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International Journal of Systems Science: Operations &
Logistics
ISSN: 2330-2674 (Print) 2330-2682 (Online) Journal homepage: https://www.tandfonline.com/loi/tsyb20
A scenario-based possibilistic-stochastic
programming approach to address resilient
humanitarian logistics considering travel time and
resilience levels of facilities
Ali Mehdi Nezhadroshan, Amir Mohammad Fathollahi-Fard & Mostafa
Hajiaghaei-Keshteli
To cite this article: Ali Mehdi Nezhadroshan, Amir Mohammad Fathollahi-Fard & Mostafa
Hajiaghaei-Keshteli (2020): A scenario-based possibilistic-stochastic programming approach to
address resilient humanitarian logistics considering travel time and resilience levels of facilities,
International Journal of Systems Science: Operations & Logistics
To link to this article: https://doi.org/10.1080/23302674.2020.1769766
Published online: 29 May 2020.
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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS
https://doi.org/10.1080/23302674.2020.1769766
A scenario-based possibilistic-stochastic programming approach to address
resilient humanitarian logistics considering travel time and resilience levels of
facilities
Ali Mehdi Nezhadroshana, Amir Mohammad Fathollahi-Fard b,cand Mostafa Hajiaghaei-Keshteli d
aDepartment of Management, Islamic Azad University, Tehran, Iran; bDepartment of Industrial Engineering and Management Systems,
Amirkabir University of Technology, Tehran, Iran; cDepartment of Electrical Engineering, École de Technologie Supérieure, University of Québec,
Montréal, Canada; dDepartment of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran
ABSTRACT
There is a great deal of interest in addressing humanitarian logistics due to the need for emergency
services in the case of disaster. Controlling both operational and disruption uncertainties in the emer-
gency management is one of challenging topics lately to propose a robust plan for humanitarian
logistics. Designing a robust and resilient humanitarian relief chain networks under both opera-
tional and disruptive risks can ensure the delivery of the essential supplies to beneficiaries. In this
paper, a humanitarian logistic network design with multiple central warehouses and local distribu-
tion centres in an integrated manner is addressed by a novel scenario-based possibilistic-stochastic
programming approach. The main real-life application of the proposed methodology is to consider
the transportation network’s routes after an earthquake to provide a plan against uncertainty in
whole levels of supply chain along with its availability. To this end, a real case study of Mazandaran
province in the north of Iran is provided to validate our methodology as well as a comprehensive
discussion and managerial insights are concluded from the results.
ARTICLE HISTORY
Received 10 September 2019
Accepted 11 May 2020
KEYWORDS
Stochastic programming;
supply chain; humanitarian
logistics; relief chain;
resiliency; multiple disasters
1. Introduction
During the last three decades, the humanitarian relief
chains (HRC) as an active research topic quickly have
been developed to consider the emergency supplies for
the clients to minimise human suering and dealing
with a performance allocation of the restricted resources
(Sahebjamnia et al., 2018). The main aim of HRC is to
design a robust plan of humanitarian logistics to con-
trol disasters (Noham & Tzur, 2018). There are several
types of disasters in nature (such as earthquake, famine,
tsunami, cyclone, hurricane, ood, etc.), man-made dis-
asters (such as terrorism, war, civil disorder, etc.), disease
(like malaria or HIV/AIDS) and extreme poverty situ-
ation (Toghi et al., 2016). Among them, the number
of natural disasters has been increased dramatically. The
main reasons behind such phenomena are the global
trend in urbanism, the population growth and land use
and stressing of ecosystems (Krim et al., 2019). This study
is a new variant of HRC to consider the transportation
network’s routes after an earthquake to provide a plan
against uncertainty in whole levels of supply chain along
with its availability.
CONTACT Amir Mohammad Fathollahi-Fard amirfard@aut.ac.ir Department of Industrial Engineering and Management Systems, Amirkabir
University of Technology, No. 424, Hafez Avenue, Tehran, Iran; Department of Electrical Engineering, École de Technologie Supérieure, University of Québec,
Montréal, Canada
In this section, we rst clarify the main needs and
benets of this study to satisfy our motivations and chal-
lenges to the eld. Next, the preliminaries and essential
denitions of HRCs are given. Finally, the contributions
of this research are discussed and highlighted.
1.1. Motivations and challenges
From an ocial report in 2005, there were 489 country-
level disasters aecting 127 countries around the globe
resulting in 104,698 people killed and 160 million peo-
pleaected(Toghietal.,2016). More recently in 2018,
an earthquake in Sarepolzahab, Iran, killed around 1500
people with 12,000 injured ones. According to the Nat-
ural Disaster Database, the earthquakes in the twentieth
century have only caused the deaths of more than 1.87
million people in the world, with an average of 2052 peo-
ple in each incident during the last three decades (EM-
DAT, 2018). Most notably, Iran is one of the most vulnera-
ble countries in the world in terms of earthquakes, which
haswitnessedmanyearthquakesoverthepastfewyears
(Saberian et al., 2019; Sohrabizadeh & Rahimi, 2017).
© 2020 Informa UK Limited, trading as Taylor & FrancisGroup
2A. M. NEZHADROSHAN ET AL.
Tab le 1. Characteristics of earthquakes in Iran from 1990 to 2018 (Saberian et al., 2019).
Year Location Rate of injuries killed Deaths rate Number of injured Scale in Richter
1990 Roudbar-Manjil 263 40,000 105,090 7.3
1997 Kermanshah 87 26,271 22,739 6.3
2003 Bam-Kerman 263 30,000 9388 6.6
2005 Qeshm 48 1600 3574 5.9
2010 Kerman 35 1254 3000 6.5
2012 East Azerbaijan 450 1500 8200 6.4
2013 Sistan and Baluchestan 1350 2600 10,000 7.7
2017 Kermanshah 630 1540 20,000 7.3
2018 Sarepol Zahab 800 1345 12,000 6.4
Table 1indicates the characteristics of earthquakes killing
around 110,000 people in three decades from 1990 to
2018 in Iran.
Although the destructive disasters eects are
inevitable, they could be decreased by a proactive
methodology along with the development of a strong
plan considering both operational and disruptive risks
of an HRC model (Klibi et al., 2018; Sahebjamnia et al.,
2017). This issue emphasises the necessity of appropri-
ate measurements to handle such disasters. Hence, this
proposal proposes a set of measurements to support
humanitarians operations after an earthquake.
Despite major contextual dierences between commer-
cial and humanitarian logistics (e.g. see Balcik & Beamon,
2008;Beamon,2004;Zhouetal.,2017), in humanitar-
ian operations, the prot maximisation as a common
objectiveincommercialsupplychainsisreplacedby
a timely and appropriate provision of aid to benecia-
ries (Hajiaghaei-Keshteli et al., 2011;Krimetal.,2019).
Accordingly, the most critical task after a natural catas-
trophe in humanitarian operations is to manage and to
execute all logistics operations, more eciently (Abdi
et al., 2019; Fathollahi-Fard et al., 2019). The humani-
tarian operations can also deliver the essential supplies,
benecially. Commonly, the rst 72 h after a natural dis-
aster is very important and its occurrence plays a vital role
(Sahebjamnia et al., 2017). This emergency actions refer
to the main reason of communities which is not expected
to stand on their own for a long time (Salmerón & Apte,
2010).
A challenge to develop an HRC system is how the
natural disasters will be answered in the most ecient
manner (Sahebjamnia et al., 2018). Considerably, the pre-
dicting of these events are strongly dicult and still open
issues.Inthiscase,severalscholarshavetriedtofor-
mulate the problems of transporting and scheduling of
large amounts to support humanitarian operations in the
emergency management. The main commodities in these
systems include food, clothing, medicine, medical sup-
plies, machinery and personnel from dierent points of
origin to dierent destinations in disaster areas (Abdi
et al., 2019; Sahebjamnia et al., 2017). The optimisation
models are useful tools to formulate these elements with
the goal of optimisation under uncertainty.
A grand challenge is the uncertainty as an inher-
ent feature of HRC models. The main issues can be
referred to the required data, especially when an HRC
model is developed by optimisation models. Particu-
larly,therequireddatamaynotbeeasilyavailablefora
real-world case study (Hajiaghaei-Keshteli & Fathollahi-
Fard, 2018). Therefore, an approach to estimate the
uncertain parameters is needed. From the literature
of HRC network design problem, researchers usually
use stochastic programming approaches to provide a
plan against uncertainties (Fathollahi-Fard et al., 2019,
2020). Generally, to deal with uncertainty, randomness
and fuzziness are two main sources (e.g. see Pishvaee
et al., 2012;Pishvaee&Torabi,2010). In this study,
we face these two kinds of uncertainties which necessi-
tate using a mixed possibilistic-stochastic programming
approach.
Most notably, the disasters tend to occur relatively
and infrequently. However, they may entail the devas-
tating ramications in a long term for both concepts of
eciency (minimising the cost of humanitarian logistics
operations) and eectiveness (saving lives) (Zhou et al.,
2017). In this regard, the resiliency dimensions should be
considered to supply demand of every client under the
case of disaster. These factors are so signicant to design
an HRC and this study contributes to both concepts of
eciency and eectiveness for a resilient HRC.
1.2. Resilient HRCs
There are dierent denitions for supply chain resilience
in the literature (e.g. Bealt & Mansouri, 2018;Galindo
&Batta,2013). The resilience is a multidisciplinary con-
cept; for example, in physics and engineering, it means
the ability of a material to return to its original form after
being bent, compressed or stretched. In social science,
it refers to the ability of having an elastic behaviour . In
particular, resilience has been used to examine responses
to major supply chain disruptions and disaster relief
eorts (Boin et al., 2010;Bruneauetal.,2003;Lodree
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 3
&Taskin,2008). Most notably, the concept of supply
chain resilience is well studied in terms of agility from the
humanitarian logistics literature (L’Hermitte et al., 2017;
Tatham et a l., 2010a,2010b).
She et al. (2003) rst dened resilience as the abil-
ity to react to unexpected disruption and restore normal
supply network operations. In the supply chain litera-
ture,ChristopherandPeck(2004)denedtheideaof
resilience as theabilityofasystemtoreturntoitsorigi-
nal state or move to a new, more desirable state after being
disturbed.Pettitetal.(2010)arguedthatthesupplychain
resilience increases as capabilities increase and vulnera-
bilities decrease. Tang (2006b)alsoidentiedresilience
as a distinctive competitive advantage of supply chains
for reducing supply chain risk from supply and demand
management view.
To de n e the operational risk,itcanbeconsidered
astheriskofachangeinvaluecausedbythefactthat
actual losses, incurred for inadequate or failed internal
processes, people and systems, or from external events,
dier from the expected losses (Lodree & Taskin, 2008).
However, the disruptive risk is the risk which arise from
natural disasters, e.g. weather or earthquake disruptions,
or man-made ones such as economic crises and terrorism
(Bealt & Mansouri, 2018).
According to the aforementioned denitions, the
resilience is considered as the ability to overcoming unex-
pected events and recovers successfully after the disrup-
tion and not to mitigate before the event actually hap-
pened (Noham & Tzur, 2018). The resilience strategies
can be employed to recover disrupted system, during a
tolerable time period and at an acceptable cost; and to
decrease the eectiveness of the disruption by altering the
levelofeectivenessofapotentialthreat.
1.3. Research contributions
Generally, the majority of HRC models aim to allocate
andtooptimiseinventorylevelsforemergencyfacili-
ties(Noham&Tzur,2018).Infact,theymostlyargued
that the best approach to address the challenge is to pro-
tect facilities better; to have multiple suppliers and to
have sucient commodities supply for a set of period
times. Since each of these strategies is related to an asso-
ciatedcost,thereisalimitationonhowalowonecan
mitigate risk in any single facility (Bozorgi-Amiri et al.,
2012,2013). Moreover, most of HRCs are designed in
the presence of a single disaster event. In this regard,
themodelsarenotresilientenough,especiallywhen
the system is aected by multiple related or subsequent
events. This motivated our attempts to assess an HRC
network design problem including a disaster event in a
real case study in Mazandaran province in the north of
Iran to make it more practical. To deal with the uncer-
tainty of the proposed problem, a novel mixed uncer-
tainty programming approach is proposed for dealing
with uncertain data when designing an HRC to nd a
robust solution in the presence of multiple related events.
Also, this work applies the concept of resilience and
measured resilience parameter for each facilities based
on resilient initiatives which are obtained from compre-
hensive literature review. The proposed multi-objective
optimisation model combines resource allocation with
emergency distribution (minimising maximum travel
distance, minimising operational costs and maximising
resiliency).
ToclosetheHRCtoreal-worldcasesandtorecent
advances in this research area, the goal of this research
is to develop a comprehensive model that describes the
integrated logistics operations in response to natural dis-
asters at the operational level of HRC. The main compo-
nents of the model are the transportation of supplies and
reliefpersonnel.Thesedicultiesmustbeperformed
to maximise the survival rate of the aected population
quickly and eciently as well as to minimise the cost of
such operations. Due to the natural uncertainty of this
problem, an inherent randomness about the realised sce-
narios has been considered in the post-disaster based
on the occurrence probabilities of earthquake scenar-
ios. To this end, the evolved data involve demand of
each relief item and usable percentage of prepositioned
relief items due to the vulnerability of the relief network’s
storage facilities and transportation routes. Furthermore,
there exist such impreciseness about the data at post-
disaster events. Most notably, the transportation time of
these evidence is based on the network’s routes under the
realised disaster scenario. Thus, to have a robust logistic
network under uncertain demands, cost, transportation
timesinthenetwork’sroutesundertherealiseddisaster
scenario, a stochastic model is developed to cope with
these uncertain parameters.
Anothercontributionofthisresearchistoconsider
multiple disaster events. As can be indicated in the lit-
erature, most of HRC network models are designed to
consider only one disaster, and they neglect the eect of
subsequent events (Zobel & Khansa, 2014). In the real
world, sudden-onset disasters are generated by multiple
related sub-disasters. For example, earthquakes and their
aftershocksleadtoasetofrelatedeventsincludingdelay-
ing the building collapses and hurricanes with levee fail-
uresalongwiththeassociateddisruptions.Earthquakes
commonly occur in transportation networks and power
grids (Liu et al., 2009;Snedikeretal.,2008). In this regard,
aresilientHRCinthepresenceofmultiplerelateddis-
astereventsshouldbedeveloped.Tothebestofour
knowledge, this is the rst attempt to design a resilient
4A. M. NEZHADROSHAN ET AL.
HRC in the presence of multiple related disaster events
using resilient measures and initiatives.
According to the study of Zobel and Khansa (2014),
characterising multi-event disasters are used to support
better disaster planning and mitigation to achieve a great
depth of information. As such, the resilience concept has
been used to examine responses to major supply chain
disruptions and disaster relief eorts (Boin et al., 2010;
Bruneau et al., 2003; Falasca et al., 2008). Hence, this con-
cept has been applied in order to design a resilient HRC
in this study.
The resilient HRC can be evaluated by dierent crite-
riasuchastherelationshipwithkeysuppliersandex-
ible facilities, etc. Based on this, it can be considered
as a multi-criteria decision-making (MCDM) problem.
The MCDM considers multiple criteria and their con-
icts, and the natural complexity of the evaluation pro-
cess (Zopounidis & Doumpos, 2002). There are many
MCDM techniques which have been applied to sev-
eral elds and can be classied into several types such
as the analytic hierarchy process (AHP), analytic net-
work process (ANP), elimination et choix traduisant
la realité (ELECTRE), preference ranking organisation
method for enrichment evaluations (PROMETHEE),
cloud-technique for the order of preference by similar-
ity to ideal solution (TOPSIS), visekriterijumska opti-
mizacija i kompromisno (VIKOR), and decision-making
trial and evaluation laboratory (DEMATEL).
As such, there are dierent real-world applications
such as supply chain and manufacturing operations
(Feng et al., 2019), product manufacturing and assem-
bly (Tian et al., 2018)andgreenassessmentofships
(Liu et al., 2020), and many other optimisation prob-
lems,toapplythesetechniquestoevaluatethecriteria.
However, a few studies have investigated the resilient
HRC using MCDM techniques (e.g. Chang et al., 2011).
This issue is a motivation for us to employ a combi-
nation of fuzzy DEMATEL and ANP method by using
the latest version of the augmented ε-constraint method
forthersttimeintheliteraturetosolvetheproposed
problem.
To cope with this paper, the main contributions are
summarised below:
•Proposing a mixed possibilistic-stochastic program-
ming (SBPSP) approach in the presence of multiple
related disaster events;
•Considering resilience measure as a resilience param-
eter for each facility by applying Multi-Criterion
Decision-Making (MCDM) tools;
•Introducing a hybrid of fuzzy DEMATEL and ANP by
using the latest version of the augmented ε-constraint
method to tackle the proposed formulation;
•Solving a real case study of Mazandaran province in
the north of Iran to validate the proposed method-
ology and to achieve the managerial insights of this
paper.
The rest of this paper is organised as follows. The lit-
erature review is provided in Section 2. The proposed
resilient HRC is formulated in Section 3. The solution
methodology with its implementation is presented in
Section4.ThecasestudyissolvedinSection5.Section
6 illustrates a comprehensive analysis and discussion on
the results. The managerial implications are expressed
in Section 7. Finally, the concluding remarks and future
works are recommended in Section 8.
2. Literature review
The concept of the humanitarian supply chain is rela-
tively an active topic. As reported, there have been more
than 50 published works in this research area during
thelastdecade(Bealt&Mansouri,2018). The HRC is
usually considered as the process and system involved
in providing humanitarian aids to help vulnerable peo-
ple (Sahebjamnia et al., 2017). The common goal of
humanitarian relief chains is to minimise the human
suering and death by developing an ecient alloca-
tion of the restricted resources (Bealt & Mansouri, 2018).
One way to achieve this is to provide rapid reactions to
disasters. The answer of a fast response to disasters is
also the fundamental of a resource management which
canbeabletoformulatethehumanitarianreliefchain
by an adequate time along with cost eciency (Toghi
et al., 2016). Optimisation techniques based on the
decision-making models could provide decision-makers
with timely and eectively solutions. However, the litera-
ture lacks proposing and using analytical methods and
mathematical models concerning the supply chain and
logistical problems in HRCs under mixed uncertainty, i.e.
both operational and disruptive risks (Sahebjamnia et al.,
2018).
InsomeoftherecentreviewarticlesonHRCs(Bal-
cik et al., 2010;Bealt&Mansouri,2018; Caunhye et al.,
2012; Galindo & Batta, 2013; Kovács & Spens, 2007),
they identied appropriate measures in dierent steps
(phases) of disasters, including pre-disaster, during disas-
ter and post-disaster. For instance, Caunhye et al. (2012)
reviewed the proposed models for post- and pre-disaster
operations. They also investigated a couple of case stud-
ies for trac control and lifeline rehabilitation. Özdamar
and Ertem (2015)presentedasurveythatfocusedonthe
response and recovery planning phases of the disaster
lifecycle. Based on these reviews, a summary of studies
on the use of OR/MS techniques to model and optimise
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 5
the emergency disaster management activities is given in
the following paragraphs.
As one of the earliest studies, Bruneau et al. (2003)
made a seminal attempt to propose resilience triangle
which represented a measure of losing a system after a
disaster, functionality. Balcik and Beamon (2008)pro-
posed the rst pre-positioning model in the HRC liter-
ature using a maximal-covering type model that deter-
mined the number and locations of the distribution cen-
tres and the quantity of supplies to be stocked at each
distribution centre in a stochastic programming frame-
work. They considered uncertainty about the location of
disasters, amount of demand by scenario-based approach
andassumedthatmultiplescenarioswouldnotoccur
simultaneously.
Duran et al. (2011) proposed an integrated location
and inventory planning model to design an international
relief pre-positioning network for CARE international.
The mixed-integer programming model was proposed to
minimise the average of response time as an objective
function. The model estimated the frequency, location
and magnitude of the potential demand based on histor-
ical data and optimised the location of warehouses and
inventory allocation, given to considered constraints. As
such, a hierarchical facility location problem was intro-
duced by Görmez et al. (2011) that considered two types
of facilities: temporary and permanent. Permanent loca-
tions of temporary facilities are the rst decisions.
There are also works in the literature to quantify the
resilienceintheeldofdisasterresilience.Zobel(2011)
extended the original term of predicted disaster resilience
to develop an approach to calculate a multi-dimensional
measure of HRC. However, the recent review papers
showed that a number of approaches were provided for
calculating predicted resilience in the presence of single
disaster event, and the models were not sucient to assess
theresilienceofasystemaectedbymultiplerelated
events (Toghi et al., 2016). Zobel and Khansa (2014)
assessed the resilience of a system followed by multiple
disaster events. This system did not have a chance to
supportfullybythetimeinthesub-eventoccurs.
The trade-o between supply chain resilience and the
cost is emphasised in the literature, repeatedly (Falasca
et al., 2008;Raticketal.,2008;She&Rice,2005). To
better understand this concept, note that Falasca et al.
(2008) developed a quantitative approach for assessing
supply chain resilience against disasters. They revealed
the relationship of three determinants of supply chain
resilience such as density, complexity and critical nodes
that were mentioned earlier by Craighead et al. (2007)on
the performance of a supply chain system and the recov-
ery time. In another research, Lodree and Taskin (2008)
analysed the eect of demand uncertainty and the occur-
rence of extreme disruptions on inventory levels and
customer service levels by nding stock-out likelihoods.
The authors represented an insurance risk management
framework for disaster relief and supply chain inventory
planning. They compared the inventory levels in the clas-
sic newsvendor solution with the levels needed regarding
thecaseofuncertainsituations.Todothisend,optimal
inventory levels were considered and the insurance pre-
mium associated with disaster relief planning was calcu-
lated. Ratick et al. (2008)proposedanemergencybackup
and storage facilities model to allocate the cost-eective
number of facilities in response to anthropogenic catas-
trophic due to increasing the resilience of supply chain.
This formulation helped managers to increase resilience
or reduce vulnerability. They also applied this approach
to a test dataset with over 900 cities and towns in the
U.S.A. for validating its.
There has been a signicant number of qualitative
researches which are useful to estimate the parame-
ters of an HRC (e.g. Kleindorfer & Saad, 2005;Neiger
et al., 2009; Sahebjamnia et al., 2017; Samani et al.,
2018;Toghietal.,2016; Wagner & Bode, 2006).
For instance, Tang (2006a)revieweddiversemodels
for managing supply chain risks and suggested post-
ponement, strategic stock investment, exible supply
base, economic supply incentives and multi-modal exi-
ble transportation for improving supply chain manage-
ment and dynamic pricing, dynamic assortment plan-
ning, silent product rollover for improving demand
management.
Accordingly, as pointed out by Samani et al. (2018),
organisations employed the resilience in three main
ways including increasing redundancy, building exi-
bility and changing corporate culture. As such, com-
panies can enhance their exibility by standardisation
of parts facilitating interchangeability which might be
achieved by relying on the similar or even identical
plant design/process or cross-training employee, post-
ponement or mass customisation strategy to respond to
demand uncertainties, customer and supplier relation-
ship management, and multiple sourcing. As Christopher
and Peck (2004)proposed,thefollowingprinciplesto
design resilient of supply chains are the supply chain
reengineering, supply base strategy, collaboration, agility
with key component exibility and creating a supply
chain risk management culture.
AccordingtoCaunhyeetal.(2012), the literature lacks
addressing multi-objective emergency logistics problem.
Bozorgi-Amiri et al. (2013) presented a multi-objective
and robust stochastic programming framework to simul-
taneously determine the location of relief distribution
6A. M. NEZHADROSHAN ET AL.
centres (RDCs) and the corresponding inventory quanti-
tiesforreliefitemsunderuncertaintyaboutdemand,sup-
plies, cost of procurement and transportation, demand
point. The model minimised the sum of the expected
value and the variance of total cost and sum of the
maximum shortages. They apply compromise program-
ming to obtain non-dominated solutions and provide
acasestudybasedonaspeciccountry-widedisaster
scenario in Iran. Döyen et al. (2012)developedatwo-
echelon two-stage stochastic facility location model in
the post-disaster for minimising the total cost of nding
the locations of facilities as well as amount of relief item
ows.
In multi-objective emergency logistics problems, Gar-
rido et al. (2015) presented a multi-objective model to
help decision-makers in the logistics of a ood emer-
gency with the aim of minimising the undesirable eects
of such events. The objectives considered were made of
distribution time and cost. The model aimed to optimise
inventorylevelsforemergencysuppliesaswellasvehi-
cles’ availability to deliver enough supplies. Huang et al.
(2015) presented an integrated multi-objective optimisa-
tion model that combines resource allocation with emer-
gency distribution, in which a time-space network was
used to incorporate the frequent information and deci-
sion updates in a rolling horizon approach. The model
includes three objective functions, i.e. lifesaving utility,
delay cost and fairness.
Sheu and Pan (2014)consideredthreeobjectives
including travel distance minimisation, operational cost
minimisation and psychological cost minimisation. The
objective functions of three-stage programming mod-
els include not only traditional objectives such as min-
imising total travel distance and operational cost, which
supply-side members focus on, but also
minimising the psychological cost experienced by
demand-side members. Another two-stage stochastic
optimisation model for minimising the expected number
of casualties was presented by Salmerón and Apte (2010).
The rst stage decides the location of facilities: ware-
houses, medical facilities and personnel, ramp spaces and
shelters. The second stage deals with the deployment of
the allocated resources.
Rawls and Turnquist (2011) extended their original
model by adding additional service quality constraints
in regard to maximum shipment distance. In a similar
work, Rawls and Turnquist (2012) proposed a two-stage
stochastic programming model to optimise pre-event
planning for meeting short-term demands for emer-
gency supplies under uncertainty. Later Toghi et al.
(2016) proposed a similar HRC model for a two-echelon
supply chain. Their main contribution is to introduce
a tailored dierential evolution algorithm to solve the
problem. Fathollahi-Fard and Hajiaghaei-Keshteli (2018)
developed a partial interdiction problem to optimise
the total cost before and after the disaster. Their main
innovation was to consider dierent defensive systems
to expand the capacity of facilities under imminent
attacks.
In another research, Cao et al. (2018) studied a
dynamic relief distribution problem with the goal of
maximising the lowest victims’ perceived satisfaction,
and minimising the largest deviation on victims’ per-
ceived satisfaction. So far, the locating medical facil-
ities have not been thoroughly analysed with respect
to a response service. It can aect casualty transporta-
tion depending on the severity of the injuries. Magh-
roh and Hanaoka (2018) developed a humanitarian
logistics as a dynamic vehicle routing optimisation dur-
ing disaster response. Their proposed model optimised
the heterogeneous vehicles, multiple trips and location
of facilities with dierent accessibilities under demand
uncertainty. They applied a modied simulated anneal-
ing algorithm with a variable neighbourhood search to
solve their model. Maharjan and Hanaoka (2018)intro-
duced a multi-objective and multi-period humanitarian
supply chain which optimised the location of tempo-
rary logistics hub for disaster response. They solved the
model with a fuzzy factor rating system under the group
decision-making. In another research, Sahebjamnia et al.
(2018) presented an integrated business continuity and
disaster recovering planning. Their model built organisa-
tionalresiliencewhichcanrespondtomultipledisruptive
incidents that may happen simultaneously. They vali-
dated their model by a furniture manufacturing company
in Iran.
More recently, Chong et al. (2019) oered a resilient
HRC considering dierent warehouses and distributers
with inventory levels and costs. The model applied for
the ood disaster and the case study of Peruvian, Peru.
Finally, Cavalcante et al. (2019)developedahybrid
approach to analyse the risk of supplier proles in the
case of digital manufacturing. Their hybrid approach was
a combination of simulation and machine learning for
adecision-makingsupportsysteminresilientsupplier
selection. They evaluated the supply costs and lead time
as well as resilience measures.
Generally speaking, the main related recent papers
duringthelastdecadehavebeencategorisedtocre-
ate a link with the literature and to compare the main
contributionsofthisstudywithothersimilarones.
Table 2shows a list of papers concerning human-
itarian logistics by the use of stochastic program-
ming from 2010 to 2019. The main characteristics of
this evaluation are their objectives, the utilised disas-
ter type, solution approach and the considered case
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 7
Tab le 2. A brief review of related works from 2010 to 2019.
Papers Objectives Disaster type
Solution
methodology Case study
Mete and Zabinsky
(2010)
Transportation, facility opening, vehicle operations and
amount of relief items in the case of post-disasters
Earthquakes Exact method Seattle
Chang et al. (2011) Transportation, facility opening, equipment rental,
penalties, shipping distance of rescue equipment
Flood DEMATEL Taipei City
Döyen et al. (2012) Establishment of facilities in terms of both pre- and post-
disaster rescue centres, the amount of relief items to
be stocked at the pre-disaster resource centres and the
amount of relief item and shortage
General Lagrangian relaxation
method
Numerical
experiments
Bozorgi-Amiri et al.
(2012)
Opening facilities, procurement, transportation, holding
and shortage costs, partially interdiction after disaster
and variance of total cost
General Metaheuristic Numerical
experiments
Bozorgi-Amiri et al.
(2013)
Opening facilities, procurement, transportation, holding
and shortage costs, partially interdiction after disaster
and variance of total cost and penalising the solutions’
infeasibility due to uncertainty
Earthquakes Exact method Iran
Jabbarzadeh et al.
(2014)
Fixed cost and variable costs of facility, operational cost,
transportation cost, inventory cost
Earthquakes Branch and bound Iran (IBTO)
Huang et al. (2015) Fixed cost and variable costs of facility, lifesaving utility,
delay cost, fairness
Earthquakes Exact method Sichuan
Garrido et al. (2015) Establishment of facilities, assignment costs, distribution
cost, distribution time, inventory costs
Flood Exact method Numerical
experiments
Tofighi et al. (2016) Fixed and variable costs of facilities, distribution time,
maximum weighted distribution time for critical items,
total cost of unused inventories and weighted shortage
cost
Earthquakes Metaheuristic Tehran
Fathollahi-Fard
and Hajiaghaei-
Keshteli
(2018)
Cost incurred before and after the partial interdiction
attempt
General Hybrid metaheuristic Numerical
experiments
Noham and Tzur
(2018)
Fixed and variable costs of facilities, distribution time,
maximum weighted distribution time for critical items
and optimal post-disaster number of facilities
Earthquakes Heuristic Israel
Cao et al. (2018) Fixed and variable costs of facilities, lowest victims’
perceived satisfaction, and minimising the largest
deviation on victims’ perceived satisfaction
General Exact Numerical
experiments
Maghfiroh and
Hanaoka (2018)
Fixed and variable cost of vehicles and facilities General Hybrid metaheuristic Numerical
experiments
Maharjan and
Hanaoka (2018)
Fixed and variable costs of facility and transportation cot
and the total unsatisfied demand
Earthquakes A fuzzy factor rating
algorithm
Nepal
Sahebjamnia et al.
(2018)
Fixed and variable costs of facility, weighted shortage cost,
inventory costs, processing and shipment costs, multiple
disruptive events
General Augmented ε-
constraint method
Tehran
Chong et al. (2019) Fixed and variable costs of facility, inventory costs,
processing and shipment costs
Flood Exact Peruvian
Cavalcante et al.
(2019)
Supply cost, lead time and resiliency measures General Hybrid of simulation
and machine
learning
Numerical
experiments
This research Fixed and variable costs of facilities, distribution time,
maximum weighted distribution time for critical items,
total cost of unused inventories and weighted shortage
cost, transportation and processing costs, presence of
multiple disaster events and resilience levels
Earthquakes Hybrid of fuzzy
DEMATEL and ANP
by using augmented
ε-constraint method
Mazandaran
province
study. To have a conclusion about the main similarities
among the papers and literature gaps, the main ndings
are:
•Most of the papers attempted to optimise the opera-
tional and inventory costs of HRCs. There is no study
minimising the maximum travelling time (distribu-
tion time) like the proposed study.
•Earthquakes are interesting topics of disaster types due
to its widespread over the world.
•Since the resilient HRC’s decisions are generally
strategic and several criteria exist to assess the
resiliency. There are several papers concerning on
MCDM techniques. There is no similar study which
has been proposed a hybrid of fuzzy DEMATEL and
ANP algorithm based on the augmented ε-constraint
method in this research area.
•To the best of our knowledge, this is the rst attempt to
solve a case study from the Mazandran province faced
several earthquakes disaster events.
In conclusion, from the literature, the main decisions
in an HRC network design problem can be categorised
into two groups:
8A. M. NEZHADROSHAN ET AL.
(i) Pre-disaster decisions: these decisions have to be
taken before the disaster and concerns, e.g. the num-
ber and location of the distribution centres (i.e. facil-
ities) and stock pre-positioning.
(ii) Post-disaster decisions: these decisions have to be
taken after the disaster and mainly involve distri-
bution planning (i.e. specifying shipment quantities
between the dierent facilities).
Overall, a large number of studies employs stochastic
programming to tackle the above problem (e.g. Bozorgi-
Amiri et al., 2012,2013;2014;Cavalcanteetal.,2019;
Döyen et al., 2012;Mete&Zabinsky,2010;Noham&
Tzu r, 2018;Toghietal.,2016). This paper follows the
same path while adding several extensions (e.g. the pos-
sibility of subsequent disasters and the presence of mul-
tiple related disaster events). As such, there is no similar
study to optimise three objectives, i.e. minimising oper-
ational costs, minimising maximum travel distance and
maximising resiliency, simultaneously.
3. Proposed resilient HRC
This paper considers three stages for the proposed HRC
network as illustrated in Figure 1.Itcanbeobserved
that a set of suppliers exists. As such, the second stage
contains central warehouses (CWs) and strategic stocks,
and the last stage consists of local distribution centres
(LDCs) in the areas, which are aected by a disaster. In
this paper, suppliers (e.g. aid agencies, governments, pri-
vate sector, etc.) play the key role to provide the required
commodities to people in devastated areas. CWs con-
tain warehouses, airports, train station and bus stations.
LDCs distributed in the whole of the city are located on
thefortiedexistingpublicfacilitieslikeschools,health
centres, etc. Using LDCs is justiable since it is not nec-
essary to open a large number of CWs that remain idle
until a disaster strikes regarding the response agency rep-
resentatives (Döyen et al., 2012; Görmez et al., 2011;
Sahebjamnia et al., 2018;Toghietal.,2016).
To describe the proposed problem, one might assume
that there are Lpotential suppliers, Ipotential CWs
along with Ccapacity levels, Jpotential LDCs, Kdemand
points, Hpotential strategic stocks and Mpotential
transportation modes. As such, there are Qrelief items.
Regarding the nature uncertainty of HRC, assume that
there are Ssets of disaster scenarios with accuracy proba-
bility of Psand Gsubsequent potential disasters. There
is a xed opening cost for the establishment of each
CW (Fc
i), each LDC (Gj) and each strategic stock (Eh).
Regarding the inventory decisions, each item qhas an
inventory holding cost (IHq). For unused item, there is
also an inventory cost for both CW and LDC as UCi
q
and ULj
q, respectively. The usable inventory ratio for each
item under a disaster scenario shas been estimated for
both CW and LDC as λi
qs and μj
qs,respectively.Thiscost
also exists for each supplier as ξs
l.Theshortagecostis
also considered by USs
qfor each item under each disaster
scenario. The transportation time regarding the trans-
portation mode mbetween a supplier and CW, as such,
aCWandanLDCareexistedbyTA
s
ijm and TBs
lim under
each disaster scenario, respectively. Similar to other sup-
ply chains, the demand level Ds
qk for each demand zone
as one of the main inherent uncertain parameters under
scenario sfor each item is considered. The storage capac-
ity is another main parameters of the model for all CWs,
LDCs,strategicstocksandsuppliersestimatedasVc,CA
j,
SAq
hand CSql,respectively.Assuch,therequiredunitof
storage capacity for each item is Aq. Regarding dierent
transportation modes, their main characteristics are the
cost and the capacity to transform the items. Accordingly,
their cost and capacity to transform between suppliers
and CWs are CTqlim and CCPlim,respectively.Assuch,to
transform between CWs and LCDs, the cost and capac-
ity of transportation modes are CTRqijkm and CAPijm,
respectively. Based on disaster scenarios, the subsequent
disasters eecting on demands and delivery time after the
major disaster in the scenario are φg
s. The main innova-
tion of the model is to consider a set of resiliency levels
for both CWs and LDCs estimated as αiand θj,respec-
tively. In the following, a comprehensive description of
resilience parameters is provided to identify the main
criteria.
3.1. Resilience criteria
In this study, the resilience is measured by calculating
a resilience level for each facility (i.e. Suppliers, CWs
and LDCs). The resilience levels are estimated based on
the resilience measures. Here, a brief review of related
works from the literature to extract the resilience mea-
sures is provided. These qualitative measures are aggre-
gated to a resilience parameter by applying MCDM tech-
niques (Zopounidis & Doumpos, 2002) regarding the
proposed hybrid algorithm of fuzzy DEMATEL and ANP.
Table 3indicates dierent criteria to evaluate resilience
measures.
These criteria are dened as follows:
•Interchangeable people (Cross-Training) – C1
AccordingtoShe(2005 )andSheandRice
(2005), exibility is the fundamental component of
enhancing the resiliency for a supply chain system.
There are several ways to create a resilient supply chain
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 9
Figure 1. Graphical illustration of the proposed resilient HRC.
Tab le 3. Measures with their supportive references for each one.
No. Criteria Supportive references
C1Interchangeable people (Cross-training) Sheffi and Rice (2005), Tang (2006b), Sheffi et al. (2003),Pettitetal.(2010), Pettit et al.
(2013), Tang and Tomlin (2008), Mete and Zabinsky (2010)
C2Flexible facilities Sheffi (2005), Sheffi and Rice (2005), Tang and Tomlin (2008), Tang (2006b), Lee (2004),
Kleindorfer and Saad (2005), Döyen et al. (2012)
C3Deep relationship with key suppliers Sheffi (2005), Sheffi and Rice (2005), Tang (2006b), Hajiaghaei-Keshteli and Fathollahi-
Fard (2018), Bozorgi-Amiri et al. (2012), Bozorgi-Amiri et al. (2013), Jabbarzadeh
et al. (2014)
C4Distributed power, empowered to take
necessary action
Sheffi (2005), Sheffi and Rice (2005),Pettitetal.(2010),Pettitetal.(2013), Fiksel (2003),
Christopher and Peck (2004), Tofighi et al. (2016)
C5Continuous communication among informed
employee
Sheffi (2005), Sheffi and Rice (2005),Pettitetal.(2010),Pettitetal.(2013), Fiksel (2003),
Peck et al. (2003), Christopher and Peck (2004), Peck (2005), Tofighi et al. (2016)
C6Sharing information either with suppliers or
customers
Christopher and Peck (2004), Kleindorfer and Saad (2005), Lee (2004), Fiksel (2003),
Peck (2005), Pettit et al. (2010,2013), Sheffi and Rice (2005), Ivanov et al. (2014),
Wicher and Lenort (2013), Noham and Tzur (2018)
C7Auto-ID technology such as radiofrequency
identification technology (RFID)
Peck (2005), Sheffi (2005, 2005b), Kleindor fer and Saad (2005), Tang (2006b), Hendricks
et al. (2009), Manuj and Mentzer (2008), Christopher and Peck (2004), Fiksel (2003),
Ivanov et al. (2014), Pettit et al. (2010,2013), Tofighi et al. (2016).
C8Process improvement Fiksel (2003), Sheffi (2005), Sheffi and Rice (2005), Pettit et al. (2010,2013), Christopher
and Peck (2004), Noham and Tzur (2018)
(in particular relief chain) via enhancing its exibility.
For example, She (2005) declared that when a com-
pany increases its supply chain exibility, it can both
withstand signicant disruptions and better respond
to demand uctuation. To ensure the delivery of ser-
vice, interchangeable people are the result of cross-
training.Italsoenablesthereliefchaintoallocateor
to transfer its resource among facilities when the need
arises.
•Flexible facilities – C2
Flexibility amounts are challenging for building all
organic capabilities that can sense threats and respond
to them, quickly (She, 2005). A rapid response involves
using standard processes and having multiple locations
with built-in interoperability. Since having redundant
productionlinesisexpensive,theexistenceofmulti-
ple capabilities at each plant location adds exibility
10 A. M. NEZHADROSHAN ET AL.
to the supply chain. Interestingly, it has been shown
that a company may not need to have the ability
to manufacture all products in all plants in order to
increase its exibility substantially. For instance, the Toy-
ota manufactures or assembles many cars in dierent
countries to address the domestic preferences of their
customers.
•Deep relationship with key suppliers – C3
As pointed out by Ste (2005), each company rely-
ing on a small group of suppliers must maintain a
deep relationship with each of them. These key suppli-
ers are vital and failure. Note that each of them can
have catastrophic eects on that enterprise. In Decem-
ber 2001, UPF-Thompson, the sole supplier of chassis
frames for Land Rover’s popular Discovery vehicles, sud-
denly stopped shipping products. The deep relationship
that Land Rover had with its sole supplier enforced it
topayosomeofUPF’sdebttoensureitsresumption
(She, 2005).Similarly,accordingtoTang(2006b), as
canbeseeninseveralinstances,thepurchaserdoesnot
have the luxury of shifting production among dierent
suppliers. The main reason would be the very limited
number of suppliers available in the market. To achieve
the exibility of shifting production among suppliers, the
buyer can provide certain economic incentives to cul-
tivate additional suppliers. In the late of 2004, Chiron,
one of the big vaccine-makers of the U.S. market, was
closed down due to bacteria pollution at this plant. In
front of a shortage of 48 million u shots, the govern-
ment oer using u shots just to certain high-risk groups.
Finally, the U.S. government by using more potential sup-
pliers attempt to provide exibility in facing this disrup-
tions situation. Even in the absence of main disruptions,
economic supply motives can be useful (Torabi et al.,
2016).
•Distributed power, empowered to take necessary action
–C
4
AnothermainissueprovidedbyShe(2005)to
enhance the resiliency of supply chains is to empha-
sise cultural changes, completely. This author argued
that empowering people to take necessary actions are
enabled the supply chain network to respond quickly. For
instance, the US Navy aircraft carrier crews can stop ight
operations if they detect emergency. This empowering
enhances the supply chain resiliency along with a quick
respond to these events. In fact, this strategy enhances
the supply chain response and its delivery performance.
Since potential disruption sometimes is not visible to
manage,theempoweredpeople,whoareclosetothe
action and can take necessary measures, play a key role
in this regard.
•Continuous communication among informed employee
–C
5
Another factor that enhances the supply chain
resiliency via its cultural change is the Continuous Com-
munication among informed employees proposed rst by
She (2005). This author argued that keeping personnel
awareisthekeyfactorofcreatingresilientorganisation.
Because,whenthedisruptiontakesaplace,employees
know the company status, what is selling and which cus-
tomer should be served rst. This action continues to
provide the knowledge and information for employees to
make better decisions in the case of unforeseen incidents.
•Sharing information either with suppliers or customers
–C
6
As declared by Christopher and Peck (2004), informa-
tion sharing enhances the visibility of the supply chain
and increases the supply chain resiliency as the result. In
fact,visibilityisanoutcomeofinformationsharingactiv-
ities between supply chain partners (Wei & Wang, 2010)
anditisthekeyfactorforcreatingaresilientsupplychain.
AccordingtoChopraandSodhi(2004), collaborative
information sharing is the essential step for an eective
crisis management system. As such, the visibility ensures
some condenses into the supply chain and prevents over-
reactions, unnecessary interventions and ineective deci-
sions in a risk event situation (Christopher & Peck, 2004).
Note that the visibility is related to eective disruption
response. The recover visibility is an important driver
of the eective timing of intervening actions throughout
the risk event (Jüttner & Maklan, 2011). Generally, shar-
ing the information among all entities of supply chain is
the base of planning and if information are insucient
or wrong, it will result in making wrong decisions. Since
the information sharing serves as a glue to maintain the
integrity of all entities of supply chain and to enhance the
coordination of entities, which is essential for eective
planning, quick response and preventive overreactions.
•Auto-ID technology such as radiofrequency identica-
tion technology (RFID) – C7
The last decades have seen a rapid development of
using new technologies for logistic activities in a sup-
ply chain system. In regard to She (2005), technologies
(e.g. transportation planning systems and RFID) not only
enhance the warning capability but also play a key role
in the supply chain visibility. This is because the quicker
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 11
a supply chain disruption is detected, the higher time
the supply chain would have to minimise the negative
eects of the disruption in a supply chain (Craighead
et al., 2007). In other words, the enhanced visibility allows
a supply chain network to detect disruption and miti-
gates its subsequent eect via eective switching resource
when the need arises among entities of this supply chain
(She, 2005).
•Process improvement – C8
The last criterion is the process improvement men-
tioned by Christopher and Peck (2004). It is generally
believed that the streamlined processes reduce the lead-
timeswhicharethekeyingredienttoenhancethevelocity
of supply chains. In fact, these actions enhanced the relief
chain ability to respond rapidly in terms of delivery and
to cope with short-term changes in the volume and mix
requirements. She (2005) worked on the concurrent
process (instead of sequential) and argued that this strat-
egy enables the reliability of the supply chain to speed
up the recovery phase. Generally speaking, the exibility
refers to re-conguration of the number of possible states
inasupplychain.Thisissuecantaketherobustnessnum-
ber of changes. This logistic system is also able to cope
with the velocity focuses on the pace of exible adapta-
tions (Stevenson & Spring, 2007). Note that the lead time
is seen as a key indicator of supply chain velocity as the
result . As such, the streamlined processes are helpful to
reduce the number of stages or activities involved. The
aimoftheirdesignistoperformtheseactivitiesinaparal-
lelratherthaninseries.Suchprocessesaree-basedrather
than paper-based. In conclusion, this strategy enhances
the supply chain resiliency via speed up recovery phase
and respond rapidly in terms of delivery.
3.2. Assumptions
The main characteristics and assumptions used in the
formulation of resilience HRC model (mainly on Toghi
et al. (2016)) are as follows:
I. The capability of suppliers and candidate CWs
may be partially disrupted by a disaster through
damage to the roads and/or destruction to facili-
ties.
II. Each CW is supplied by suppliers (with limited
capacity).
III. Each LDC is supplied by CWs, multiple CWs or
strategic stocks.
IV. Strategic stock is located in the safe places nor-
mally outside of the expected disaster areas.
V. Each strategic stock ships the items directly to the
nearest LDCs. There is the limitation of distance
and each strategic stock can ship the items to the
LDCs which are located at the acceptable distance
far away from the strategic stock.
VI. Transportation between suppliers and CWs or
strategic stock and LDCs are considered to be
multi-mode (train, plane, helicopter, truck, motor-
cycle, etc.). The capability of each mode or rout
may be partially disrupted by a disaster through
damagetotheroads.Overall,thepossibledestruc-
tion of transportation routes at dierent levels is
considered.
VII. The resiliency level is calculated for each facility
(i.e. suppliers, CWs, LDCs).
VIII. The multiple disasters (subsequent minor post-
disasters) are taken into account in the mod-
elling.Itisassumedthattheseminordisasterscan
increase the initial demand and impact on the
delivery time.
IX. More than one kind of relief commodity must be
delivered. Accordingly, each commodity is associ-
ated with a dierent volume and a dierent cost of
procurement, storage and transportation.
X. Each supplier and LDC can deliver a given num-
ber of relief commodities and it is based on the
suppliers’ exibility level.
XI. Inventory may be stored at CWs, LDCs and strate-
gic stocks. Similar to suppliers, each CW, LDC and
strategic stock can keep one or several kinds of
relief commodity. Consequently, they can deliver
a given number of service and commodity.
XII. The majority of parameters are uncertain (i.e.
demand, cost, transportation time, etc.) and
depend on various factors, including the disaster
scenario and the impact of the disaster.
XIII. Due to capacity limitations, the proposed model
considers a number of capacity levels for each can-
didate CW where appropriate capacity should be
determined for each selected CW.
3.3. Notations
The following notations are used in the formulation of
the proposed resilience HRC model:
Indices
lIndex of potential suppliers, l=1, 2, 3, ...,L
iIndex of potential CWs, i=1, 2, 3, ...,I
jIndex of potential LDCs, j=1, 2, 3, ...,J
kIndex of aected areas; demand points, k=1, 2, 3,
...,K
12 A. M. NEZHADROSHAN ET AL.
hIndex of potential strategic stocks, h=1, 2, 3, ...,H
mIndex of potential transportation mode, m=
1, 2, 3, ...,M
sIndex of potential disaster scenarios, s=1, 2, 3,
...,S
qIndexofreliefitems,q=1, 2, 3, ...,Q
cIndex for storage capacity levels of CWs, c=
1, 2, 3, ...,C
gIndex of potential subsequent disasters, g=1, 2, 3,
...,G
Parameters
Fc
iEstablishing cost of the ith CW at capacity
level c
GjEstablishing cost of the jth LDC
EhEstablishing cost of the hth strategic stocks
IHqInventory holding cost of item q
UCi
qUnit inventory cost of unused item qat the
ith CW
ULj
qUnit inventor y cost of unused item qat the jth
LDC
λi
qs Usable inventory ratio of the qth item at the
ith CW under scenario s
μj
qs Usable inventory ratio of the qth item at the
jth LDC under scenario s
ξs
lUsable capacity ratio of the lth supplier under
scenario s
USs
qUnit shortage cost of item qin disaster sce-
nario s
TAs
ijm Transportation time between the ith CW and
jth LDC via mode mto reect the road and
trac conditions in disaster scenario s
TBs
lim Transportation time between the lth sup-
plier and the ith CW via mode mto reect
the road and trac conditions in disaster
scenario s
ζs
ijm 1, if mode mis available under scenario s
between the ith CW and jth LDC; 0 otherwise
ωs
lim 1, if mode mis available under scenario s
between the lth supplier and ith CW; 0 oth-
erwise
Ds
qk Demand level for the qth item at the kth
demand point under scenario s
VcStorage capacity of each CW established at
capacity level c
CAjStorage capacity of the jth LDC
SAq
hStorage capacity of the hth strategic stock for
the qth item
CSql Storage capacity of the lth supplier for the qth
item
CAPijm Capacity of transportation mode between the
ith CW and jth LDC via mode m
CCPlim Capacity of transportation mode between the
lth supplier and the ith CW via mode m
CTqlim Cost of transportation mode between the lth
supplier and the ith CW via mode mfor the
qth item
CTRqijkm Cost of transportation mode between the ith
CW and jthLDCtodemandpointkvia mode
mfor the qth item
AqRequired unit of storage capacity of the qth
item
PsProbability of occurring the scenario s
αiResiliency level of the ith CWs
θjResiliency level of the jth LDCs
φg
sSubsequentdisasterseectsondemandsafter
the major disaster in scenario s(gis the num-
ber of minor disaster in scenario s)
ϕg
sSubsequentdisasterseectsondeliverytime
after major disaster scenario s(gis the num-
ber of minor disaster in scenario s)
ρql 1, if supplier lth capable to deliver the qth
item
Decision variables
Yc
i1, if the ith candidate CW is opened at capacity
level c;0,otherwise
Oj1, if the jth candidate LDC is opened; 0, otherwise
γh1, if the hth candidate strategic stock is opened;
0, otherwise
τl1, if the lth candidate supplier is selected; 0, oth-
erwise
Rqi Inventory level of the qth item at the ith CW
Uqj Inventory level of the qth item at the jth LDC
UIs
qi Unused inventory level of the qth item at the ith
CW under disaster scenario s
URs
qj Unused inventory level of critical item qat the jth
LDC under disaster scenario s
Ns
ijm 1, if transportation mode mis selected between
the ith CW and jth LDC under scenario s
Cs
lim 1, if transportation mode mis selected between
lth supplier and ith CW under scenario s
xs
qjk Amount of the qth critical item to be delivered
from the jth LDC to demand point kunder dis-
aster scenario s
zs
qijkm Amount of the qth item to be delivered from CW
ito demand point kvia jth LDC and transporta-
tion mode munder disaster scenario s
vs
qhjk Amount of the qth item to be delivered from
strategic stock hto demand point kvia jth LDC
underdisasterscenarios
ws
qlim Amount of the qth item to be delivered from sup-
plier lto the ith CW via transportation mode m
underdisasterscenarios
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 13
ηs
qk Amount of unfullled demand for the qth item
in demand point kunderdisasterscenarios
Tmax Amount of maximum transportation time under
disaster scenario s
3.4. Problem formulation
Here, a multi-objective mixed-integer linear program-
ming is introduced to simultaneously determine the loca-
tion of CWs, LDCs and the corresponding inventory
quantities for relief items. The model is to consider the
distribution quantities from supplier to CWs, from CWs
to the aected areas (LDC) and from strategic stock to
LDC as well. The presented model allows minimising the
expected total cost, cost variability and maximising cus-
tomer satisfaction. In the second stage, a relief distribu-
tion plan is developed based on various disaster scenar-
ios. The model considers the uncertainty in the locations
where the demands might arise. As such, the possibility
that some of the prepositioned supplies at CWs or sup-
pliers might partially be destroyed by the disaster exists.
To the best of our knowledge, there is no similar work
accounting for three important objectives (i.e. time, cost
and satisfaction level) and other aforementioned aspects,
simultaneously. At the end, the proposed multi-objective
mixed-integer possibilistic linear programming model of
resilient HRC is as follows:
Min TC
=
i
c
Fc
i.Yc
i+
j
Gj.Oj+
h
Eh.γh
+
q
k
i
IHq.Rki +
q
k
j
IHq.Ukj
+
s
Ps.⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
qiUCi
q.UIs
qi +qjULj
q.URs
qj
+qkUSs
q.ηs
qk
+qlimCTqlim.ws
qlim
+qijkmCTRqijkm.zs
qijkm
⎫
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎭
(1)
Min =Tmax (2)
Max =
i
c
αi.Yc
i+
j
Oj.θj(3)
Subject to:
q
Aq.Rqi ≤
c
Vc.Yc
i∀i∈I(4)
c
Yc
i≤1∀i∈I(5)
q
Aq.Uqj ≤CAj.Oj∀j∈J(6)
j
xs
qjk +
i
j
m
zs
qijkm +
h
j
vs
qhjk
=Ds
qk
g
(1+φg
s)−ηs
qk ∀k∈K,q∈Q,s∈S
(7)
k
xs
qjk +URs
qj =μj
qs.Uqj ∀j∈J,q∈Q,s∈S(8)
j
k
m
zs
qijkm+UIs
qi =λi
qs.Rqi ∀i∈I,q∈Q,s∈S
(9)
q
k
zs
qijkm
≤ζs
ijm.CAPijm .Ns
ijm ∀i∈I,j∈J,m∈M,s∈S
(10)
i
m
ws
qlim ≤ρql.ξs
l.CSql.τl∀q∈Q,l∈L,s∈S
(11)
q
ws
qlim
≤ωs
lim.CCPlim .Cs
lim ∀l∈L,i∈I,m∈M,s∈S
(12)
k
j
vs
qhjk ≤SAq
h.γh∀h∈H,q∈Q,s∈S(13)
⎡
⎣TAs
ijm.
g
(1+ϕg
s)⎤
⎦.Ns
ijm
≤ζs
ijm.TMax ∀i∈I,j∈J,m∈M,g∈G,s∈S
(14)
⎡
⎣TBs
lim.
g
(1+φg
s)⎤
⎦.Cs
lim
≤ωs
lim.Tmax ∀l∈L,i∈I,m∈M,g∈G,s∈S
(15)
ws
qlim
≤M.Cs
lim.ωs
lim ∀l∈L,i∈I,m∈M,q∈Q,s∈S
(16)
zs
qijkm
≤M.Ns
ijm.ζs
ijm
∀k∈K,j∈J,i∈I,m∈M,q∈Q,s∈S(17)
14 A. M. NEZHADROSHAN ET AL.
zs
qijkm,xs
qjk,ηs
qk,ws
qlim,Tmax,vs
qhjk,URs
qj,Uqj ,Rqi ,UIs
qi
≥0∀i∈I,j∈J,l∈L,k∈K,h∈H,q∈Q,s∈S
(18)
Oj,Yc
i,τl,γh,Ns
ijm,Cs
lim
∈{0, 1}
∀i∈I,l∈L,m∈M,c∈C,j∈J,h∈H,s∈S
(19)
The objective function in Equation (1) minimises
the total operating costs of selected CWs and LDCs,
and their inventory costs. The last part of this objective
function minimises the total cost of unused inventories
and the shortage cost of unmet demands and trans-
portation cost of items. The second objective function
in Equation (2) minimises the maximum travel time
betweeneachpairofCW/LDCanddemandpointfor
the items. The third objective function in Equation (3)
maximises the weighted resilience level of each facility i.e.
CW/LDC.
To limit the feasible area of the model, there is a set
of constraints from Equations (4) to (19). The constraint
in Equation (4) enforces the restrictions on the available
capacity of CWs. The constraint in Equation (5) implies
that only one CW with specied capacity level could
be constructed at each candidate site. The constraint in
Equation (6) enforces the restrictions on the available
capacity of LDCs. The constraint in Equation (7) deter-
mines the unsatised demands for critical items. The
right hand of Equation (7) determines the initial demand
plus demands added after the subsequent of minor dis-
asters. The constraints in Equations (8) and (9) ensure
that the distributed quantity of each item plus respective
unused inventory is equivalent to their corresponding
inventory levels in respective of CW/LDCs. The con-
straint in Equation (10) represents the restrictions on the
available capacity of the transportation system between
pair of CW/LDCs. The constraint in Equation (11)
enforces the restrictions on the available capacity of sup-
pliers. Each supplier can deliver a given number or a set
of critical items depend on the suppliers’ exibility level.
Additionally, each supplier may loss its capacity partially
or totally and right hand of constraint in Equation (11)
guarantees these conditions. The constraint in Equation
(12) ensures the restrictions on the available capacity of
the transportation system between pair of supplier/CWs.
The constraint in Equation (13) restricts the available
capacity of strategic stock. The constraints in Equations
(14) and (15) calculate the maximum travel time. The
constraints in Equations (16) and (17) ensure that the
quantity of each item will be shipped if the transportation
system is available. Finally, the constraints in Equations
(18) and (19) determine both non-negative continuous
and binary types of decision variables, respectively.
4. Solution algorithm
To develop a novel scenario-based possibilistic-stochastic
programming (SBPSP) approach, a set of multiple solu-
tion procedures including a new hybrid ANP and fuzzy
DEMATEL approach by using the latest version of an
augmented -constraint method in three main steps is
presented as follows:
Step 1. DEMATEL and Fuzzy ANP
The proposed solution approach starts with identifying
the resiliency level of each facility. This process is carried
out based on a set of criteria (C1–C8)whichweremen-
tioned in Section 4.1. To do this end, a hybrid of ANP and
fuzzy DEMATEL approach is applied for ranking them.
Noteworthy, the Analytic Hierarchy Process (AHP) pro-
posed by Saaty (1990) only considers the inuence ows
between various elements with hierarchically structured
the linear relationships. Its main drawback is that this
approach does not consider the nonlinear ows; interac-
tions or interdependencies such as a cycle (mutual outer
dependencies) and loop (inner dependencies) between
elements. In regard to making an account for the inter-
action and the interdependencies between the rankings
of the mentioned criteria, a hybrid approach of Ana-
lytic Network Process (ANP) and fuzzy Decision Making
Trial and Evaluation Laboratory (DEMATEL) techniques
has been applied for the rst time from the literature to
calculate the resiliency level of facilities.
The DEMATEL method was founded based on the
graph theory which uses a matrix calculation to visu-
alise the problem and to calculate the impact strength of
existing relations (Tzeng et al., 2007). A fuzzy DEMATEL
method is adopted in this study to derive the network in
a more comprehensive and quantitative manner (Chang
et al., 2011). Due to page limitation, more details about
the DEMATEL method are provided in Appendix 1.
Furthermore, the ANP is a general form of AHP pro-
posed by Saaty (2008), in which a network of interre-
lationships between the elements of a decision problem
can be used instead of a linear hierarchy structure (Torabi
et al., 2014). The main step of ANP is to identify a suit-
able network structure for the decision problem. The rst
step of ANP is determining the network structure of the
problem. This methodology is usually identied via con-
ducting a brain storming meeting or a Delphi process
(Chang et al., 2011).
Asmentionedearlier,thisstudyemploysahybrid
approach of fuzzy DEMATEL and ANP for identifying
resiliency level of each facility to consider the benets
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 15
of both methods. The main contribution of the pro-
posed hybrid algorithm is that the fuzzy DEMATEL
method to nd the casual relationships among them
(Chen et al., 2011;Tzengetal.,2007). According to the
network constructed from the meaningful inuences,
facilities’ resiliency levels are ranked by ANP method.
In the proposed hybrid algorithm, the fuzzy ANP is
applied to capture experts’ viewpoints towards dier-
ent facility through pairwise comparisons (based on the
eight criteria which were mentioned in Section 4.1) to
nd resiliency level of each facility. Interested readers are
referred to Chung et al. (2005) for details of ANP method.
Taken together, the novel cluster weighting proposed by
Yang and Tzeng (2011)isappliedinthispapertoincor-
porate the DEMATEL results in the fuzzy ANP method.
More details about the proposed hybrid method are given
in Appendix 2.
Step 2. Augmented -constraint method
In this step, the multi-objective formulation (presented
in Section 3.4) is transformed into an equivalent sin-
gle objective model by using the weighted augmented
-constraint method (Esmaili et al., 2011). The main rea-
son behind of this action is referred to numerous recent
studies which have utilised the -constraint method to
solve a multi-objective model (e.g. Sadghiani et al., 2015;
Sahebjamnia et al., 2017,2018). The proposed augmented
-constraint method is the latest version of this method-
ology adopted from Sahebjamnia et al. (2018). In this
method, one of the objectives is optimised, while other
objectives are added as a set of constraints (Görmez et al.,
2011;Mavrotas,2009).Formoredetails,interestedread-
ers may refer to Esmaili et al. (2011), Fathollahi-Fard et al.
(2020), Liu et al. (2020), Mavrotas (2009) and Torabi et al.
(2013). The applied algorithm is called ‘weighted aug-
mented e-constraint method’(Esmaili et al., 2011)that
involves an augmented term in its objective function to
ensure yielding an ecient solution for each vector
(Mavrotas, 2009). By applying the weighted -constraint
method, the basic multi-objective problem is converted
to the following model:
min θ1f1(x)−range1×δ
×θ2sl2
range2
+θ3sl3
range3
+...+θp
slp
rangep
s.t. : (20)
fp(x)+slp=εp;∀p=2, 3, ...,p
x∈X;slp∈R+
where xis the decision vector, Xis the feasible deci-
sion space and are the Pobjectives being minimised. The
parameter δis a very small number (usually between
10−6and 10−3), θp,range
pand slpdenote, respectively:
the priority (where pθp=1) and the range of the
pth objective function, and the slack variable of respec-
tive constraint. The range of each constrained objective
(rangep) is calculated and divided into npequal intervals
and εpvalues are nally calculated as follows (Esmaili
et al., 2011).
rangep=fmax
p−fmin
p;εl
p=fmax
p−rangep
np
×l;
∀p= 1, l=0, 1, 2, ...,qp−1. (21)
where fmax
pand fmin
pdenote the maximum and minimum
(i.e. the nadir and ideal) values of objective p,respectively,
and lis the grid point’s number.
In this study, the rst objective function given in
Equation (1) is considered as the main objective of the
corresponding weighted augmented ε-constraint model
while the second and third objective functions in Equa-
tions (2) and (3) are added to the constraints.
Step 3. Scenario-based possibilistic-stochastic pro-
gramming
Regarding the proposed possibilistic scenario-based
model (Section 4.4), a number of parameters are impre-
cise as they are extracted from experts according to their
subjective knowledge and past experience about the value
of these parameters. Moreover, most of the facility loca-
tion problems considering random facility disruptions
assume that probabilistic information about the disrup-
tionsisavailable.Inthisstudy,similartorecentstud-
iesofthisarea(Noham&Tzur,2018;Toghietal.,
2016), we applied a possibilistic programming to deal
with uncertainty. Therefore, the extended model under
each scenario is a possibilistic programming problem for
which the recently developed possibilistic programming
method(Xu&Zhou,2013)isadoptedtoconvertittoa
crisp counterpart.
In practice, decision-makers have dierent opti-
mistic–
pessimistic attitudes. In this respect, the possibility (Pos)
and necessity (Nec) are two measures that demonstrate
attitudes which are extremely optimistic and pessimistic.
However, the measure Me is more exible to avoid
extreme attitudes and to be more realistic (i.e. something
between optimistic and pessimistic views). More infor-
mation about Me method can be found in (Sadghiani
et al., 2015; Xu&Zhou,2013). Xu and Zhou (2013)
dened the fuzzy measure Me as follows:
Me{A}=Nec{A}+λ(Pos{A}−Nec{A})(22)
where AisasetinP(S), and (S,P(S), Pos) is possibil-
ity space, and λ(0≤λ≤1)is an optimistic–pessimistic
16 A. M. NEZHADROSHAN ET AL.
parameter to determine the combined attitude of
decision-maker and (Pos{A}−Nec{A})is the range
within which the value of the measure changes from
pessimistic to an optimistic one. Consider the following
possibilistic chance-constrained programming (PCCP):
max f(x,ξ)
s.t. : gr(x,ξ) ≤0r=1, 2, ...,p(23)
x∈X
where ξisasetoffuzzyvariablestaintedwithepistemic
uncertainty.
The expected value and chance-constrained operators
based on the measure Me are used to deal with the impre-
cise (i.e. possibilistic) objective function and constraints,
respectively. Therefore, the PCCP is re-written as follows:
max E[f(x,ξ)]
s.t.:Ch{gr(x,ξ) ≤0}≥δrr=1, 2, ...,p
(24)
x∈X
where Eis the expected value operator, Ch is the chance-
constrained operator and δr,r=1, 2, .., p,isthemini-
mum acceptable condence level on the rth possibilis-
ticconstraintsetbythedecision-makeraccordingtoits
importance.
Assume that ˜
ci=(ci1,ci2,ci3),i=1, 2, ...,n,arepos-
itive triangular fuzzy variables, so the expected value
of the objective function according to formula (24) is
computed as:
E[
n
i=1
˜
cT
i.xi]=
n
i=1
((1−λ)
2.ci1+ci2
2+λ
2.ci3).xi(25)
Here, the measure Me is used as the chance-constrained
operator:
Ch{gr(x,ξ) ≤0}≥δr↔Me{gr(x,ξ) ≤0}
≥δrr=1, 2, ...,p(26)
Xu and Zhou (2013) used rough set theory and divided
the feasible region of the model to obtain two models
named the lower approximation model (LAM) and the
upper approximation model (UAM), and applied possi-
bility (Pos) and necessity (Nec) measures to solve these
two models. Based on Xu and Zhou (2013), we would
have the following formulations:
Nec{˜
aT
jx≤˜
bj}≥δj⇔bj−δjαb
j
≥aT
jx+(1−δj)βaT
jxj =1, 2, ...,m
(27-1)
Nec{˜
aT
jx≥˜
bj}≥δj⇔bj+(1−δj)βb
j
≤aT
jx−δjαaT
jxj =1, 2, ...,m(27-2)
Pos{˜
aT
jx≤˜
bj}≥δj⇔bj+(1−δj)βb
j
≥aT
jx−(1−δj)αaT
jxj =1, 2, ..m
(28-1)
Pos{˜
aT
jx≥˜
bj}≥δj⇔bj−(1−δj)αb
j
≤aT
jx+(1−δj)βaT
jxj =1, 2, ..m
(28-2)
where the mean value aji is a real number, αa
ji and βa
ji are
the left and right spreads of ˜
aji,αb
jand βb
jare the left and
right spreads of ˜
bj.
The LAM and UAM can be obtained based on Equa-
tions (29) and (30), respectively. The equivalent mod-
els for the lower approximation model and the upper
approximation model are as follows:
LAM :
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
En
i=1
˜
cT
i.xi=
n
i=1(1−λ)
2.ci1+ci2
2
+λ
2.ci3.xi,i=1, 2, .., n
s.t.
bj−δjαb
j≥aT
jx+(1−δj)βaT
jx
j=1, 2, ...,m
xi≥0, i=1, 2, ...,n
(29)
UAM :
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
En
i=1
˜
cT
i.xi=
n
i=1(1−λ)
2.ci1+ci2
2
+λ
2.ci3.xi,i=1, 2, .., n
s.t.
bj+(1−δj)βb
j≥aT
jx−(1−δj)αaT
jx
j=1, 2, ...,m
xi≥0, i=1, 2, ...,n
(30)
Also, an enhanced version of measure Me is proposed
by Torabi et al. and interested readers are referred to
Torabi et al.
Disruptions are formulated by a set of scenarios, in
whichasubsetoffacilitiesmightbesimultaneouslydis-
rupted under each scenario (Snyder & Daskin, 2006). In
this study, to account for all disruption scenarios and
reach an optimal solution in all scenarios, we apply the
scenario-based robust optimisation programming. The
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 17
Figure 2. Novel SBPSP approach.
robust optimisation framework was rst introduced by
Mulvey et al. (1995)todealwithmulti-scenariooptimi-
sation problems. Overall, a general form of a scenario-
based robust model is formulated as follows (Mirzapour
Al-E-Hashem et al., 2011):
Min w1
s∈S
s.ψs
+γ
s∈S
sψs−
s∈S
s.ψs+2θs
+w2
s∈S
s.δs(31)
Ax =b(32)
ψs−
s∈S
s.ψs+θs≥0 (33)
x≥0, θs≥0, s∈S(34)
Where Sis the set of scenarios and sdenotes the like-
lihood of scenario s,s∈Ss=1.Also, the parameter δs
represents the infeasibility of the model under scenario s
due to uncertainty in some of the parameters. Hence, if
the model is feasible under scenario sthen δs=0.
Finally, γis the weight devoted to the solution vari-
ance and ψs=f(x)isthecostorbenetfunctionof
scenario s. when ψsis greater than s∈Ss.ψsthen θs=
0andwhens∈Ss.ψsis greater than ψsthen θs=
s∈Ss.ψs−ψs.Itshouldbenotedthattherstterm
of the objective function in Equation (31) represents the
robustness of the solution. It attempts to seek a solu-
tion that is optimal in all scenarios (Mulvey et al., 1995;
Sadghiani et al., 2015), and the second term represents
the model robustness. The model robustness guarantees
the feasibility of the solution in all scenarios using penalty
functions (Mulvey et al., 1995), weighted by w1and w2,
respectively.
In summary, the possibilistic-stochastic programming
method is applied for imprecise parameters in the model,
and also the model involves several random scenarios,
each of which formulates a specic disruption scenario
with a given likelihood (Golmohamadi et al., 2017). In
fact, the novel SBPSP approach is developed. Figure 2
summarises the steps of the proposed approach.
5. Case study
In this section, the proposed model is tested and validated
based on a case study as one of the main contributions of
this proposal. The main purpose of this experiment is to
demonstrate the correctness and appropriateness of the
results. In fact, this research is motivated by the com-
plex problem of designing a humanitarian relief chain
in Mazandaran province in Iran. Designing novel deci-
sion models under major disasters is required to inform
decision-makersofthisprovinceasoneofthemostprob-
ability cases of natural disaster in Iran. We hope this
proposal is useful for better response to potential dis-
asters. However, we believe the general features of our
model can be implemented in other similar cases.
18 A. M. NEZHADROSHAN ET AL.
Figure 3. A schematic map of Mazandaran.
Tab le 4. Demand of the relief items per family.
Item Demand Unit Item Demand Unit Item Demand Unit
15Set 111Box212#
21# 121#223Pair
3 2 Pair 13 1.5 # 23 3 #
41# 141#241#
52# 152Pair252Kg
67# 162kg269#
71# 172.5kg277#
8 2 Pair 18 3 kg 28 1 Pair
92# 192kg292#
10 1 # 20 1 # 30 1 Box
In regard to the case study, a set of details to the
design of HRC in one of the northern province of
Iran, Mazandaran province, is provided as follows. This
province covers an area of 23,842 km (SCI.org). Mazan-
daran is one of the most densely populated provinces
in Iran and has diverse natural resources, especially
large reservoirs of oil and natural gas . According to
the census of 2006, the population of the province
was 2,922,432 of which 53.18% were urban dwellers,
46.82% villagers and the remaining were non-residents
(https://www.amar.org.ir/). Sari is the capital city of the
province. As shown in Figure 3, the Mazandaran is
divided into 15 suburbs.
It should be noted that the demands are estimated
based on the population and number of aected people
according to each scenario addressed in JICA (2000)as
well as 30 relief items needed by each family as dened in
Tog h i et al . ’s ( 2016)report(seeTable4). The relief items
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 19
Tab le 5. Candidate zones for establishing CWs inside the province.
No. Candidate zone Operating cost Resiliency level No. Candidate zone Operating cost Resiliency level
1 Behshahr 11.3 BR 0.409 9 Ramsar 13.3 BR 0.164
2 Neka 12.6 BR 0.301 10 Amol 11.6 BR 0.108
3 Sari 14.3 BR 0.34 11 Babolsar 16.3 BR 0.203
4 Savadkoh 10.3 BR 0.209 12 Noor 13.3 BR 0.4
5 Qaemshahr 13 BR 0.551 13 Noshahr 10.5 BR 0.320
6 Jooybar 10.7 BR 0.304 14 Chaloos 14.7 BR 0.109
7 Mahmoodabad 11 BR 0.102 15 Tonekabon 10 BR 0.203
8 Babol 16.7 BR 0.108
include water, some types of food, health items (such as
drugs, bandages, rst aid kits), cloths, accommodation
(like tents, blankets), relief equipment, etc.
In regard to the reduction rates of dierent supplies,
no historical data were available. Therefore, a state-of-
the-art possibilistic approach is utilised to incorporate
imprecise parameters in the form of fuzzy numbers based
on experts’ subjective knowledge and professional feel-
ings. Transportation times are estimated by taking into
account the distance between the districts as well as esti-
mated destruction ratios. Destruction ratios for partial
and complete of disasters are, respectively, estimated at
0.1 and 0.01 in respective districts.
6. Results and discussions
In this section, the results of the proposed model are
presented and discussed. The resiliency level for each
supplier and each candidate CWs or LDs are calcu-
lated and summarised in Table 5;extractedfromhybrid
DEMATEL-ANP method (see Section 4, step 1). Also,
basedonajointresearchbetweenCenterforEarthquake
StudiesofTehranandJapan,itisassumedthateachLDC
is capable of fullling the requirements of 5000 families
(each consists of ve people) and could be constructed
in each district. The average operating costs for setting
upeachLDCareestimatedat1.2billionRials.Itshould
be noted that the model accounts for available public
facilities such as parks, schools and especially mosques
as the potential LDCs. Moreover, several candidate loca-
tions around or inside the Mazandaran province have
been nominated for establishing required CWs or strate-
gic stocks. The established strategic stocks by considering
a set of candidate zones are given in Table 6.Thecapacity
ofeachCWandstrategicstockscouldbeselectedfrom
three capacity levels: 50, 100 and 150 thousands fami-
lies. In addition, the average operating costs for setting
up each strategic stocks and CW are estimated at 11.2 and
12.5 billion Rials, respectively. With the help of experts,
other cost rates have been estimated, i.e. the holding,
shortage and unused inventory costs. Due to page lim-
itation, the aforementioned data have not presented
here.
Tab le 6. Candidate zone for establishing strategic stocks.
Candidatezonefor
strategic stock Distance (km) Operating cost Capacity
Tehran 159 14.2 BR 200
Qazvin 322 11.3 BR 110
Alborz 252 12.4 BR 130
Golestan 346 10.3 BR 120
Gillan 338 12.3 BR 160
Semnan 420 7.4 BR 80
Tab le 7. Probabilities of different earthquake scenarios.
Disaster scenarios Probability Number
Scenario 1 0.123 3
Scenario 2 0.065 2
Scenario 3 0.202 1
Scenario 4 0.0937 4
Scenario 5 0.0765 5
Scenario 6 0.123 3
Scenario 7 0.091 1
Scenario 8 0.065 6
Scenario 9 0.109 2
Scenario 10 0.0518 1
From the results, generally, an increase in the number
of disruption scenarios leads to an increase in the solu-
tion time, signicantly. Note that the number of scenarios
is not considered more than 14 in several similar studies
(see, e.g. Gutiérrez et al., 1996;Kouvelisetal.,1992;Sahe-
bjamnia et al., 2018; Snyder & Daskin, 2006;Toghietal.,
2016). Thus, we consider 10 disruption scenarios in our
case study. Since, the level of a disaster scenario depends
on the occurrence time, the probability of a disaster for
days and nights are separately presented in Table 7.The
proposed mathematical model is coded in the optimisa-
tion software GAMS 23.5 and solved by the solver CPLEX
12.2 in a computer with 1.7GB CPU and 6.0GB RAM.
The sensitivity analysis was conducted for the con-
dence levels (δ), and the results are presented in Table 8.
It can be seen in this table that when the condence level
increases, all of the objective values are escalated signif-
icantly. In fact, by increasing the condence level, the
feasible zone increases. This means that the nal solu-
tion is likely to be worse. In contrast, when the condence
level (δ)isdecreased,wecangetbetterresultssincethe
feasible region is expanded, which can be observed in
20 A. M. NEZHADROSHAN ET AL.
the improvement of objective values in Table 8.Fur-
thermore, the Me measure is exible which enables
the decision-makers with the upper and lower bounds
of the optimal decision. This interval can be obtained
with changing the degree of optimistic–pessimistic atti-
tudes (λ).Ifdecision-makersholdanoptimisticattitude
towards the objectives, they can choose a bigger opti-
mistic–pessimistic parameter λand if they are very cau-
tious on the chance constraints, they can choose greater
condence levels δ. After deciding on the parameters,
the decision-maker will be given a solution, which meets
their requirements.
Table 9shows the results of sensitivity analysis car-
riedoutfortheweightvector(θ).Itcanbeseenthatthe
value of (θ) may aect the location of the facilities and the
structure of the network. Therefore, changing the weights
would aect the objectives’ values considerably as well
as the structure of the network. This provides high ex-
ibility for decision-makers to account for their preferred
weights. In our case study, the weights were set to (0.4,
0.3, 0.3). Figure 4indicates the optimal objective values in
two dierent cases: based on each scenario and in under
mixed uncertainties.
Inspecting the results in Table 10, it is evident that
the subsequent disasters can aect the number of the
facilities of the network. The geographical location of
Mazandaran province may enhance the chance of sub-
sequent disasters because it includes small and big rivers
ow in the tension of its south and north that are divided
to three areas such as western, central and eastern. Thus,
it is important to consider the subsequent disasters. It
can be observed in Table 10 that the structure of the
network and allocated inventory are both aected when
considering subsequent disasters.
7. Managerial implications
This paper presents a model for developing a relief net-
work to cope with possible major disruptions, the min-
imum numbers of required facilities (CWs, LDs and
strategic stocks), and each transportation mode be avail-
able in each selected supply facility (as the eet sizing
decisions). As such, the demand coverage patterns are
determined by the developed model. This study has been
motivated by the urgent need for a relief supply chain net-
work in Mazandaran to prepare for potential disasters.
Since no historical data are available, we apply the state-
of-the-art possibilistic programming in order to deal with
imprecise data. This fuzzy chance constraint program-
ming (FCCP) provides enough exibility by considering
input data.
The important observation is that even constructing
all candidate CWs and LDCs is not sucient. The main
Tab le 8. Sensitivity analysis with different parameters, w1=w2=0.5.
Me approach interval
λ
0 0.2 0.4 0.5 0.6 0.8 0.95 0.99
[LAM,UAM] [LAM,UAM] [LAM,UAM] [LAM,UAM] [LAM,UAM] [LAM,UAM] [LAM,UAM] [LAM,UAM]
0.5 [3.944E+11, 3.609E+11] [3.745E+11, 2.932E+11] [3.645E+11, 2.586E+11] [2.945E+11, 2.456E+11] [2.865E+11, 2.378E+11] [2.744E+11, 1.913E+11] [2.343E+11, 1.566E+11] [2.124E+11, 1.1236E+10]
0.7 [4.454E+11, 3.511E+11] [4.2002E+11, 3.011E+11] [4.0002E+11, 2.947E+11] [3.4232E+11, 2.876E+11] [3.312E+11, 2.745E+11] [3.05E+11, 2.43E+12] [2.832E+11, 2.215E+11] [2.713E+11, 1.915E+11]
0.8 [4.811E+11, 3.912E+11] [4.6122E+11, 3.613E+11] [4.4532E+11, 3.265E+11] [3.9232E+11, 3.133E+11] [3.844E+11, 2.811E+11] [3.743E+11, 2.692E+11] [3.344E+11, 2.411E+11] [3.198E+11, 2.012E+11]
0.9 [5.216E+11, 4.16E+11] [5.012E+11, 3.8E+11] [4.523E+11, 3.316E+11] [4.032E+11, 3.016E+11] [3.976E+11, 2.966E+11] [3.854E+11, 2.713E+11] [3.013E+11, 2.566E+11] [2.915E+11, 2.566E+11]
1 [5.876E+11, 4.222E+11] [5.721E+11, 3.999E+11] [5.421E+11, 3.546E+11] [4.365E+11, 3.466E+11] [4.219E+11, 3.109E+11] [4.197E+11, 2.954E+11] [4.044E+11, 2.815E+11] [3.972E+11, 2.215E+11]
LAM, lower approximation model; UAM, upper approximation model,
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 21
Tab le 9. Sensitivity analysis on objective functions weights vectors.
Confidence level
δ=0.9; λ=0.5
w1=w2=0.5 (0.4, 0.3,0.3) (0.4, 0.3,0.3) (0.4, 0.3,0.3) (0.4, 0.3,0.3) (0.4, 0.3,0.3) (0.4, 0.3,0.3)
Obj 1: Total cost 4.446E+11 3.446E+11 3.346E+11 2.646E+11 3.446E+11 3.446E+11
Obj 2: Time 49894 50896 54893 58895 53092 53093
Obj 3: Resilience 13.653 14.053 14.653 15.253 15.853 16.453
Number of facilities (Suppliers, CWs, LDs) (7,4,8,20) (7,4,8,17) (7,3,8,17) (6,2,6,16) (6,2,7,16) (6,2,7,16)
CWs, central warehouses; LDs, local distribution centres.
Figure 4. Comparison of objective functions of scenarios with optimal solution under mixed uncertainties.
Table 10. Test analysis on subsequent disasters.
Confidence level
δ=0.9; λ=0.5
w1=w2=0.5
Subsequent
disaster
No subsequent
disasters
Obj 1: Total cost 3.346E+11 2.341E+11
Obj 2: Time 54,893 34,896
Obj 3: Resilience 14.653 12.32
Number of facilities
(Suppliers, SS,
CWs, LDs)
(7,3,8,17) (7,1,5,14)
Inventory fraction
(SS, CWs, LDs)
(0.43, 0.23, 0.34) (0.11, 0.65, 0.24)
CWs, central warehouses; LDs, local distribution centres; SS, strategic stock.
reason behind of this is stated as follows. Each CWs and
LDs may lose its capacity partially or completely due
to the disruptions. In order to satisfy all demands aris-
ing from the aected area, therefore, the model selected
strategic stocks to compensate the shortage and reduces
the delivery time. Accordingly, the scientic denition
of strategic stock states ‘strategic stocks are located in
the safe places normally outside of the expected disas-
ter areas’ and each strategic stock ships the items directly
to the nearest LDCs not all the LDCs. This means that
there is the limitation of distance and each strategic stock
can ship the items to the LDCs which are located at the
acceptable distance far away from strategic stock. As can
be seen in Figure 5, three strategic stocks are selected
and located in Gilan, Golestan and Qazvin provinces.
Thesethreelocationsarenotthenearestone.However,
the roads and transportation mode between these three
locations and demand point are signicantly more reli-
able than those between the nearest locations such as
Tehr a n.
Figure 5showsthattwooutofthreestrategicstocksare
locatedinthewesternareaswithahigh-densitypopula-
tion. The majority of HRC network models are designed
under this assumption that there is only one disaster and
they neglect the eect of subsequent events (Zobel &
Khansa, 2014).
In the real world, sudden-onset disasters are followed
by multiple related sub-disasters. The popular exam-
ples of these disasters are earthquakes and their after-
shocks, along with related events such as delayed build-
ing collapses; and hurricanes with levee failures and the
associateddisruptionsintransportationnetworksand
power grids. In fact, subsequent disasters may enhance
the severity of disruptions and increase the demand and
delivery time. Moreover, the geographical location of
Mazandaran province may enhance the chance of sub-
sequent disasters. Its inequalities slope is from west to
east and is in parallelism of Caspian Sea. Alborz Moun-
tainswithsmallandbigriversowintensionofitssouth
and north that are divided to three areas such as western,
central and eastern. Thus, it is important to consider the
subsequent disasters. The number of strategic stocks that
22 A. M. NEZHADROSHAN ET AL.
Figure 5. The location of strategic stocks.
has been selected in condition of considering subsequent
disasters is more when the subsequent disasters are not
included in modelling (Table 10).
Also, the fraction of inventory allocated among facili-
ties is signicantly aected under conditions that subse-
quent disasters are considered. Meanwhile,
subsequent disasters are considered more inventory frac-
tion which is allocated to strategic stocks. For example,
under condition of subsequent disasters, not only the
number of strategic stocks increased from 1 to 3 but
also the proportion of allocated inventory to strategic
stocks have been increased from 0.11–0.43 as revealed in
Table 10.
8. Conclusion
In this paper, a novel SBPSP approach was devel-
oped for designing the resilient HRC network under
a mixed uncertainty i.e. both operational and disrup-
tion risks. Therefore, a novel mixed-integer model for
humanitarian logistics network design problem was
proposed. The humanitarian logistics network involves
multiple CWs and LDCs with dierent resilient level
whichwascalculatedbasedontheresilienceparame-
ters extracted from literature and by applying hybrid
MCDM technique employing both DEMATEL and ANP
methods.
The proposed SBPSP model introduced enough ex-
ibility when designing a relief network by changing the
control parameters and provided a set of compromise
solutions that is highly important due to the strategic
nature of the problem. Also, we applied a exible possi-
bilistic programming proposed by Xu and Zhou (2013)
which enables the decision-makers to hold an optimistic
attitude towards the objectives, through changing the
degree of optimistic–pessimistic attitudes (λ). The results
showed that considering both subsequent disasters and
decision-makers’ preferences on weights of objective
functions may aect the objectives’ values considerably,
the structure of network and the inventory levels in facil-
ities. Therefore, changing the weights of the objective
functions would aect the objectives’ values consider-
ably as well as the structure of network. This provides
high exibility to decision-makers to account for their
preferred weights.
This study opens several directions for future works.
Firstly, more intensive analyses on the proposed math-
ematical model by analysing the key parameters may
need to be explored. Secondly, a novel MCDM tech-
nique can be applied to the proposed problem and com-
pare with own method. Since the model is a multi-
objective optimisation and is dicult in large-scale net-
works, the multi-objective metaheuristic algorithms can
be examined on this model. Moreover, other scopes of
this research can develop some useful tools after natu-
ral disasters. Another promising future research direc-
tion is considering dynamic situations leading to develop
multi-period models.
Acknowledgements
The authors would like to thank especially Professor Seyedali
Mirjalili, associate professor at Torrens University Australia.
HeisanativeEnglisheditorinhigh-rankedjournalssuchas
Applied Soft Computing, Applied Intelligence and Advances in
Engineering Software. He helped us to correct the English writ-
ing and his insightful suggestions and comments are very useful
toimprovethispaper.Wealsowishtothanktheco-editorin-
chief, Professor Konstantaras, and anonymous reviewers for
their constructive and very useful suggestions.
Disclosure statement
No potential conict of interest was reported by the author(s).
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE: OPERATIONS & LOGISTICS 23
Notes on contributors
Ali Mehdi Nezhadroshan is a master student at department
of management in Islamic Aazad University (IAU). He earned
his B.Sc. in biomedical engineering from IAU (2017). He is
interestedinbusinessmanagement,healthcaresystems,sup-
ply chain and logistics along with mathematical model and
optimization algorithms.
Amir Mohammad Fathollahi-Fardwas born and raised in Sari,
Iran.AmiriscurrentlyaresearchassociateatÉcoledeTech-
nologie Supérieure, University of Québec, Montréal, Canada.
He earn his PhD in Industrial Engineering from Amirkabir
University of Technology (Tehran Poly-technique), Tehran,
Iran (2021). He also received his BSc (2016) and MSc (2018)
degreesinIndustrialEngineeringfromUniversityofSci-
ence and Technology of Mazandaran, Behshahr, Iran. His
researches are about Supply Chain Management, Sustainable
Operations Management, Transportation and Logistics Opti-
misation and Health Care Management. He evaluated these
concepts with the use of Operations Research, Optimisation
algorithms mainly by using Heuristics and Multi-Criterion
Decision-Making methods. He has published more than 50
papers in the above areas in high-ranked journals e.g. JCLP,
ASOC, CAIE, NCAA, EAAI, INS etc.
Mostafa Hajiaghaei-Keshteliwas born and raised in Babol,
Iran.HeearnedhisBScfromIranUniversityofScience&Tech-
nology, Tehran, Iran (2004); MSc from University of Science &
Culture, Tehran, Iran (2006); and PhD from Amirkabir Univer-
sity of Technology (Tehran-Polytechnic), Tehran, Iran (2012);
allinIndustrialEngineering.Heiscurrentlyanassociatepro-
fessor in Industrial Engineering at University of Science &
Technology of Mazandaran, Behshar, Iran. He has over 15
years of experience in Business Development, System Analysis,
Inventory and Project Management. Mostafa also has worked
for many corporations in Iran and has held the positions of
consulter, planning and project manager and VP. The main
focusofhisresearchisintheareaofInventoryControl,Supply
Chain Network, Transportation and Meta-heuristics. He has
published more than 100 scientic papers in high-ranked jour-
nals such as ESWA, CAIE, KNOSYS, JCLP, INS, NCAA, IEEE,
ASOC etc.
ORCID
Amir Mohammad Fathollahi-Fard http://orcid.org/0000-00
02-5939-9795
Mostafa Hajiaghaei-Keshteli http://orcid.org/0000-0002-99
88-2626
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Appendices
Appendix 1
In this paper, triangle fuzzy DEMATEL is applied to map the
interdependencies. To address the issue, the following steps
should be considered (Torabi et al., 2014):
Step 1. Calculating the Average Matrix A
Askacommitteeofexpertstoexpresstheirviewpoints
towards the relation between criteria with uncertain linguis-
tic terms and calculate the average matrix; each member of the
experts’ committee indicates her/his opinion about the inu-
ence degree of criterion ion criterion jdenoted Xk
ij from which
the matrix provided by Kth expert is constructed as Xk.
Step 2. Transforming the average matrix into the initial direct-
relation matrix
In this study, the average matrix Awhose elements are in the
form of triangular fuzzy numbers is transformed into the initial
direct-relation matrix by the Converting Fuzzy data into Crisp
Scores (CFCS) method (Chang et al., 2011).
Step 3. Calculating the normalised initial direct matrix D
The direct matrix Djust account for direct inuence ows
between criteria.
s=min ⎡
⎣
1
min
in
j=1|aij|,1
max
jn
i=1|aij|⎤
⎦(A1)
D=s.A(A2)
Step 4. Calculating the total relation matrix T
The total inuence matrix denoted by T,reectsthetotal
inuence degree among criteria whose elements are denoted
by tij which indicates the total direct and indirect inuence of
criterion ion criterion j.Equation(A3)calculatesthematrixT
T=D.(1−D)−1(A3)
Step 5. Dening a threshold value to create impact relation
map
Dene a threshold value to construct impact relation map.
In this paper, threshold value is dened by expert. However,
there are some algorithms such as mean de-entropy (MMDE)
developed by Tzeng et al. (2007)tosetaproperthresholdvalue.
Step 6. Map the network
Map the interdependencies among criteria based on the
total relation matrix and the dened threshold value.
Appendix 2
Atthelastbutnottheleast,accordingtothenetworkcon-
structed from the meaningful inuences, facilities’ resiliency
levels are ranked by ANP method. The interested reader is
referred to Chung et al. (2005) for details of ANP method. In
this paper, the novel cluster weighting proposed by Yang and
Tze ng (2011) is applied to incorporate the DEMATEL results
in the fuzzy ANP method. The fuzzy ANP steps are as follows:
Step 1. Develop unweighted super-matrix through pairwise
comparisons.
Step 2. Calculate the weighted super-matrix via multiply-
ing derived matrix from DEMATEL method by defuzzied
unweighted super-matrix.
Step 3. Rise the weighted super-matrix to limiting power to
acquire global priority vectors which are weights of each KPI
and denote it by Wf .
