed ambulances in each scenario. The fourth term
represents the impact of other scenarios on the other ones. The fifth term investigates
the feasibility of the problem.
When the assignment of ambulances to the stations is done, a location must be
established in that place as a station (Equation (3)). The final assignment of a location
is directly linked with the number of ambulances that is demanded in each scenario
(Equation (4)). The total number of ambulances that are required in each scenario
should be at least percent of the total demand (Equation (5)). The number of
required ambulances for each demand in each scenario would be less than the
demand (Equation (6)).
72
The total time that a path is formed must be less than the standard time T.
Otherwise, the path will transform to a special path (Equation (7)). In simple words,
when the total time for the process of going from the emergency station up to
carrying injured people to the hospital is more than the standard time (which is
calculated by the experts based on the probability of injured survival) then, a special
path of emergency is provided which reduces the time in terms of management and
physical structure. In management terms, it is based on the traffic control of the
region and in structural terms, it can help be by establishing an emergency path.
The path is constructed when the emergency station is established (Equation
(8)). The path is constructed according to the number of assigned ambulances
(Equation (9)). Equations (10) and (11) are the limitations of robust linearization.
Equation (12) guarantees the formation of a path of ambulance station.
Equation (13) shows the maximum standard deviation in the gas emissions.
Equation (14) and Equation (15) show the minimum standard for establishing safety
and environmental approaches, respectively. Equation (16) and Equation (17) show
the minimum and the maximum allowable difference in the gas emissions by
different stations with each other. Equation (18) and Equation (19) show the
minimum and the maximum allowable difference in the safety training quantity in
different stations with each other. Finally, Equation (20) and Equation (21) show the
minimum and the maximum allowable difference in the environmental approaches
observed by different stations. Type of the variables is specified in constraints (22).
1.2. Hybrid Robust Model
In order to have a hybrid robust model demand parameters are considered as a
triangular fuzzy number. Therefore, the model aims to increase the responsiveness
chance for the needs of each demand point. To have this hybrid robust model,
Equation (6) changes to Equations (6a), (6b) and (6c).
- d
is
0
i,
j
(6a)
()
-1
d
is
-
,,
(6b)
(1 - 2)(d
is
- ) + 2d
is
,,
(6c)
73
=
(14)
()
(15)
, 0
(16)
The number of required ambulances for each demand in each scenario is less
than the demand (Equation (6a)). For demand, the chance of being a proportion of the
demand point in each scenario from each location is based on the distribution
probability. Here, the distribution for the probability coefficients of the variable is
based on the normal distribution with the average of zero and variance of one
(Equation (6b)). Also, the chance of being a proportion of the demand point in each
scenario from each location is based on the fuzzy demand. For this constraint, it is
assumed that the maximum confidence is 50 percent (Equation (6c)). Also, Equations
(17) and (18) are added to be suitable for the problem type.
4. S
OLUTION METHOD
In this section, a heuristic and a metaheuristic algorithm (namely Simulated
Annealing (SA)) are developed to solve the proposed model. The heuristic is applied
to generate initial solutions; the SA is applied to improve these solutions. SA is a
classical global search heuristic that simulates the physical annealing process in the
field of optimization (Kirkpatrick et al, 1983).
4.1.
S
OLUTION
R
EPRESENTATION
To show the binary variables, we used a single-row matrix that is related to
emergency station locations. Its dimension is
1 I
in which columns are potential
locations for establishing the emergency station. This matrix's elements are zero and
one in a way that zero and one correspond to establishment and non-establishment of
the emergency station.
j
1
2
j
X
X X ... X
(23)
For example, the solution representation for this matrix can be written as Fig.
2 if four candidate locations exist for establishing the transfer points.
74
Emergency station
1
0
0
0
Fig. 2. Solution representation for initial solution
After that, a constructive heuristic algorithm is used to generate initial
servicing routes for ambulances. The steps of the algorithm are as follows:
1-
Provide a set of stations by a decreasing order of related total cost
(establishing, assigning, emission, and training costs). Assign ambulances to the
established station with respect to the minimum cost. Assign a demand point to the
ambulance randomly.
2-
Select next demand point with respect to the related constraints such as
considering the standard time to service. In addition, we should select that demand
point which has the least cost of establishing a path and least traversing time. If we
have multiple points satisfy these constraints, select one of these randomly and
service it.
3-
If standard time limitation has been violated, send another ambulance.
Otherwise, service other demand points.
4-
If all demand points are being serviced, go to 5. Otherwise, go to 2.
5-
Stop the algorithm. Report the solution.
The solution representation for the constructed routes of ambulances in a
station is presented in Fig. 3.
We have some ambulances assigned to the established stations. Each row
represents the constructed tours of the ambulances. If we have no demand point to
service, zero is put in the matrix.
hospital
Demand point
#Ambulance in established
station
1
0
0
0
4
6
5
2
1
1
0
0
0
0
3
7
1
2
Fig. 3. Solution representation for initial solution
4.2. S
IMULATED
A
NNEALING
A
LGORITHM
Simulated annealing is techniques which have been applied to problems that
are both difficult and important. The simulated annealing begins its search for a
75
random initial solution. The iteration loop that characterizes the main procedure
randomly generates in each iteration only one neighbor ' of the current solution .
The variation for the value of the objective function () is tested for each neighbor
generation (Hwang, 1998). To test this variation, = (') - () is obtained. If the
value of is less than zero, then the new solution ' will be automatically accepted to
replace . Otherwise, accepting the new solution ' will depend on the probability
established by the Metropolis criteria, which is given by (-/), where is a
temperature parameter, a key variable for the method. Therefore we have:
() =
-
(24)
Fig. 4 shows the simulated annealing pseudo-code.
Fig. 4. Simulated annealing pseudo code
Local searches used in this algorithm are as below:
1.
Change the established station to non-established station and choose
another one to be established.
In constructed routes by ambulances:
2.
Reverse the sequence of the serviced demand point in each solution.
3.
Select a part of a solution is selected randomly and changes its sequence.
Input: Cooling schedule.
s=s
0
; /* Generation of the initial solution */
T=Tmax; /* Starting temperature */
Repeat
Repeat /* At a fixed temperature */
Generate a random neighbor s';
= (
) - ()
;
If 0 Then s=s' /* Accept the neighbor
solution */
Else Accept s' with a probability
-
;
Until Equilibrium condition
/* e.g. a given number of iterations executed at
each temperature T */
T=g(T); /* Temperature update */
Until Stopping criteria satisfied /* e.g. T<Tmin */
Output: Best solution found.
76
It is noticeable that feasibility of the new generation of solutions is checked
after applying these local searches.
Besides a pseudo code, the solution method can be illustrated by a flow chart in
Fig. 5.
Input & Generate Initial
Solution
Estimate Initial
Temperature
Generate New Solution
Check New Solution
Update Solution
Update and Adjust
Temperature
START
STOP
Accept New
Solution?
Terminate
Search?
No
Yes
No
No
Yes
Fig. 5. Simulated annealing pseudo code
77
-
Algorithm Stop Criterion
It has considered a maximum number of iterations for stopping the algorithm.
In addition, another stopping criterion is considered as the maximum number of
iterations with no improvement for the increasing the efficiency and decreasing waste
time. Finally, report the solution with best objective value.
5. C
OMPUTATIONAL
R
ESULTS
In the first step, we generate three instances in the different size (small,
medium and large) to evaluate the performance of the proposed algorithm. Then these
three instances are solved both by the proposed algorithm and by GAMS software.
Instance information is shown in Table 8. It is worthy to say the model has analyzed
through the GAMS and Baron Solver software in 1000 seconds. The obtained result
is presented in Table 7. The GAP calculated in Table 1 is based on the formulation
below.
=
-
× 100
(25)
Table 1. The Obtained Results by solving instance problems
Instances
GAMS
Objective
SA Objective
GAP (%)
CPU
(seconds)
SA Run time
(seconds)
Small-Sized (P1)
1206.028
1217.36466
0.94
16.53
12.075
Medium-Sized
(P2)
3960.044
4013.7422
1.356
504.04
39.85
Large-Sized (p3)
11046.6612
10846.01
0
1000
103.41
As it can be seen in Table 7, SA has shown appropriate performance in
comparison with GAMS software. It has so much better results in the large-sized
instance. In the following, we apply a sensitivity analysis on the small-sized instance
to investigate the effect of uncertainties.
Due to the fact that Hessian matrix is the limitations of the feasible area and the
positive semi-definite objective function and also the problem is linear. Therefore, the
feasible area of the problem and the objective function are convex. Hence, in this
convex planning type, the problem involves the optimum point which is attained by
solving the problem. In other words, the solution is convergent to the optimum point.
78
After demand simulation, the problems can be analyzed e.g., for the first
problem, the model was solved and analyzed by considering four candidate location
for the emergency stations to satisfy three demand points and to transfer the injured
to three hospitals. The problem is assignment scenario based on fuzzy demand. Data
for sample problems is shown in Table 2 in details. Also, the parameters are
generated randomly.
Table 2. Data for sample problem
Parameters
Small-sized instance
problem
Medium-sized
instance problem
Large-sized
instance problem
Number of applicants
3
20
40
Number of potential
emergency stations
4
9
16
Number of hospitals
3
6
12
Number of scenarios
3
3
5
T
100
350
350
0.7
0.8
0.9
0.3
0.4
0.5
()
-
1.64
1.64
1.64
90
90
90
0.2
0.3
0.4
dd
10
10
10
The first problem is a robust. The second problem has the constraint of
scenario allocation based on fuzzy demands and the third problem has the constraint
of scenario allocation based on a probable meeting of the demand. Parameters
of ,,
,
,
,
are changed in the interval of 20 percent decrease and 20 percent
increase in order to investigate the sensitivity of the problem to them. We can say, we
are going to observe what would happen if we decrease these parameter with the
range of (0.8 parameter, 0.9 parameter, 1.1 parameter, and 1.2 parameter), what is the
trend of decreasing and increasing in the objevctives. Therefore, in the tables and
figures below, their effect on the objective function and main variables of the
problem is investigated. The numerical results are shown in Table 3.
79
Table 3. Investigating the changes of parameters
Objective function
Parameter changes intervals
-20%
-10%
0
+10%
+20%
Objective function in
problem 1 for the changes
of
1205.023
1205.526
1206.028
1206.53
1207.033
Objective function in
problem 2 for the changes
of
3953.189
3954.441
3960.044
3965.659
3975.277
Objective function in
problem 3 for the changes
of
10830.17
10832.55
10846.01
10866.41
10887.03
Objective function in
problem 1 for the changes
of
1208.454
1206.331
1206.028
1205.725
1205.421
Objective function in
problem 2 for the changes
of
3970.049
3969.183
3960.044
3955.092
3954.101
Objective function in
problem 3 for the changes
of
10961.97
10955.57
10846.01
10830.57
10825.76
Objective function in
problem 1 for the changes
of
infeasible
1233.79
1206.028
1177.033
686.7957
Objective function in
problem 2 for the changes
of
infeasible
4106.332
3960.044
3865.168
3391.905
Objective function in
problem 3 for the changes
of
infeasible
infeasible
10846.01
8542.75
7171.075
Objective function in
problem 1 for the changes
of
1204.107
1204.828
1206.028 1208.50871 1205.91299
Objective function in
problem 2 for the changes
of
3955.751
3950.97928 3960.044 3973.78781 3972.97531
Objective function in
problem 3 for the changes
of
10820.67
10822.2233 10846.01 10860.1803 10888.8155
Objective function in
problem 1 for the changes
1203.158
1203.74303 1206.028 1205.33843 1204.95753
80
of
Objective function in
problem 2 for the changes
of
3951.391
3950.14039 3960.044
3970.5546
3953.09893
Objective function in
problem 3 for the changes
of
10818.39
10815.7238 10846.01 10831.9276 10913.8556
Objective function in
problem 1 for the changes
of
1186.361
1219.56797 1206.028 1189.08611 1244.58472
Objective function in
problem 2 for the changes
of
3931.572
3931.23674 3960.044
4222.7267
3913.91952
Objective function in
problem 3 for the changes
of
10723.33
10815.7238 10846.01 10698.2319 10827.5008
b) Analysis of in Problem2
3940
3960
3980
-20%
-10%
0
10%
20%
Objective function in
problem 1
3940
3960
3980
-20%
-10%
0
10%
20%
Objective function in
problem 2
10800
10850
10900
-20%
-10%
0
10%
20%
Objective function in
problem 3
1202
1204
1206
1208
1210
-20%
-10%
0
10%
20%
Objective function in
problem 1
a) Analysis of
in Problem1
b) Analysis of in Problem 3
c) Analysis of in Problem1
81
3940
3950
3960
3970
3980
-20%
-10%
0
10%
20%
Objective function in
problem 2
10700
10800
10900
11000
-20%
-10%
0
10%
20%
Objective function in
problem 3
0
500
1000
1500
-10%
0
10%
20%
Objective function in
problem 1
3000
3500
4000
4500
0
10%
20%
Objective function in problem
2
0
5000
10000
15000
0
10%
20%
Objective function in
problem 3
1200
1202
1204
1206
1208
1210
-20%
-10%
0
10%
20%
Objective function in
problem 1
e) Analysis of in Problem2
f) Analysis of in Problem3
g) Analysis of
in Problem1
h) Analysis of
in Problem2
i) Analysis of
in Problem 3
j) Analysis of
in Problem1
82
3930
3940
3950
3960
3970
3980
-20%
-10%
0
10%
20%
Objective function in
problem 2
10750
10800
10850
10900
-20%
-10%
0
10%
20%
Objective function in
problem 3
1200
1202
1204
1206
1208
-20%
-10%
0
10%
20%
Objective function in
problem 1
3920
3940
3960
3980
-20%
-10%
0
10%
20%
Objective function in
problem 2
10750
10800
10850
10900
10950
-20%
-10%
0
10%
20%
Objective function in
problem 3
1150
1200
1250
-20%
-10%
0
10%
20%
Objective function in
problem 1
k) Analysis of
Problem 2
l) Analysis of
in Problem 3
m) Analysis of
in Problem 1
n) Analysis of
in Problem 2
o) Analysis of
in Problem 3
p) Analysis of
in Problem 1
83
Fig. 6. Investigating the object function of the problems against the changes of the parameters
As it can be seen in the diagram, total cost (Objective function value) changes
with respect to the parameters changes. Most of these changes in total cost generate
linear reduction and increase. Also, covering the demand to increase confidence level
in giving services can be met through increasing the number of the ambulances in the
stations, and this leads to a total cost and jeopardizing feasibility of the problem.
Considering the obtained results from the presented models, it can be found out
that using each one of these models can be very practical if they are used
proportionately with the available conditions and objectives. The reason for this
finding is that each one of the presented models has some relative advantages
proportionate with their practical objectives. The more important the meeting of the
demands becomes, the more practical the third problem will become and the more
important the cost is, the more practical the second problem will be. On the other
hand, by analyzing some weak points, it was clarified that by being aware of these
points, better decisions can be made. That is, if a milder slope exists before or after
these points, investing or providing facilities in that line will not be economical and it
will be better to make decisions or developments towards the direction where a
sharper slope can lead to the objectives so that the objective can be reached to faster
and in less time. Sometimes having better objectives require more facilities,
providing of which in turn requires more time. Therefore, the direction of the milder
slope is taken so that the facilities required for achieving the best objective can be
provided over time. In general, the right decisions can be made by determining
objectives and having proportionate analyses. In order to achieve it, this algorithm
has been presented in this paper so that the emergency problem can be modeled and
analyzed with different objectives and be used in appropriate time.
3600
3800
4000
4200
4400
-20%
-10%
0
10%
20%
Objective function in
problem 2
10600
10650
10700
10750
10800
10850
10900
-20%
-10%
0
10%
20%
Objective function in
problem 3
q) Analysis of
in Problem 2
r) Analysis of
in Problem 3
84
6. C
ONCLUSION
Relief at the time of accidents is vital due to endangering people's lives. Relief
should be provided at a standard time to reduce risks and increasing the survival of
the injured. On one hand, there are resource constraints like budget constraints to
form integrated relief systems. On the other hand, for a better understanding of the
relief issue, the problem has to be analyzed in uncertain space so that the results are
closer to what happens in real life. In addition, environmental, behavioral safety and a
green approach are considered as regional pollution coefficient besides safety drive
training for ambulance drivers and emissions of ambulances. The issue of disaster
and relief logistic are studied in six steps in this paper the multi-level integrated
modeling of emergency station location, allocation and finding ambulance routes
have been done according to meeting fuzzy and stochastic demands using robust
planning. The problem is analyzed in terms of the obtained results. Such that the
second model has led to less cost considering fuzzy demands and the probability of
meeting demands is high in the third model. Each one of these findings can be used
according to their applications. For future research, some suggestions are
recommended as follows:
·
Locating emergency centers in moving manner in various periods
·
Classifying ambulances according to their services
·
Considering ambulances with supportive services for the problem. By
sensitivity analysis, the number of supportive ambulances in each emergency location
with regards to the required demand is determined to increase the confidence
coefficient.
·
Specifying distribution of usage of ambulances, so that emergency
locations can lend their idle ambulances to the locations with higher demand.
·
Considering ambulance and path maintenance, so that the accessibility to
these resources is determined.
·
For more justice, an objective function can be defined to decrease the
unsatisfied demand.
85
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Frequently asked questions
What is the subject of this document?
This document presents language preview that includes biographies, preface, table of contents, chapter summaries, and a case study of disaster management in Kashan, Iran.
What is the first chapter about?
Chapter 1 is about Humanitarian Relief Logistics, covering Introduction, Facility Location, Distribution, Discharge, and a Conclusion.
What is the second chapter about?
Chapter 2 focuses on "A Supportive Human-Based Robust Humanitarian Logistics Model Especially Considering to Disaster Management," using Kashan, Iran, as a case study. It delves into problem definition, mathematical modeling, solution methods like the ε-Constraint Method and Metaheuristic approaches (Genetic algorithm), result analysis, and conclusion.
What topics are covered in chapter 3?
Chapter 3 explores "A Modern Humanitarian Logistics Model under Factual Conditions of Urban Public Health Specially Considering to Environmental Issues." Topics include introduction, literature review, problem definition, solution methods like Simulated Annealing, and computational results.
What are the main objectives sought in the proposed models?
The main objectives are diminishing costs, expanding the scope of harmed individuals, minimizing traveling time and distance, assisting lifesaving, increasing the likelihood of survival, and diminishing the harm caused by disasters.
What are some limitations faced when planning disaster relief?
Limitations include scarcity of disaster vehicles, funding shortages, lack of skilled labor, and road and vehicle failures. The document emphasizes the need to consider both determined and unforeseen constraints for effective disaster management.
What kind of optimization methods are used in this document for solving models?
Deterministic, Meta-heuristic models and stochastic models are implemented. These solving methods are applied algorithmically in order to identify and solve the problem step by step.
What types of reverse logistics costs and physic costs are included in this document?
The costs includes reverse logistics and physic costs and covers the aim of minimizing the procurement cost of logistics, environmental and operational costs and psychic costs.
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