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International Journal of Production Research
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tprs20
Integrated approaches for logistics network
planning: a systematic literature review
Aura Maria Jalal, Eli Angela Vitor Toso & Reinaldo Morabito
To cite this article: Aura Maria Jalal, Eli Angela Vitor Toso & Reinaldo Morabito (2021): Integrated
approaches for logistics network planning: a systematic literature review, International Journal of
Production Research, DOI: 10.1080/00207543.2021.1963875
To link to this article: https://doi.org/10.1080/00207543.2021.1963875
Published online: 09 Sep 2021.
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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH
https://doi.org/10.1080/00207543.2021.1963875
REVIEW
Integrated approaches for logistics network planning: a systematic literature
review
Aura Maria Jalal , Eli Angela Vitor Toso and Reinaldo Morabito
Department of Production Engineering, Federal University of São Carlos, São Carlos, SP, Brazil
ABSTRACT
Researchers and practitioners often separate logistics network planning into strategic, tactical, and
operational decisions. Due to the interdependence among these levels of decisions, their integration
can bring important cost reductions and better network responsiveness in scenarios where there is
business change. However, integrated problems entail challenges, such as decision timing, and they
are more difficult to model and solve. This article presents a literature review of integrated problems
in logistics network planning. The objective is to identify the main integrated decisions, their scopes,
integration approaches, and the solution methods used. Although this review addresses research
with decisions at different hierarchical planning levels, we observed that integration of strategic
and tactical decisions is more common and some of the integration approaches are single-level
mono-period models, single-level multi-period models, multi-time scale models, and multi-level
models. There is a predominance of aggregated data in these studies. Regarding the solution meth-
ods, there is a predominance of heuristic approaches over exact ones, including methods based
on decomposition or sequential procedures. Based on the findings of this systematic review, we
draw a conceptual framework presenting the main modelling assumptions, integration strategies,
and solution methods to the integrated problems, and we also discuss some promising research
opportunities.
ARTICLE HISTORY
Received 15 August 2020
Accepted 23 July 2021
KEYWORDS
Logistics network; integrated
planning; supply chain
management; optimisation;
systematic literature review
1. Introduction
Logistics network planning (LNP) involves making deci-
sions about the number, location, and capacity of the
facilities (factories, warehouses, and distribution cen-
tres – DCs), as well as selecting suppliers, allocating
products to plants, choosing distribution channels, and
transportation modes, and determining ows of raw
materials, semi-nished and nished products through
thenetwork.Theaimistomeetcustomerdemands
and reduce xed and variable costs of acquisition, pro-
duction, storage, and transportation (Cordeau, Pasin,
and Solomon 2006). These decisions are set in dier-
ent scopes of the planning horizon and involve dierent
levels of details, conguring the levels of strategic, tacti-
cal, and operational decisions. The strategic level involves
long-term planning decisions that aect the structure
and capacity of the network. The tactical level includes
medium-term decisions related to the allocation and
distribution of materials and products among the facil-
ities. The operational level refers to decisions related
to manufacturing, warehousing, distribution, and ful-
lling demand operations (Gebennini, Gamberini, and
Manzini 2009).
CONTACT Eli Angela Vitor Toso eli@ufscar.br
The relationship between decision levels and plan-
ning horizons varies according to the supply chain (SC)
context and planning concepts (Fleischmann, Meyr, and
Wagn e r 2002). In practice, the decisions cross the bound-
ariesofhierarchicallevelsandareassociatedwiththe
various stages of the SC, therefore they have impacts on
the overall performance of the SC (Manzini et al. 2008).
Particularly in LNP, there are four types of decisions that
are strongly interrelated (Ballou and Masters 1993). The
rst deals with facility location (production or storage
facilities) and demand allocation to the facilities. The
second deals with inventory management decisions that
involve inventory control. blackThe third includes pro-
duction planning at a tactical level and the main tasks
are demand assignment to sites, process selection, and
lot-sizing. The fourth is transportation decisions, such
as vehicle routing and transportation mode selection.
Most of the studies in LNP focus on economic objectives
(e.g. minimising costs), although service level is a grow-
ing concern in SC. Thus, some decisions include man-
aging customer service levels (Arabzad, Ghorbani, and
Tavak k o li-Mog h addam 2014; Ballou and Masters 1993;
Liao, Hsieh, and Lai 2011; Liao, Hsieh, and Lin 2011).
© 2021 Informa UK Limited, trading as Taylor & FrancisGroup
2A. M. JALAL ET AL.
AccordingtoCordeau,Pasin,andSolomon(2006), due
to the importance of the interactions among these deci-
sions, important benets can be obtained by approach-
ing the network as a whole and integrating the deci-
sions. The integration allows the distribution networks
to react to the dynamic conditions of the business envi-
ronment, in addition to the potential cost reductions and
improvements.
Mathematical models that integrate decisions in LNP
can identify opportunities in which strategic decisions
canbeadaptedtothevariabilitythatoccursatother
hierarchical levels. Nevertheless, decision timing and fre-
quency, and the computational complexity of optimis-
ing integrated problems are some challenges regarding
integration (Liu et al. 2020). Due to the dierent plan-
ning horizon lengths for each level, the time periods
used to model each decision level should also be dier-
ent,adaptedtoeachdecisiontypeandtheinterdepen-
dence among them (Biuki, Kazemi, and Alinezhad 2020;
Brunaud and Grossmann 2017). Thus, LNP becomes
extremely complicated, while it is essential to formu-
late representative models and apply appropriate solution
methods to address the planning challenges arising from
integration.
In recent years, several authors have addressed dif-
ferent problems proposing models and solution meth-
ods to support decision-making in LNP considering
the integration of dierent hierarchical levels (Manzini
et al. 2008). In this context, our objective is to develop a
systematic literature review focusing on two main ques-
tions from a broader perspective: (i) how did the authors
integrate designing, planning, and operations decisions
in logistics networks under a dynamic and uncertain
environment, and (ii) what are the research gaps and
opportunitiesinthisarea?Toaddresstheseresearch
questions, we developed a systematic review based on the
protocol-driven methodology proposed by Denyer and
Traneld (2009). A systematic review enables us to iden-
tify relevant studies, evaluate their contributions, and
summarise their results.
From this literature review, we aim to understand
how the integration levels have been made by the
operations management/operation research community.
Therefore, the reference papers are analysed in terms
of dierent decision-making levels, integration strate-
gies/approaches, and solution methods. Furthermore,
we examine the planning horizons of the models and
the timing of the decisions involved. Finally, we high-
light some gaps and point out opportunities for future
research. To present our research ndings, we designed a
conceptual framework with the challenges and benets of
the integrated LNP, the main characteristics and premises
of the modelling, as well as the integration proposals and
solution methods identied in the literature review. To
thebestofourknowledge,noreviewpaperhasexamined
thesameaspectstakenintoaccountinthispaper.
The rest of this paper is structured as follows. Section 2
indicates the contribution of this work when compared to
other reviews published on this topic. Section 3describes
the review methodology used in this article and in
Section 4, a descriptive analysis is presented. Section 5
reportsadetailedoverviewoftheintegrateddecisions
and strategies for integration in LNP. Section 6discusses
the solution methods and approaches used to solve the
integrated models. Section 7presents our conceptual
framework and some research gaps. Finally, Section 8
presents our concluding remarks.
2. Recent related literature reviews
We initially searched for literature reviews and seminal
works that have been published on integrated optimisa-
tion problems in LNP, aiming to identify if these papers
provide insights or address issues such as integrating
decisions with dierent planning horizons, main inte-
grated decisions, and methods to solve the integrated
models. Analysing these articles was an important step to
dene our literature review protocol. Table 1shows the
papers found and their scope in the period from 2000
to 2020. Integrated optimisation in the eld of network
design has received more attention and there are several
reviews addressing dierent integrated problems.
In the rst decade of the 2000s, Melo, Nickel, and
Saldanha-da Gama (2009) developed a literature review
of facility location and SC management. The authors
addressed the decisions in SC network design, solution
Tab le 1. Literature reviews in recent years on integrated optimi-
sation problems in LNP (2009 onwards).
Paper Research focus
Is it a
systematic
review?
Number of
papers
Time
horizon
Melo, Nickel, and
Saldanha-da
Gama (2009)
Facility location
models in SC
No 120 1997–2007
Farahani
et al. (2014)
Location-inventory
problem in SC
No 73 1976–2013
Prodhon and
Prins (2014)
Location-routing
problems
No 72 2007–2013
Drexl and
Schneider (2015)
Variants of the
location-routing
problem
No n/a 2006–2013
Govindan, Jafarian,
and Nour-
bakhsh (2015)
Reverse logistics
and closed-loop
SC
Yes 382 2007–2013
Barbosa-Póvoa,
da Silva, and
Carvalho (2018)
OR for sustainable
SC
Yes 220 1999–2015
Farahani
et al. (2018)
OR models in USFL Yes 110 1970–2017
n/a, non applicable.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 3
approaches (exact/heuristics), and some modelling fea-
tures, namely, the number of layers, commodities, the
nature of the planning horizon (single/multi-period),
and the type of data (deterministic/stochastic). They con-
cluded that tactical and operational decisions related to
inventory and production were often integrated with
location, while others such as vehicle routing and trans-
portation mode selection were relatively neglected until
that moment.
Farahani et al. (2014) presented a literature review
of the Location-Inventory (LI) problems, which aims to
integrate location with inventory management and con-
trol decisions. The review focuses on the key modelling
attributes, the objective function cost components, the
solution methods adopted, and the real-world applica-
tions investigated. The authors also veried the time
structure of the models and concluded that most of the
proposed models assume a planning horizon with a sin-
gle period.
Taking into account that vehicle routing can improve
transportation costs in facility location problems, Prod-
honandPrins(2014) focus on location-routing problems
in their review. According to these authors, several stud-
ies have already shown that although the location of facil-
ities is a strategic decision and that vehicle routes must
be built at the tactical and operational decision levels,
thesedecisionsareinterdependentandthetotalcostof
the system can be excessive if they are addressed sepa-
rately.TheyalsoestablishedthatallLRproblemswith
multiple periods were recently proposed, although the
selection of clients to be served in each period shows
the tactical dimension that was missing between the
strategic decision level (location) and the operational
decision level (route). The community has been propos-
ing new variants of this problem, which include con-
sidering new characteristics (e.g. stochastic parameters,
continuous location, multi-layers, multi-objectives) and
the incorporation of other decisions, for example, Inven-
tory-LR, Pickup-and-delivery-LR, and Split-delivery-LR
(Drexl and Schneider 2015). Farahani et al. (2018)devel-
oped a survey on the specic context of Urban Service
Facility Location (USFL), concluding that routing deci-
sions are often integrated into USFL models. However,
other decisions, in particular, eet sizing and inven-
tory management decisions, are rarely addressed in
these models.
Sustainability has been increasingly considered in SC
management. Govindan, Soleimani, and Kannan (2015)
and Barbosa-Póvoa, da Silva, and Carvalho (2018)
present literature reviews on sustainable SC, reverse
logistics, and closed-loop SC. The reviews found that
optimisation models applied to strategic levels are the
most preponderant studies. Barbosa-Póvoa, da Silva, and
Carvalho (2018) identied 59 out of 220 articles address-
ing the integration of strategic decisions (long-term
planning) and tactical decisions concerning inventory,
demand, and supply planning. Govindan, Soleimani, and
Kannan (2015) concluded that strategic decisions, for
example, designing and capacity, were successfully inte-
grated with tactical decisions, for instance, network ows;
however, operational decisions, such as production and
inventory, remained separate. Both articles pointed out
the need for approaches to integrate decisions of dif-
ferent levels into the sustainable SC. Other related inte-
grated SC planning problems are production-routing
problems (Adulyasak, François Cordeau, and Jans 2015)
and inventory with transportation issues (Engebrethsen
and Dauzère-Pérès 2018); however, these topics do not
include network decisions and are out of the scope of the
present review. The literature reviews in Table 1show fre-
quent decisions addressed in LNP studies and indicate
trends and gaps in the integrated planning in SC. Nev-
ertheless, these reviews did not particularly address our
research question of how to deal with dierent planning
horizons of decisions in the integration.
3. Literature review protocol
We performed an extensive literature review on models
and solution methods to address the integrated planning
of logistics networks, ranging from strategic to opera-
tional decisions. To ensure the consistency and quality
of the work, we used a systematic research method-
ology (Jesson, Matheson, and Lacey 2011;Traneld,
Denyer, and Smart 2003). We observe in Table 1that
this methodology was more used to develop literature
revisions in LNP in recent years. The methodology was
structured over three phases: planning, conducting and
reporting. Table 2presents a summary of the research
protocol and the methods applied in each of these
three phases.
3.1. Planning
For the literature review, the constructs established were
strategic, tactical, and operational planning, logistics net-
work, integrated planning, and optimisation. We did a
survey regarding the most common words found in arti-
cles. A keyword-based bibliometric analysis on the initial
sample was performed to better understand which key-
words are usually used in papers addressing integrated
decisions. Figure 1presents a network visualisation of
the keywords using the VOSviewer®(van Eck and Walt-
man 2010).
Thereafter, we constructed the search string by com-
bining synonyms of the keywords, as shown in Table 3.
4A. M. JALAL ET AL.
Tab le 2. Research protocol.
Phases Steps Data
Planning Study strategy Definition of constructs, key words,
research strings, database, and period
Conducting Material collection Analysis of inclusion and exclusion
criteria
Filter 1: title, abstracts and key-words
assessment
Filter 2: introduction and conclusion
assessment
Full reading
Reporting Descriptive analysis W’s analysis (When, Who, What, and
Where)
Category selection Classifications in groups
Material evaluation Answer questions, find relevant
information and detect research gaps
(Adapted from Denyer and Tranfield 2009; Jesson, Matheson, and Lacey 2011;
Tranfield, Denyer, and Smart 2003).
Tab le 3. Search string.
((location* OR ‘network design’ OR ‘network NEAR/2 configuration’)
AND (integrat* OR join OR simultaneous)
AND (network OR ‘supply chain*’ OR logistics)
AND (decision* OR strategic OR tactical OR operational )
AND (inventory OR transport* OR distribution OR production OR routing
OR ‘fleet siz*’)
AND (optimiz* OR optimisation OR programming OR model* OR
‘mathematical formulation’)).
We studied peer-reviewed articles published since
2000 in the context of LNP indexed in international jour-
nals, searching among electronic bibliographical sources
including Scopus®and Web of Science®and using a
research string. We considered three criteria for these
papers: (i) the paper should be written in English; (ii)
the paper should address strategic decisions, such as net-
work design or facility location; and (iii) the paper should
include other decision variables related to tactical and
operational planning, simultaneously.
3.2. Conducting
For the data collection, we applied the search string in
the databases on 30 June 2020, covering the accepted
papers (available online) from January 2000 to this date,
resulting in 2894 papers (including duplicated papers in
the databases). Then, the following lters were applied:
(i) document type, including articles, articles in press,
reviews, reiterations, excluding proceeding papers; (ii)
areas, including Web of Science®categories: Opera-
tions research management science, Engineering indus-
trial, Engineering manufacturing, Multidisciplinary sci-
ences, Management, Computer science interdisciplinary
applications, Business or computer science information sys-
tems, Engineering multidisciplinary, Mathematics applied,
Computer science articial intelligence, Mathematics inter-
disciplinary applications, Transportation science technol-
ogy, Transportation;andScopus
®categories: Engineering,
Decision Sciences, Business, Management and Account-
ing, Computer Science, Mathematics, Multidisciplinary.
The information from the papers was exported (Bib-
Tex ) from databases to software StArt®(State of the Art
through Systematic Review). After an initial review, dupli-
cated articles (exported from the databases) were deleted,
resulting in a sample of 778 documents. Afterwards, an
article selection step was carried out, applying inclusion
criteria related to alignment and scope. After reading the
title, abstract, keywords, introduction and conclusions,
a sample of 190 articles was selected. In the full reading
stage, 131 papers were classied.
3.3. Reporting and disseminating results
To extract information from the papers, three steps were
followed as shown in the stage reporting in Table 2, i.e.(i)
Figure 1. Keyword bibliometric analysis.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 5
a descriptive analysis, (ii) a category selection and (iii) a
material evaluation. A descriptive analysis was made to
obtain an understanding of integrated problems in LNP,
a category selection was made using groups of similar
articles in terms of decisions, model structure, integra-
tion approaches and solution methods. The following
questions were used as motivation:
(1) When were the articles published? From which
countries are the authors’ aliations? What are the
most used keywords?
(2) What are the main decisions, assumptions, model
structures and objectives functions?
(3) How the time structure of decisions at dierent hier-
archical levels has been addressed?
(4) What are the modelling approaches used to integrate
decisions at dierent levels?
(5) Whatarethesolutionmethodsused?
The following sections present discussions to cope
with the aforementioned questions and a conceptual
framework that helps to visualise the main results of our
literature review.
4. Description of selected sample
This section presents some statistics from the obtained
sample applying our research protocol. Figure 2(a) shows
the top 10 journals that published the articles. The
distribution of these reference papers in terms of their
publication date is shown in Figure 2(b). The number
of articles exploring the integration of the decision lev-
els has grown over the past 20 years, reaching its peak in
2016. Nevertheless, we found that more than 50% of these
papers were published over a ve-year period from 2015
to 2020. As this research was carried out in June 2020,
it is expected that in 2020 the number of articles will be
even greater. The countries with more authors’ aliations
are Iran, United States, China, United Arab Emirates, and
Canada.
5. Detailed analysis of the literature
In this section, a detailed analysis of the methodologies
to integrate decisions, the main decisions and the main
features of the integrated LNP are presented aiming to
understand which decisions have been integrated and
how the research community has been integrating these
decisions.
5.1. Model structures to integrate decisions
Animportantissueindistributionnetworkplanning
concerns timing decisions, i.e. the coincidence of deci-
sions with proper time horizons (Badri, Bashiri, and
Hossein 2013). The impact of strategic level decisions
spansoveragreaterperiodthantacticalleveldecisions,
whichcouldbeevenyearsastheydealwithdecisions
Figure 2. Statistics of the reference papers. (a) Top 10 journals of the reference papers and (b) publication date distribution of the
reference papers.
6A. M. JALAL ET AL.
Working
periods
Planning
periods
Control
Horizon
Planning
Horizon
Design
Horizon
Daily to Weekly decisions
Monthly to yearly decisions
Yearly to multi-annual decisions
Implementation
period
Aggregation
Aggregation
Figure 3. Decision-time hierarchy in the LNP (Amiri-Aref, Klibi, and Babai 2018).
that cannot change easily. Tactical decisions have time
horizons of months and operational decisions are typ-
icallymadeonadailybasis(Hiassat,Diabat,and
Rahwan 2017). The timing among these decisions, as
well as the distinct time-horizon granularity, should be
taken into account when modelling integrated problems.
Amiri-Aref, Klibi, and Babai (2018) present a timing
structure illustrated in Figure 3.
The lower layer of Figure 3corresponds to the opera-
tional level, composed of a set of discrete periods where
managers make daily or weekly decisions. At this level,
information such as demands, lead times, prices, capac-
ities, costs and sourcing availability are less uncertain.
The short-term operational decisions can be revised in
each working period. The tactical level corresponds to
the multi-period horizon illustrated by the intermediate
layer. The granularity of the planning periods requires the
aggregation of working periods and the operational deci-
sions. These medium-term decisions are addressed from
monthly to annual periods. At the upper layer, long-term
decisions are made, which are generally decisions related
to network design regarding yearly to multi-annual peri-
ods. The elapsed time between the network design and
usageperiodimpliesthatthesedecisionsaremadewith
partial information (Amiri-Aref, Klibi, and Babai 2018).
We analysed the techniques or strategies for inte-
grating decisions in the mathematical modelling of
the reference papers. Four groups were identied,
namely: (i) single-level mono-period models, (ii) single-
level multi-period models, (iii) multi-timescale models,
and (iv) multi-level models. Figure 4summarises the
time-horizon granularity for the strategic, tactical and
operational levels, in agreement with dierent horizons:
long-term (design) horizon, mid-term (planning) hori-
zon and short-term (control) horizon, shown in Figure 3.
Single-level models integrate decisions at dierent
planning levels through a mathematical model that incor-
poratesalldecisionssimultaneously.Thesemodelscanbe
mono or multi-period. Single-level mono-period mod-
els make decisions by aggregation of dierent problem
parameters for the entire planning horizon, as shown
in Figure 4. Govindan, Jafarian, and Nourbakhsh (2019)
develop a model to design a sustainable supply chain
integrating location decisions of industrial plants and dis-
tributioncentreswithdecisionsofvehiclesroutingusing
a single-level mono-period model. Ahmadi-Javid and
Azad (2010) propose a model that integrates location,
inventory, and routing decisions using the same strat-
egy. Generally, integrating decisions using a single-level
mono-period model allows for making long-term deci-
sions without the concern of variability in the mid and
short-term decision-making.
Single-level multi-period models take into account
dynamic decisions according to problem parameters that
vary among periods. Network design decisions, such
as location, are generally dened for the entire plan-
ning horizon and the tactical and/or operational deci-
sions (e.g. production, inventory, and transportation) are
addressed for each period, which enables us to dierenti-
ate decisions from strategic and tactical/operational lev-
els. Rae-Majd, Pasandideh, and Naderi (2018) consider
this time granularity to address the inventory-location-
routing problem, while Darvish and Coelho (2018)con-
sider the DC location used for a specic number of
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 7
Figure 4. Decision-time in integration strategies in the LNP.
periods joint with production, inventory, and transporta-
tion decisions. This approach also maintains the idea that
location decision is valid for a longer period if compared
to other decisions. Periodic decisions require detailed
information about the parameters. Single-level multi-
period models allow for making more accurate decisions
byperiod;however,ittakesmorecomputationaleortif
compared to single-period models.
In multi-timescale models, the planning horizon is
divided into macro-periods in which strategic and/or tac-
tical decisions are made. Each macro-period is divided
into micro-periods, where tactical and/or operational
decisions are regarded. Timescale models are also single-
level models and have similar characteristics to multi-
period models, since parameters and decisions are
dened for distinct periods. However, this approach
canbemoreadvantageouswhenthedecisionstobe
integrated dier in terms of periodicity and frequency
over the planning horizon, enabling us to properly con-
sider the timing of each decision. For instance, Salema,
Póvoa, and Novais (2009) and Salema, Barbosa-Povoa,
and Novais (2010) address location decisions for the
entire horizon; demand allocation decisions in macro-
period; and production, inventory, and product ow in
micro-periods. Some articles consider lead time in oper-
ations, in particular, in production, transportation and
supply activities. Authors have dened time operators
for these activities that can locate the macro and micro
periods at which each operation begins and ends, tak-
ing into account their lead time (Amiri-Aref, Klibi, and
Babai 2018; Badri, Bashiri, and Hossein 2013;Bashiri,
Badri, and Talebi 2012; Fattahi, Mahootchi, and Hus-
seini 2016; Salema, Póvoa, and Novais 2009;Salema,
Barbosa-Povoa, and Novais 2010). We note that timescale
models present a time structure similar to the GLSP
(General Lotsizing and Scheduling Problem) model pro-
posedbyFleischmannandMeyr(1997), which integrates
mid-term decisions (lot-sizing) and short-term decisions
(sequencing).
Multi-level models consider two and three levels to
integrate decisions of distinct hierarchical levels. At
therstlevel,amodelissolvedandnewinformation
becomes available for the decision-maker. This solution
is used as input parameters for the next level model. In the
case of three-level models, for instance, Manzini, Accorsi,
and Bortolini (2014), the solution of the second model
feeds into the third model, that is, the multi-level models
are solved hierarchically. Generally, the strategic deci-
sions are addressed at the rst level and then, tactical
and operational decisions are considered. Thus, the solu-
tions of some lower-level models provide feedbacks to the
upper-level models, including information from the last
solved models and, iteratively and interactively, searches
for a better solution. This approach is obviously with a
loss of optimality. Commonly, the rst level deals with
location decisions in a single period, while the second
and third levels (if there are any) deal with detailed deci-
sions in multiple periods, for instance (Manzini, Accorsi,
and Bortolini 2014). This enables us to dierentiate the
planning horizon for the dierent decision levels and, at
the same time, reduce the computational eort by the
model decomposition in two or three models.
8A. M. JALAL ET AL.
Tab le 4. Approaches for integrating decisions in the mathematical modelling of the reference papers.
Mono period models Multi-period models
Ahmadi-Javid and Azad (2010); Ahmadi-Javid and Hossein Seddighi (2012);
Ahmadi-Javid and Hoseinpour (2015b); Ahmadi-Javid, Amiri, and Meskar (2018);
Ahmadi-Javid and Hoseinpour (2015a); Alavi et al. (2016); Alenezi
and Darwish (2014); Angazi (2016); Arabzad, Ghorbani, and Tavakkoli-
Moghaddam (2014); Aryanezhad, Jalali, and Jabbarzadeh (2010); Azizi
and Hu (2020); Cabrera et al. (2016); Candas and Kutanoglu (2007); Dai
et al. (2018); Wheatley, Gzara, and Jewkes (2015); Diabat, Richard, and Codring-
ton (2013); Firoozi et al. (2014); Ghaderi and Burdett (2019); Ghezavati,
Jabal-Ameli, and Makui (2009); Gholamian and Heydari (2017); Govindan,
Jafarian, and Nourbakhsh (2015); Govindan, Jafarian, and Nourbakhsh (2019);
Govindan et al. (2020); Guo et al. (2018); Guo et al. (2020); Hammami,
Frein, and Bahli (2017); Jeet and Kutanoglu (2018); Kabadurmus and Erdo-
gan (2020); Kaya and Urek (2016); Keskin and Üster (2012); Lagos et al. (2015);
Li et al. (2013); Liao, Hsieh, and Lin (2011); Liao, Hsieh, and Lai (2011); Liu
et al. (2020); Miranda and Garrido (2004); Miranda, Garrido, and Ceroni (2009);
Miranda and Garrido (2006); Monteiro, Leal, and Raupp (2010); Naimi Sadigh,
Fallah, and Nahavandi (2013); Nakhjirkan and Rafiei (2017); Nakhjirkan,
Rafiei, and Kashan (2019); Nasiri, Davoudpour, and Karimi (2010); Nasiri,
Ghaffari, and Davoudpour (2015); Puga and Tancrez (2017); Schuster Puga,
Minner and Tancrez (2019); Qazvini, Amalnick, and Mina (2016); Sadjadi
et al. (2016); Sadjady and Davoudpour (2012); Saragih et al. (2019); Schwardt
and Dethloff (2005); Shahabi et al. (2013); Shavandi and Bozorgi (2012);
Sherafati and Bashiri (2016); Shu, Ma, and Li (2010); Singh et al. (2015);
Soleimani, Chaharlang, and Ghaderi (2018); Tancrez, Lange, and Semal (2012);
Tang and Yang (2008); Tapia-Ubeda, Miranda, and Macchi (2018); Tapia-Ubeda
et al. (2020); Tavakkoli-Moghaddam, Makui, and Mazloomi (2010); Tiwari
et al. (2010); Tsao et al. (2012); Tsiakis, Shah, and Pantelides (2001); Halit,
Keskin and Çetinkaya (2008); Wang et al. (2013); You and Grossmann (2008);
Yuchi et al. (2016); Zheng, Yin, and Zhang (2019).
Ahmadi, Torabi, and Tavakkoli-Moghaddam (2016); Akbari and
Karimi (2015); Alshamsi and Diabat (2018); Azizi, Hu, and Mokari (2020);
Biuki, Kazemi, and Alinezhad (2020); Brahimi and Khan (2014);
Candas and Kutanoglu (2020); Cardoso, Barbosa-Póvoa, and Rel-
vas (2013); Darvish and Coelho (2018); Darvish et al. (2019); Diabat and
Richard (2015); Diabat (2016); Diabat, Battaïa, and Nazzal (2015); Diabat
and Deskoores (2016); Etebari (2019); Fattahi and Govindan (2017);
Forouzanfar et al. (2018); Gebennini, Gamberini, and Manzini (2009);
Ghorbani and Akbari Jokar (2016); Govindan et al. (2014); Govindan,
Jha, and Garg (2016); Guerrero et al. (2015); Karakostas, Sifaleras, and
Georgiadis (2019); Khatami, Mahootchi, and Farahani (2015); Lin, Gen,
and Wang (2009); Martins et al. (2017); Mogale, Cheikhrouhou, and
Tiwari (2020); Mota et al. (2018); Motaghedi-Larijani, Jabalameli, and
Tavak koli (2012); Mousavi et al. (2017); Nekooghadirli et al. (2014);
Rabbani, Heidari, and Yazdanparast (2019); Sadeghi Rad and Naha-
vandi (2018); Rafie-Majd, Pasandideh, and Naderi (2018); Soleimani,
Seyyed-Esfahani, and Shirazi (2016); Yu, Normasari, and Luong (2015);
Zeballos et al. (2014); Zeballos, Méndez, and Barbosa-Povoa (2018);
Zhalechian et al. (2016).
Multi-level models Multi-timescale models
Das and Sengupta (2009); Ghomi-Avili et al. (2018); Ghomi-Avili et al. (2021);
Hiassat, Diabat, and Rahwan (2017); Kim and Lee (2015); Manzini et al. (2008);
Manzini (2012); Manzini, Accorsi, and Bortolini (2014); Manzini and Geben-
nini (2008); Mousavi, Tavakkoli-Moghaddam, and Jolai (2013); Mousavi
et al. (2014); Rappold and Van Roo (2009); Sabri and Beamon (2000); Solak,
Scherrer, and Ghoniem (2014); Zhang and Xu (2014).
Amiri-Aref, Klibi, and Babai (2018); Badri, Bashiri, and Hossein (2013);
Bashiri, Badri, and Talebi (2012); Fattahi, Mahootchi, and Husseini (2016);
Salema, Póvoa, and Novais (2009); Salema, Barbosa-Povoa, and
Novais (2010).
See the author-date citation in Table A1 in Appendix.
Table 4presents the approaches for integrating deci-
sions in the mathematical modelling of the reference
papers. Most of the papers (88%) integrate decisions
at dierent levels through a single-level mathematical
model. Notably, 53% of the referenced papers consider
single-level and mono-period models (i); 30% consider
single-level and multi-period models (ii); and 5% use
multi-timescale models (iii) to address dierent decision
levels. Moreover, 12% of the papers are multi-level mod-
els with two and three levels, and almost 75% of the
multi-level models address a multi-period context.
Based on our review, single-level mono-period mod-
els can be eective to integrate strategic and tactical
decisions in static situations where the data aggregation
does not impact the tactical decisions. When data vari-
ability is signicant, parameters can be described by a
probability distribution function, as we will discuss this
further. On the other hands, single-level multi-period
models are indicated when there is variability in param-
eters among periods aecting the periodical decisions
(and the data aggregation is not recommended). Thus,
more accurate decisions need to be made by the period
which is usually related to tactical and operational ones.
Timescales models can introduce more details by incor-
porating macro-periods and micro-periods, and address-
ing distinct decisions according to their timing. This
integration approach corroborates the assumption that
LNP decisions have dierent time-horizon length and
granularity, according to Figure 3proposed by Amiri-
Aref, Klibi, and Babai (2018). Thus, timescale models
aim to optimise decisions from distinct hierarchical lev-
els simultaneously. Multi-level models are also based on
the same assumption. However, dierent from timescale
strategies, multi-level models are optimised sequentially
and, even using looping techniques to improve the solu-
tions, it is more dicult to nd an optimal solution. In
either case, multi-level models can be very useful in many
practicalcontextswhenanoptimalsolutiondoesnot
mean a substantial impact in LNP decisions that are not
simultaneously made.
5.2. Main integrated decisions
LNP decisions addressed by the papers can be clas-
sied into four categories, namely, (i) location, (ii)
inventory, (iii) production and (iv) transportation. As
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 9
Tab le 5. Integration of decisions in reference papers.
Location-transportation Location-inventory Location-production
Ahmadi-Javid, Amiri, and Meskar (2018); Arabzad,
Ghorbani, and Tavakkoli-Moghaddam (2014);
Azizi and Hu (2020); Etebari (2019); Ghaderi
and Burdett (2020); Karakostas, Sifaleras,
and Georgiadis (2019); Kim and Lee (2015);
Mousavi, Tavakkoli-Moghaddam, and
Jolai (2013); Nakhjirkan and Rafiei (2017);
Nakhjirkan, Rafiei, and Kashan (2019); Schwardt
and Dethloff (2005); Solak, Scherrer, and
Ghoniem (2014); Soleimani, Chaharlang, and
Ghaderi (2018); Tavakkoli-Moghaddam, Makui,
and Mazloomi (2010).
Ahmadi, Torabi, and Tavakkoli-Mogha-
ddam (2016); Ahmadi-Javid and Hosein-
pour (2015b); Ahmadi-Javid and Hosein-
pour (2015a); Amiri-Aref, Klibi, and Babai (2018);
Aryanezhad, Jalali, and Jabbarzadeh (2010); Azizi,
Hu, and Mokari (2020); Cabrera et al. (2016);
Candas and Kutanoglu (2007); Candas and
Kutanoglu (2020); Dai et al. (2018); Wheatley,
Gzara, and Jewkes (2015); Diabat, Richard, and
Codrington (2013); Diabat and Richard (2015);
Diabat (2016); Diabat, Battaïa, and Naz-
zal (2015); Diabat and Deskoores (2016);
Firoozi et al. (2014); Ghezavati, Jabal-Ameli,
and Makui (2009); Jeet and Kutanoglu (2018);
Kaya and Urek (2016); Keskin and Üster (2012);
Khatami, Mahootchi, and Farahani (2015);
Lagos et al. (2015); Li et al. (2013); Liao, Hsieh,
and Lin (2011); Liao, Hsieh, and Lai (2011);
Lin, Gen, and Wang (2009); Liu et al. (2020);
Miranda and Garrido (2004); Miranda and Gar-
rido (2006); Mousavi et al. (2017); Naimi Sadigh,
Fallah, and Nahavandi (2013); Nasiri, Davoud-
pour, and Karimi (2010); Nasiri, Ghaffari, and
Davoudpour (2015); Schuster Puga, Minner and
Tancrez (2019); Rappold and Van Roo (2009);
Sadjadi et al. (2016); Schuster Puga, Minner and
Tancrez (2019); Shahabi et al. (2013); Shavandi
and Bozorgi (2012); Shu, Ma, and Li (2010);
Soleimani, Seyyed-Esfahani, and Shirazi (2016);
Tang and Yang (2008); Tapia-Ubeda, Miranda, and
Macchi (2018); Tapia-Ubeda et al. (2020); Tsao
et al. (2012); Halit, Keskin and Çetinkaya (2008);
Wang et al. (2013); You and Grossmann (2008);
Zhang and Xu (2014).
Calvete, Galé, and Iranzo (2014); Govindan, Jafar-
ian, and Nourbakhsh (2015); Tsiakis, Shah, and
Pantelides (2001).
Ahmadi-Javid and Azad (2010); Ahmadi-Javid and Hossein Seddighi (2012); Alenezi and Dar-
wish (2014); Angazi (2016); Biuki, Kazemi, and Alinezhad (2020); Darvish et al. (2019); Forouzan-
far et al. (2018); Gholamian and Heydari (2017); Ghorbani and Akbari Jokar (2016); Govindan
et al. (2020); Guerrero et al. (2015); Guo et al. (2018); Hiassat, Diabat, and Rahwan (2017);
Kabadurmus and Erdogan (2020); Martins et al. (2017); Miranda, Garrido, and Ceroni (2009); Mogale,
Cheikhrouhou, and Tiwari (2020); Mousavi et al. (2014); Nekooghadirli et al. (2014); Puga and Tan-
crez (2017); Qazvini, Amalnick, and Mina (2016); Rabbani, Heidari, and Yazdanparast (2019); Rafie-
Majd, Pasandideh, and Naderi (2018); Sadjady and Davoudpour (2012); Saragih et al. (2019); Tan-
crez, Lange, and Semal (2012); Yuchi et al. (2016); Zeballos et al. (2014); Zhalechian et al. (2016);
Zheng, Yin, and Zhang (2019).
Akbari and Karimi (2015); Alavi et al. (2016); Badri, Bashiri, and Hossein (2013); Bashiri, Badri, and
Talebi (2012); Cardoso, Barbosa-Póvoa, and Relvas (2013); Darvish and Coelho (2018); Das and
Sengupta (2009); Fattahi, Mahootchi, and Husseini (2016); Fattahi and Govindan (2017); Geben-
nini, Gamberini, and Manzini (2009); Ghomi-Avili et al. (2018); Ghomi-Avili et al. (2021); Hammami,
Frein, and Bahli (2017); Manzini et al. (2008); Manzini and Gebennini (2008); Motaghedi-Larijani,
Jabalameli, and Tavakkoli (2012); Sabri and Beamon (2000); Salema, Póvoa, and Novais (2009);
Salema, Barbosa-Povoa, and Novais (2010); Singh et al. (2015); Yu, Normasari, and Luong (2015);
Zeballos, Méndez, and Barbosa-Povoa (2018).
Alshamsi and Diabat (2018); Brahimi and Khan (2014); Govindan et al. (2014); Govindan, Jha, and Garg (2016); Manzini (2012); Manzini, Accorsi,
and Bortolini (2014); Monteiro, Leal, and Raupp (2010); Mota et al. (2018); Sadeghi Rad and Nahavandi (2018); Sherafati and Bashiri (2016); Tiwari
et al. (2010).
See the author-date citation in Table A1 in Appendix.
mentioned before, these decisions are typically estab-
lished in dierent scopes of the planning horizons but
they are interrelated. Several authors have addressed
some interactions among these decisions, originating
traditionalproblemsintheliteraturethatintegrate
dierent planning levels. Table 5presents the integra-
tion of decisions in the reference papers: Location-
Inventory (LI), Location-Transportation (LT), Location-
Production (LP), Location-Inventory-Transportation
(LIT), Location-Inventory-Production (LIP) and
Location-Inventory-Production-Transportation (LIPT).
A single article considered the intersection of location-
transportation-production (LTP) (Govindan, Jafarian,
and Nourbakhsh 2019), as shown in Figure 5.
Figure 5presents an overview in terms of the num-
berofarticlesthataddressdecisionsofeachcategoryand
the integration among them. All articles consider loca-
tion decisions. The most frequent integration is location
and inventory management, with 113 articles. In turn,
41 of these articles consider transportation decisions,
10 A. M. JALAL ET AL.
Tab le 6. Decisions and classification in static vs. dynamic and deterministic vs. stochastic.
Decisions Number % Static Dynamic Deterministic Stochastic
Location DCs location 131 100% 56% 44% 51% 49%
Plant location 34 26% 41% 59% 47% 53%
Demand allocation 95 73% 73% 27% 49% 51%
Capacity selection 37 28% 32% 68% 54% 46%
Supplier selection 9 7% 78% 22% 67% 33%
Technology selection 9 7% 44% 56% 67% 33%
Inventory Inventory level 84 63% 45% 55% 48% 52%
Order quantity 52 40% 69% 31% 46% 54%
Order point 26 20% 77% 23% 54% 46%
Safety stock 19 15% 89% 11% 0% 100%
Production Production quantity 37 28% 30% 70% 65% 35%
Production allocation 7 5% 14% 86% 71% 29%
Processes selection 6 5% 17% 83% 83% 17%
Transportation Routing 38 29% 55% 45% 58% 42%
Mode selection 20 15% 45% 55% 70% 30%
Inventory
113
Production
37
Transportation
56
22
30
11
50
14
3
Location 131
1
Figure 5. Number of publications covering the different decision
categories in SC.
and 11 of these articles also consider production
decisions.
Table 6presents more details about the decisions in
each category, the number of articles considering each
decision, the percentage in the sample, and their clas-
sication in static vs. dynamic and deterministic vs.
stochastic.
According to Table 6,allthearticlesconsidertheloca-
tion of intermediate facilities (e.g. DCs, hubs and collec-
tion centres) and 26% of them also consider the loca-
tion of production/re-manufacturing facilities. Despite
the dynamic business environment and frequent changes
(political, tributary, and social) that may arise over time,
only a few articles cope with the network redesign, allow-
ing for opening and closing facilities or allowing for
expanding capacity on the planning horizon. Several arti-
cles take into account the location of collection facili-
ties for processing post-consumer products, which lead
to properly disposing of waste or integrating waste as
raw materials in a circular economy (Barbosa-Póvoa,
da Silva, and Carvalho 2018). Other strategic decisions
Inventory level
84
Order quantity
52
Order point
26
13
3
13
50
2
18
5
Other
8
Inventory decisions
131
Figure 6. Number of publications covering the inventory deci-
sions of Figure 5.
associated with facility location are dening, selecting or
adding capacity to facilities (28%). Less explored deci-
sions are supplier selection, eet sizing, vehicle alloca-
tion, and pricing. According to Table 6, the decision con-
cerning the location of intermediate facilities did not tend
to be static or dynamic, deterministic or stochastic. How-
ever, some network design decisions, such as supplier
selection, are made mainly in a static and also determinis-
tic context. Other decisions, such as technology selection
and capacity selection, are made mainly in a dynamic and
deterministic context.
Concerning inventory management, some models
deal with inventory decisions in several layers: plants,
warehouses, and retailers. According to Table 6,afre-
quently integrated decision in LNP is the inventory level
denition (63%). Other inventory decisions are order
quantity (40%), replacement point (20%), and safety
stock (15%), and these decisions are made mainly in a
static way, according to Table 6. Moreover, 23% of articles
that include inventory decisions consider lost sales, back
order, or early delivery. Figure 6presents the number
of articles that address the three most frequent inven-
tory decisions of Figure 5and the intersections among
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 11
them. Observe that 18 articles address only order quan-
tity and 2 address only order point, but most decisions
are combined.
Production decisions, in turn, include the amount to
be produced (28%), allocation of production to facilities
(5%), and selection of production processes or technolo-
gies(5%).AccordingtoTable5,inLNP,productiondeci-
sions are frequently integrated with inventory decisions,
particularly the inventory level. In Table 6, the produc-
tion category excels at making decisions in a dynamic
and deterministic context. The 37 articles that consider
the decision of production quantity denition are inte-
grated with the dierent decision categories as shown in
Figure 5.
The transportation decisions refer to the selection of
transportation alternatives and vehicle routing. Only 15%
of the studies incorporate the selection of transportation
alternatives and 29% consider routing. Within vehicle
routing problems, there are decisions associated with the
denition of routes and the selection of predened routes.
Studies look at homogeneous and homogeneous vehi-
cleeets.AccordingtoTable6, transportation decisions
are made mainly in a deterministic context, i.e. mode
selection (70%) and routing (58%).
AlessaddresseddecisioninLNPistoallowlost
sales (14%) or even not fullled demand at the specied
deadline, as well as backlogs/delays (11%) or advances
(1%), considering penalties in both cases. These decisions
appear in the reference papers which address location-
inventory decisions.
Figure 7presents the relations between the integrating
approaches and the main integrated decisions in the ref-
erence papers. The strategy of a single-level model dom-
inates in all types of integration, particularly LI integra-
tion. In these models, dierent decisions are made simul-
taneously considering aggregated data or average data
(e.g. demand, capacity, costs). Some authors consider
uncertainty in modelling, aiming to reduce the impact of
this assumption over the decision-making process.
5.3. Features of the integrated problems
This subsection presents a description of the main
characteristics of the integrated problems related to
data aggregation, data uncertainty and performance
measures.
5.3.1. Data aggregation
As mentioned before, many articles (49.6%) deal with
decisions in the same period, without taking into account
the dierences in nature and frequency of decision levels.
Thisfactcanleadtosub-optimalandevenimpractical
decision-making.
The most frequent decision addressed in the multi-
period context is the DC location ; however, in most
reference papers, this decision is made for the entire
planning horizon. Production quantity is regarded pre-
dominantly for multi-period horizons represented by
continuous variables, which are more treatable for solv-
ing integrated problems. Incorporating multiple periods
usually increases the number of integer decision vari-
ables and constraints of the problem. Consequently, it
increases the size of the problem and the time to solve it.
To deal with this complexity, authors in the literature have
devised dierent exact and heuristic solution methods.
In this context, it is common to nd sequential heuristics
based on Lagrangian relaxation, Benders decomposition
approaches, and meta-heuristics.
In real contexts, the portfolio of a company often con-
sists of dierent products with dierent physical charac-
teristics, demand patterns, costs, among others. Despite
this, only 42% (55 articles) of the articles propose mod-
elsthatconsidermultipleproducts.Dependingonthe
context of the distribution network, dierent alternatives
are available for transporting products: modal (railways,
roadways, airways, waterways and pipelines), freight type
(truckload and less-than-truckload) and dierent vehi-
cle sizes. However, only 15% of the articles (19 articles)
consider multiple transportation mode. Moreover, only
Figure 7. Relations between integrating strategies and main integration in reference papers.
12 A. M. JALAL ET AL.
Figure 8. Time aggregation in the most frequent decisions of the sample.
8articlescopewithamulti-period,multi-productand
multi-modal context (Alshamsi and Diabat 2018;Govin-
dan, Jha, and Garg 2016; Manzini et al. 2008;Manzini
and Gebennini 2008;Martinsetal.2017;Motaetal.2018;
Sadeghi Rad and Nahavandi 2018; Zeballos et al. 2014).
Figure 8shows a relationship between the most fre-
quent decisions in the sample and the data aggrega-
tion in periods, products and transportation modes. As
expected, models with two categories of decision (LI, LP,
LT) present more aggregated data, while models with
more integrated decisions (LIPT) consider less aggre-
gated data.
Logisticsnetworksconsistofdierententities,such
as suppliers, factories, warehouses, retailers and nal
consumers. The reference papers addressed networks
mainly with three and two entities, i.e. with two eche-
lons (60%, 78 articles) and one echelon (39%, 51 articles),
respectively.
5.3.2. Data uncertainty
The input parameters of models in the reference papers
are deterministic, stochastic, possibilistic and fuzzy. The
terms fuzzy and possibilistic are often used in an equiva-
lent way in the reference articles. 43% of the articles take
into account variability and uncertainties in the parame-
ters. The main uncertain parameter addressed is demand.
LIPmodelsalsoconsideruncertaintiesincapacities,sup-
ply lead times and costs, while LIT models also consider
uncertain costs and transportation times. LIPT models
address uncertainty in facility opening and transporta-
tion costs, capacities and recovered products fraction in
reverse logistic contexts.
AccordingtoRabbani,Heidari,andYazdanparast
(2019), uncertainty should be acknowledged to ensure
reliability in the decision-making process. Uncertain-
ties are addressed through dierent techniques. Accord-
ing to Rae-Majd, Pasandideh, and Naderi (2018), there
are three dierent and widely used methods for deal-
ing with uncertainty in modelling and optimising the
SC: (i) distribution-based approaches, (ii) scenario-based
approaches and (iii) fuzzy programming approaches.
In distribution-based approaches, probability distri-
bution functions are used to model the uncertain param-
eters. Thus, several authors incorporate the parameters of
the distribution function in the mathematical modelling.
The Normal distribution is widely used with a specic
mean and variance (Alavi et al. 2016;Aryanezhad,Jalali,
and Jabbarzadeh 2010; Das and Sengupta 2009;Liao,
Hsieh, and Lin 2011;Monteiro,Leal,andRaupp2010;
Nakhjirkan and Raei 2017; Nasiri, Davoudpour, and
Karimi 2010; Puga and Tancrez 2017; Rae-Majd, Pasan-
dideh, and Naderi 2018;SchusterPuga,Minnerand
Tancre z 2019; Shahabi et al. 2013;YouandGross-
mann 2008), as well as lead time (Alavi et al. 2016)
and transportation time (Das and Sengupta 2009). The
Poisson distribution is also used to model uncertain
parameters of demand and lead time (Gholamian and
Heydari 2017; Jeet and Kutanoglu 2018). Sadjady and
Davoudpour (2012) addressed uncertain demand and
lead time, which follow Poisson and Exponential distri-
butions, respectively. They applied a queuing approach
to obtain the annual quantities of ordering, purchase and
shortage, and also the mean inventory in the steady-state
condition.
In scenario-based approaches, some discrete sce-
narios with relevant levels of probability are used to
describe the expected occurrence of specic results
(Rae-Majd, Pasandideh, and Naderi 2018). Thus, sev-
eral authors addressed the uncertainty with two-stage
scenario-based stochastic programming, separating the
decision variables into two stages. First stage variables
are decided upon before the realisation of the stochas-
tic parameters. Once the uncertain events have taken
place,furtheradjustmentscanbemadethroughthe
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 13
second-stage variables. Often, two-stage stochastic pro-
gramming models assume that the stochastic param-
eters can be represented as random variables with a
known probability distribution, or well approximated
using a nite number of possible realizations, called sce-
narios. The number of scenarios should be appropriate to
ensure both, the representativeness of the random vari-
ables and the computational tractability of the stochastic
models. The objective is to identify decision variables
at the rst stage that seems to be balanced, in view
of all the possible scenarios of the stochastic parame-
ters.Thisapproachisusedinseveralarticles(Amiri-
Aref,Klibi,andBabai2018;Angazi2016;Fattahiand
Govindan 2017; Ghaderi and Burdett 2019; Ghezavati,
Jabal-Ameli, and Makui 2009;Khatami,Mahootchi,and
Farahani 2015;Shu,Ma,andLi2010;Tsiakis,Shah,and
Pantelides 2001; Zeballos et al. 2014; Zeballos, Méndez,
and Barbosa-Povoa 2018).
In fuzzy-based approaches, parameters are regarded as
fuzzy numbers with membership functions. Fuzzy pro-
gramming can be applied when situations are not clearly
dened and thus are uncertainty, or an exact value is not
critical to the problem. Ahmadi, Torabi, and Tavakkoli-
Moghaddam (2016) considered possibilistic demand and
capacity, Dai et al. (2018) considered capacity and carbon
emissions, Shavandi and Bozorgi (2012) and Govindan
et al. (2020) considered demand, Zhalechian et al. (2016)
consider demand, cost, distance, created job oppor-
tunities and regional development, and Sherafati and
Bashiri (2016) proposed a fuzzy approach with all fuzzy
parameters.
Robust optimisation is another approach to deal with
uncertain parameters in optimisation problems. It con-
structs a solution that is feasible for any realisation of the
uncertainty in a given set. Akbari and Karimi (2015)used
robustoptimisationandsolvedthemodelsusinggeneral
purpose optimisation solvers.
It should be noted that, whereas stochastic program-
ming approaches assume that there is a probabilistic
description of the uncertainty, robust optimisation works
with a deterministic, set-based description of the uncer-
tainty. In two-stage stochastic programming models,
there is a challenge to dene properly the number of
scenarios in order to be appropriate to ensure both, the
representativeness of the random variables and the com-
putational tractability of the stochastic models. The di-
culty of solving the robust optimisation models does not
rise compared with the stochastic models (Bertsimas and
Sim 2004). Regarding distribution-based approaches, the
parameter of the distribution function can be used in
modelling, but sucient information about the param-
eters is needed to dene an appropriate probability dis-
tribution function. Despite this, it is possible that the
Tab le 7. Modeling approaches to face data uncertainty.
Approach
Single-level
mono-period
Single-level
multi-period
Multi-level
models
Timescale
models
LI Deterministic 12 7
Distribution-based 20 0 2
Fuzzy-based 2 1
Scenario-based 2 3 1
LP Deterministic 1 0 1
Scenario-based 2 0
LT Deterministic 7 2 2
Distribution-based 2 0
Scenario-based 1 1
LIP Deterministic 1 5 2 4
Distribution-based 1 0 2
Scenario-based 2 1 1
Robust optimisation 0 1 1
LIT Deterministic 6 6 1
Distribution-based 7 3 1
Fuzzy-based 1 1
Scenario-based 2 1
LIPT Deterministic 1 7 2
Distribution-based 1
Fuzzy-based 1
Tot al 7 0 39 16 6
data does not adjust itself to any probability distribution
function. On the other hand, the results of fuzzy-based
approaches depend on choosing an appropriate member-
ship function and basic rules, which is one of the most
challenging aspects in this approach.
Table 7shows the distribution of reference articles
among deterministic and the dierent approaches to
addressuncertainty.Itisremarkablethatmostarticles
use single-level models to integrate dierent decisions
(LI, LT, LIP, LIT, LIPT) and these models are mainly
deterministic.
However, some of these integrations consider uncer-
tainty through distribution-based, fuzzy-based, and
robust optimisation approaches. Multi-level models
which integrate all decision categories (LIPT) are
mainly deterministic models. In the same way, multi-
timescale models to LIP are deterministic, but the dif-
ferent timescales address decisions in periods with less
uncertainty.
5.3.3. Performance measures
We analyse the types of performance measures used in
the integrated problems. Figure 9depicts dierent objec-
tive functions that measure performances.
Most articles have a single and economic objective,
mainly minimising total cost or maximising prot. The
minimisation objective predominates with 69% of the
studies (90 articles) minimising the total cost, as shown
in Figure 9(a), expressed through the sum of several
cost components that depend on the modelled decisions.
Some cost components are: facility opening, transporta-
tion,storage,routingandvehicleortechnologyacquisi-
tion. Some objective functions minimise total investment
14 A. M. JALAL ET AL.
Cost
69%
Profit
14%
Multiple
mesuares
17%
Environ-
mental
41%
Service-
level
36%
Environ-
mental
and social
23%
Figure 9. Performance measures in integrated problems. (a) Performance measures and (b) multiple objectives.
derivedfromadecision,forinstance,investmentinopen-
ing warehouses (Nasiri and Davoudpour 2012). On the
other hand, prot maximisation objectives receive less
attention, only 14% (18 articles) of the articles. Under
prot maximisation, it is not always attractive for a
company to meet all demands of all customers. This
occurs when serving certain customers generates addi-
tional costs higher than the corresponding revenues.
Thus, some models include decisions such as delivery
delays and lost sales, under penalties in the objective
function.
Somepapersproposemodelswithmultipleandcon-
icting objectives. This approach is especially useful for
situations where objectives cannot be added because they
have dierent units (Brunaud and Grossmann 2017).
Increasing environmental, legislative, and social con-
cerns are forcing companies to take into account the
impact of their operations on the environment and soci-
ety. Thus, in addition to economic factors, objectives
relatedtocustomerresponsivenessandsocialandenvi-
ronmental impacts are taken into account in mathemat-
ical models. Among the articles studied, 17% (22 arti-
cles) are found in this category. All the multi-objective
models have at least one economic objective. The pie-
chart Figure 9(b)isasub-chartofFigure9(a) and
out of the 17% of papers that consider multiple mea-
sures, 41% consider environmental measures in combi-
nation with economic measures, 36% consider service-
level measures in combination with economic measures,
and 23% consider environmental and social measures
in combination with economic measures. Most multi-
objective models integrate decisions through a single-
model (91%). Multi-level models also address several
objectives (9%). The main integration in multi-objective
models is LIT with objectives related to environmental
impacts, demand fullment, and delivery times (Biuki,
Kazemi, and Alinezhad 2020; Forouzanfar et al. 2018;
Govindan et al. 2020;Mogale,Cheikhrouhou,and
Tiwari 2020;Nekooghadirlietal.2014;Qazvini,Amal-
nick, and Mina 2016;Rabbani,Heidari,andYazdan-
parast 2019;Zhalechianetal.2016). Multi-objective LI
models also involve objectives such as demand responses
and delivery times (Ahmadi, Torabi, and Tavakkoli-
Moghaddam 2016; Liao, Hsieh, and Lai 2011;Liao,Hsieh,
and Lin 2011; Naimi Sadigh, Fallah, and Nahavandi 2013;
Nasiri and Davoudpour 2012). LT and LIPT models
consider environmental objectives, for instance, min-
imising pollutant gas emissions (Govindan et al. 2014;
Govindan, Jha, and Garg 2016;Govindan,Jafarian,and
Nourbakhsh 2019;SadeghiRadandNahavandi2018;
Soleimani, Chaharlang, and Ghaderi 2018) and minimis-
ing the environmental impacts through the life cycle
analysis methodology (Mota et al. 2018).
Socialobjectivesaremorediculttomeasurecom-
paredtoeconomicobjectives,therefore,theyaremore
dicult to dene and use. A social objective aims to max-
imise the social benet measured through indicators. The
main social indicator is creating job opportunities with
dierent denitions, for instance, the number of jobs cre-
ated by the SC in countries with less economic develop-
ment (Mota et al. 2018). The maximisation of job creation
is also used by Biuki, Kazemi, and Alinezhad (2020)and
Zhalechian et al. (2016). Govindan, Jha, and Garg (2016)
proposed other social objectives in terms of economic
welfare and growth, responsibilities towards stakehold-
ers, extended producer responsibilities and employment
practices. Govindan, Jafarian, and Nourbakhsh (2019)
presented several social indicators: variable and xed job
opportunities; equity between customers in terms of their
access (distance); potential damage that may occur in the
process of establishing facilities, shipment of products,
manufacturing and handling; level of customer satisfac-
tion in terms of time delivery; the equity of workers in
termsofthestandarddeviationofdistancespassedby
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 15
vehicles and the standard deviation of work-load in facil-
ities; and the work damage during the manufacturing
process.AccordingtoFarahanietal.(2014), the response
time to the customer can be considered as a social objec-
tive, as the customer needs are primarily regarded despite
thecostthattheservicemayrepresentforthecompany.
Some social and environmental objectives are used as
constraints in other articles. Demand fullment policies
derive constraints related to service levels, stock levels
and safety stocks. Frequently, the consideration of ser-
vice levels and safety stocks involves non-linear expres-
sions. Most of the mathematical models in the sample
show some non-linearity (89%), of which very few arti-
cles present strategies to linearise the non-linear models
(9%).
A comparison of the performance measures between
our analysis and the review presented by Melo, Nickel,
and Saldanha-da Gama (2009) shows an increase in mod-
els considering multiple measures, particularly including
environmental and social ones. This result seems to cor-
roborate a tendency in the literature of incorporate sus-
tainable issues in a multiple perspectives of performance
measures.
5.3.4. Applications
Regarding applications in the industrial sector, most
applications of the proposed models and methods
were made in European countries, including electronic,
glass, pharmaceutical, consumer goods, and copier re-
manufacturer companies. Moreover, there were applica-
tions in Iran in dierent companies, such as bread, lters,
light automobile parts, and household goods. In Pak-
istan, an application was in a lube oil company. There is
alsoacaseinanIndianplasticmanufacturerandother
applications in cell phones, packaged gases, automotive
timing belts, and steel pipe products. We also note that
thereareseveralapplicationsinservicepartslogistics.
The applications in industrial sectors represent only 30%
of the reference articles. These articles present integrated
problems based on case studies and also use real data or
generated instances based on real data.
Most articles present axiomatic research assuming ide-
alisedproblems,i.e.theyareinterestedindeveloping
approaches to improve addressed problems in the liter-
ature, to nd better solutions to newly dened problems,
or to compare various methods to solve a specic prob-
lem (Bertrand and Fransoo 2002). These works consider
generated data sets. We note that the mathematical for-
mulations of these articles are inspired by other pieces
of research that might have been originally motivated by
real problems. However, the discussion about the model
assumptions and data structure in practical contexts is
frequently neglected in the revised papers. Most authors
focus only on describing the main research contribu-
tion, which is often based on idealised problems. The
lack of analysis about the fundamentals and premises to
formulate LNP models can be a primary obstacle to the
practitioners.
6. Solution methods for integrated problems in
LNP
The methods used to solve the integrated LNP optimisa-
tion models can be classied into exact and non-exact
methods. Exact solution methods include techniques able
to nd optimal solutions: Benders decomposition (BD)
(Benders 1962), column generation (Savelsbergh 2008),
branch-and-cut (B&C), branch-and-price (B&P), and
decomposition methods with exact solutions. Non-exact
solution methods include heuristics and meta-heuristics.
Taking into account that the integration of decisions sug-
gests addressing problems simultaneously, an idea for
solving the models is the decomposition of the inte-
grated problem into subproblems that are easier to solve
with exact or heuristic methods, for instance, Benders
decomposition based heuristics. Some heuristic meth-
ods explore features of mathematical programming with
exact, heuristics, and meta-heuristics methods, called
matheuristics. Table 8presents the solution methods
used in the articles of the sample.
6.1. Exact methods
About 35% of referenced articles use exact approaches
to solve models for integrated problems, mainly Ben-
ders decomposition (BD) and branch-and-cut (B&C)
as shown in Table 8.Awell-knownapproachused
in some revised papers is the Benders decomposition
method, a technique for partitioning variables aiming
to solve large-scale problems with complicating vari-
ables. Alshamsi and Diabat (2018) proposed an accel-
erated Benders decomposition algorithm to a large-
scale reverse SC network design with production, inven-
tory and transportation decisions. Azizi and Hu (2020)
applied a Benders decomposition algorithm for pickup
anddeliverySCdesignwithLRanddirectshipment.
Wheatley, Gzara, and Jewkes (2015)presentedanexact
solution methodology using logic-based Benders decom-
position for an LI problem with service constraints.
Khatami, Mahootchi, and Farahani (2015) applied Ben-
ders’ decomposition to solve a stochastic mixed inte-
gerprogrammingmodelfortheconcurrentredesignof
a forward and closed-loop SC network with demand
and return uncertainties. Tapia-Ubeda et al. (2020)pro-
posed a generalised Benders decomposition to spare
parts SC network design problems and Zheng, Yin, and
16 A. M. JALAL ET AL.
Tab le 8. Solution methods found in the reference articles.
Methods Authors
Exact
BD Alshamsi and Diabat (2018); Azizi and Hu (2020); Wheatley, Gzara, and Jewkes (2015); Khatami, Mahootchi, and
Farahani (2015); Ramezani and Kimiagari (2016); Tapia-Ubeda, Miranda, and Macchi (2018); Tapia-Ubeda
et al. (2020); Zheng, Yin, and Zhang (2019)
B&B Darvish et al. (2019)
B&P Ahmadi-Javid, Amiri, and Meskar (2018)
Column generation Shu, Ma, and Li (2010)
General purpose solvers (B&C) Ahmadi, Torabi, and Tavakkoli-Moghaddam (2016); Akbari and Karimi (2015); Azizi and Hu (2020); Azizi, Hu,
and Mokari (2020); Bashiri, Badri, and Talebi (2012); Brahimi and Khan (2014); Cardoso, Barbosa-Póvoa,
and Relvas (2013); Candas and Kutanoglu (2007); Das and Sengupta (2009); Fattahi, Mahootchi, and
Husseini (2016); Gebennini, Gamberini, and Manzini (2009); Ghomi-Avili et al. (2018,2021); Govindan, Jha,
and Garg (2016); Govindan et al. (2020); Guerrero et al. (2015); Hammami, Frein, and Bahli (2017); Kabadurmus
and Erdogan (2020); Manzini (2012); Manzini et al. (2008); Manzini and Gebennini (2008); Manzini,
Accorsi, and Bortolini (2014); Martins et al. (2017); Mota et al. (2018); Motaghedi-Larijani, Jabalameli,
and Tavakkoli (2012); Mousavi et al. (2014); Nasiri and Davoudpour (2012); Schuster Puga, Minner and
Tancrez (2019); Qazvini, Amalnick, and Mina (2016); Sadeghi Rad and Nahavandi (2018); Sabri and
Beamon (2000); Salema, Póvoa, and Novais (2009); Salema, Barbosa-Povoa, and Novais (2010); Sadjadi
et al. (2016); Shahabi et al. (2013); Sherafati and Bashiri (2016); Soleimani, Seyyed-Esfahani, and
Shirazi (2016); Soleimani, Chaharlang, and Ghaderi (2018); Tsiakis, Shah, and Pantelides (2001); Yu, Normasari,
and Luong (2015); Zeballos et al. (2014); Zeballos, Méndez, and Barbosa-Povoa (2018)
Heuristics
Specific/sequential heuristics Diabat (2016); Miranda, Garrido, and Ceroni (2009); Mousavi, Tavakkoli-Moghaddam, and Jolai (2013); Puga
and Tancrez (2017); Rappold and Van Roo (2009); Schwardt and Dethloff (2005); Singh et al. (2015); Tancrez,
Lange, and Semal (2012); Tsao et al. (2012); Halit, Keskin and Çetinkaya (2008); Zhang and Xu (2014)
LR based heuristics Ahmadi-Javid and Hoseinpour (2015b,2015a); Alenezi and Darwish (2014); Badri, Bashiri, and Hos-
sein (2013); Candas and Kutanoglu (2020); Diabat, Richard, and Codrington (2013); Diabat and
Richard (2015); Diabat, Battaïa, and Nazzal (2015); Etebari (2019); Miranda and Garrido (2004,2006); Nasiri,
Davoudpour, and Karimi (2010); Rafie-Majd, Pasandideh, and Naderi (2018); Sadjady and
Davoudpour (2012); You and Grossmann (2008)
BD based heuristics Solak, Scherrer, and Ghoniem (2014)
Non-exact
Outer approximation method Angazi (2016); Jeet and Kutanoglu (2018); Monteiro, Leal, and Raupp (2010)
Sample average approximation Amiri-Aref, Klibi, and Babai (2018); Ghaderi and Burdett (2019)
Meta-heuristics
Evolutionary algorithms Cabrera et al. (2016); Calvete, Galé, and Iranzo (2014); Guo et al. (2020); Liao, Hsieh, and Lin (2011); Liao, Hsieh,
and Lai (2011); Lin, Gen, and Wang (2009); Nasiri, Ghaffari, and Davoudpour (2015); Tavakkoli-Moghaddam,
Makui, and Mazloomi (2010); Tiwari et al. (2010); Wang et al. (2013)
Genetic algorithm Arabzad, Ghorbani, and Tavakkoli-Moghaddam (2014); Aryanezhad, Jalali, and Jabbarzadeh (2010); Diabat and
Deskoores (2016); Firoozi et al. (2014); Forouzanfar et al. (2018); Ghezavati, Jabal-Ameli, and Makui (2009); Hias-
sat, Diabat, and Rahwan (2017); Mogale, Cheikhrouhou, and Tiwari (2020); Naimi Sadigh, Fallah, and
Nahavandi (2013); Nakhjirkan and Rafiei (2017); Nakhjirkan, Rafiei, and Kashan (2019); Nekooghadirli
et al. (2014); Rabbani, Heidari, and Yazdanparast (2019); Shavandi and Bozorgi (2012); Tang and Yang (2008)
Imperialist competitive algo Alavi et al. (2016); Nekooghadirli et al. (2014)
Simulated annealing Fattahi and Govindan (2017); Keskin and Üster (2012); Nekooghadirli et al. (2014); Saragih et al. (2019)
Tabu search Kim and Lee (2015); Yuchi et al. (2016)
Particle swarm algo Forouzanfar et al. (2018); Govindan et al. (2014); Mousavi et al. (2017); Mogale, Cheikhrouhou, and Tiwari (2019)
VNS Karakostas, Sifaleras, and Georgiadis (2019)
Hybrid meta-heuristics Ahmadi-Javid and Azad (2010); Biuki, Kazemi, and Alinezhad (2020); Dai et al. (2018); Ghorbani and Akbari
Jokar (2016); Govindan, Jafarian, and Nourbakhsh (2015,2019); Li et al. (2013); Liu et al. (2020); Gholamian
and Heydari (2017); Guo et al. (2018); Kaya and Urek (2016); Zhalechian et al. (2016)
Matheuristics Ahmadi-Javid and Hossein Seddighi (2012); Darvish and Coelho (2018); Lagos et al. (2015)
Number and authors of articles are in Table A1 in Appendix.
Zhang (2019) applied it to solve a location-inventory-
routing problem.
Generally, in integrated models solved with BD,
location and customer assignment decisions are tem-
porarily xed, while tactical and operational deci-
sions are yielded in a sub-problem. Ramezani and
Kimiagari (2016) xed variables representing nancial
decisions to solve iteratively subproblems with logistics
decisions (location, allocation, distribution) and other
nancial decisions in a closed-loop SC network. Darvish
et al. (2019) proposed an exact method based on the
interplay between two branch-and-bound algorithms
that run in parallel called the enhanced parallel exact
method.
Shu, Ma, and Li (2010) developed a column genera-
tion method to solve the LI problem under uncertainty in
the long life-cycles of warehouses. The authors explicitly
model the possible combinations of retailers that can be
served, and they solve the problem by initially consid-
ering only a subset of combinations and adding others
iteratively, until the best allocation is found.
Ahmadi-Javid, Amiri, and Meskar (2018) addressed a
location-routing-pricing problem, aiming at maximising
prot. The problem is reformulated to a set-packing mas-
ter problem and elementary shortest path subproblems,
by using the Dantzig-Wolfe decomposition. A branch-
and-price algorithm is used as the solution method
afterreformulatingthemodel.Alocationproblemis
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 17
addressedinthemasterproblemwithasubsetofroutes
and new routes are added iteratively to this master prob-
lem using heuristic and exact label-setting algorithms.
Some articles solve problems using general-purpose
optimisation solvers, such as CPLEX, GUROBI, LINGO
and XPRESS, which are also considered here in the
exact category, because an exact method is usually
incorporated into these solvers, often a branch-and-cut
method. The main decisions integrated in these articles
are location-allocation, ows and inventory levels.
6.2. Non-exact methods
Non-exact methods include algorithms that return a fea-
sible solution in nite computational time with absent
accuracy of such solution quality, i.e. without a certicate
of optimality of the solution. Most of the articles stud-
ied (about 64%) present non-exact solution approaches,
which is expected since location problems are dicult to
solve (NP-hard) When location problems are combined
with other problems, the resulting integrated problem
involves a greater number of constraints and complicat-
ingvariables,andconsequentlyitisalsodiculttosolve.
In this case, authors often resort to heuristic methods that
can nd feasible solutions within acceptable run times to
the integrated problems.
Benders decomposition is an attractive methodol-
ogy to develop heuristics because it can take advantage
of problem structures Rahmaniani et al. (2017). Other
sequential algorithms consist of separating decisions and
solving parts of the problem sequentially (Diabat 2016;
Miranda, Garrido, and Ceroni 2009; Rappold and Van
Roo 2009;Singhetal.2015;Tsaoetal.2012;Zhang
and Xu 2014). Guerrero et al. (2015) proposed a relax-
and-price heuristic for the location-inventory-routing
problem, a hybridisation between column generation,
Lagrangian relaxation, and local search. Lagrangian
relaxation (LR) is usually used as a decomposing strategy.
This leads to relaxing some restrictions of the problem,
called coupling restrictions, and are penalised (dualised)
in the objective function and, generally, the resulting
problem can be decomposed into independent problems.
Heuristics based on Lagrangian relaxation are widely
used in the sample, as shown in Table 8.
Some authors have also proposed algorithms inspired
by meta-heuristics, namely simulated annealing (Fat-
tahi and Govindan 2017;KeskinandÜster2012;
Nekooghadirli et al. 2014;Saragihetal.2019), tabu
search (Kim and Lee 2015;Yuchietal.2016), particle
swarm optimisation (Forouzanfar et al. 2018;Govindan
et al. 2014;Mousavietal.2017; Mogale, Cheikhrouhou,
and Tiwari 2019), and meta-heuristics based on evolu-
tionary algorithms (Cabrera et al. 2016; Calvete, Galé,
and Iranzo 2014;Liao,Hsieh,andLai2011;Liao,
Hsieh, and Lin 2011;Lin,Gen,andWang2009;Nasiri,
Ghaari, and Davoudpour 2015;Tiwarietal.2010;
Wang e t a l. 2013). An evolutionary algorithm fre-
quently used is the well-known genetic algorithm
(Arabzad, Ghorbani, and Tavakkoli-Moghaddam 2014;
Aryanezhad, Jalali, and Jabbarzadeh 2010;Diabatand
Deskoores 2016; Firoozi et al. 2014; Ghezavati, Jabal-
Ameli, and Makui 2009; Hiassat, Diabat, and Rah-
wan 2017; Naimi Sadigh, Fallah, and Nahavandi 2013;
Nakhjirkan and Raei 2017; Shavandi and Bozorgi 2012;
Tang and Yang 2008).Authorshavealsoproposedhybrid
meta-heuristics, in particular, simulated annealing with
tabu search (Ahmadi-Javid and Azad 2010)andsimu-
lated annealing with genetic algorithm (Gholamian and
Heydari 2017;Guoetal.2018). Some articles com-
bine several meta-heuristics, such as simulated anneal-
ing, tabu search and genetic algorithm with variable
neighbourhood search (VNS) (Kaya and Urek 2016).
Some heuristic methods explore features of mathematical
programming with exact, heuristics and meta-heuristics
methods, called matheuristics. For instance, a hybrid
Lagrangian relaxation and an ant colony optimisation
algorithm to solve a distribution network design problem
(Lagos et al. 2015).
An idea for solving the integrated models is the
decomposition into subproblems that are easier to solve.
Ahmadi-Javid and Hossein Seddighi (2012)presented
a heuristic method in three phases: location, routing-
1 and routing-2. After determining a suitable initial
solution, a simulated annealing algorithm and a hybrid
ant colony optimisation algorithm are implemented to
improvethesolutioninthersttwophasesandinthe
thirdphase,respectively.DarvishandCoelho(2018)pro-
posed a matheuristic based on a hybrid of variable neigh-
bourhood search and exact methods. The problem is
divided into two subproblems that are then solved in
an iterative manner. In the rst level, the authors apply
a heuristic in order to decide location and production
allocation. In the second level, transportation, inven-
tory allocation at plants and rented DCs are determined
exactly by solving an integer linear programming sub-
problem. Finally, they improve the obtained solution by
solving the model presented with exact methods for a
very short-time period.
Some optimisation models have multiple objectives
and are solved with methods that do not guaran-
tee optimal solutions for each objective. This is the
case when multiple objectives are transformed into
a single objective by a weighted sum of each cri-
terion (Naimi Sadigh, Fallah, and Nahavandi 2013)
or by goal programming Arabzad, Ghorbani, and
Tavak k o li-Mog h addam ( 2014). Some authors also use an
18 A. M. JALAL ET AL.
evolutionary approach (non-dominated sorting genetic
algorithm) to deal with multiple objectives (Forouzan-
far et al. 2018; Liao, Hsieh, and Lin 2011;Mogale,
Cheikhrouhou, and Tiwari 2020; Naimi Sadigh, Fallah,
and Nahavandi 2013;Nekooghadirlietal.2014). Govin-
dan et al. (2014) proposed a hybrid meta-heuristic, com-
bining a particle swarm algorithm and an adapted multi-
objective variable neighbourhood search algorithm.
6.3. Analysis of solution methods for each type of
integration
There is a predominance of non-exact methods over
exact methods to solve logistic network planning prob-
lems. In order to determine if there is some trend in the
solution methods according to the decisions involved in
the model and the integration strategies used, Figure 10
shows the participation of each category of method that
involves these decisions.
StudiesonLI,LT,andLITareaddressedmainlyby
heuristics and meta-heuristics. This is because mod-
els with decisions represented by integer variables and
associated with non-linear expressions in mathemati-
cal programming are dicult to approach with exact
methods. In particular, models with decisions such as
inventory policy denition, order point, and order num-
berweremainlyaddressedthroughheuristicsandmeta-
heuristics. Moreover, models with decisions represented
byintegervariables,suchasdemandallocationand
vehicle routing, are largely addressed through heuris-
tics and meta-heuristics. The LIP integration, that gen-
erally addressed inventory levels and production quan-
tity decisions using continuous variables, is often solved
by exact methods, predominantly by general-purpose
solvers. Models that additionally integrate transportation
decisions, LIPT, are addressed more diversied solution
methods, 64% by exact methods and 36% by non-exact
methods.
The integration of decisions may increase the di-
culty to solve the models. A strategy of a single-model is
preponderant. To solve these models, heuristic methods
are commonly used, customised heuristics, Lagrangian
relaxation-based heuristics, as well as meta-heuristics
based on evolutionary algorithms, particularly genetic
algorithm. Only 28% of the articles that use this strategy
are solved with exact methods, predominantly solvers of
general purpose (25%). Multi-level models use heuristic
andexactsolutionapproaches.Modelswithintercon-
nected timescales use general-purpose solvers.
7. Discussions about research gaps and
opportunities
Researchers and practitioners of operation management
and operations research communities often classify deci-
sions into strategic, tactical, and operational, based on
the time horizon of impact, therefore these decisions
are dealt separately. When the members of the logistics
networktrytooptimisetheirrelativeperformance,the
performance across the network might not be optimal.
This is true also when each level is optimised regard-
less of the others, hence, this leads to a sub-optimality
of decisions and excessive costs. Recently, many studies
showed signicant savings when regarding integration of
decision levels (Hiassat, Diabat, and Rahwan 2017).
In this context, the present study used a systematic
literature review to better understand how this integra-
tion is developed in optimisation models; what the main
integrated decisions involved are; what types of prob-
lems are treated and what their main features are; how
the data is addressed; which solution methods are used
to solve the integrated problems; and what research gaps
and opportunities are identied. Figure 11 summarises
the challenges and benets of integrated planning, and
also the main ndings of the literature review, allowing a
betteroverviewofwhathasbeendoneonthistopic.
Figure 10. Participation of each category of method that involves these decisions.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 19
Figure 11. Conceptual framework of the main findings of the literature review towards research opportunities.
The integration of decisions levels in the network
planning implies taking (some of) strategic, tactical
and operational decisions simultaneously. Consequently,
benets can be obtained, as shown in Figure 11.Theinte-
gration eliminates conict and incompatibility among
decisions and goals of dierent departments in a com-
pany.Italsohelpstoreactmorequicklytothedynamic
conditions of the environment. Moreover, the integrated
planning reduces the logistics network costs and more
information is exploited. Nevertheless, this integration
presents challenges in modelling and solving problems,
as pointed out in Figure 11. Integrated planning implies
dealing with dierent decision timing (scope, periodic-
ity, and frequency), as well as taking into account several
logistics components and dealing with the variability and
uncertainty of important problem parameters (Monteiro,
Leal, and Raupp 2010). Integrated planning also implies
mathematical models with a greater number of variables
(continuous and integer). It increases the diculty of
solvingthemodels,whichreectsinlargerexecution
times. The requirements for large amounts of complex
and hard to obtain data are other challenges (Miranda,
Garrido, and Ceroni 2009).
The reference papers of our review address the inte-
gration of: Location-Inventory (LI), Location-
Transportation (LT), Location-Production (LP),
Location-Inventory-Transportation (LIT), Location-
Inventory-Production (LIP), location-transportation-
production (LTP), and Location-Inventory-Production-
Transportation (LIPT). Figure 11 presents the main
decisionsbyhierarchicallevel.Thestudieshavefocused
mainly on handling strategic and tactical decisions
for the entire planning horizon. The main decisions
addressed at the strategic level are facility location, net-
work design, and demand allocation, generally dened
for the entire planning horizon. Tactical and opera-
tional decisions are associated with production, inven-
tory and transportation management. The main deci-
sions in inventory management refer to inventory lev-
els, order quantities and replacement points. Produc-
tion decisions, in turn, include production quantities
and production allocation which are typical master pro-
duction planning (mid-term). In transportation manage-
ment, the decisions considered are vehicle routing and
transportation alternatives selection. Very few studies
incorporate the selection of transportation alternatives,
notwithstanding it is a common characteristic in real
contexts.
Regarding our main research question, the approaches
to integrate decision levels can be classied into: (i)
single-level and mono-period models; (ii) single-level
and multi-period models; (iii) multi-level models; (iv)
multi-time-scales models, as shown in Figure 11.Single-
level, mono-period, and deterministic models integrate
decisions of dierent hierarchical levels without taking
into account the variability or uncertainties from the
lower levels. These models can be eective when these
variability and uncertainties are not signicant for the
planning results. To include these issues, some authors
formulate similar models considering stochastic, possi-
bilistic and fuzzy parameters.
The consideration of multiple periods when dealing
with tactical decisions is the most common strategy iden-
tied. It allows re-evaluating the shorter-period decisions
during the planning horizon, while strategic decisions are
evaluated for the entire horizon or the macro-periods in
the case of multi-scale models. This approach requires
more computational eort to solve the problems. Other
approaches are multi-level models that allow the consid-
eration of further details and decisions. Some of these
20 A. M. JALAL ET AL.
models used a feedback mechanism to pass information
from the bottom to the top level.
Most articles have a considerably simplied data
aggregation, as pointed out in Figure 11,whichcould
means sub-optimal solutions of the models and in
decision-making. Most companies have multiple
products; however most studies aggregated them into a
single product. Critical analysis about modelling assump-
tions and data generation aligned with practical prob-
lems could provide more interesting managerial insights.
For models considering some inventory decisions (safety,
replacement point, order point) historical data could be
used to estimate the demand through probability distri-
butions. However, this may not be eective if demand is
seasonal, therefore these assumptions need to be carefully
evaluated. In this same sense, in the practice of trans-
port activities, dierent alternatives related to modal,
freight type and vehicle capacity are available ; how-
ever, they are overlooked as they are considered a single
mode of transportation. A possible reason is that tak-
ing into account multiple periods in modelling increases
the diculty of solving problems. Particularly, dening
an appropriate transportation cost structure for dier-
entdecisionlevelsisverydicult.Inapracticalcontext,
there are issues such as quantity discounts, which are
established by the carriers to encourage organisations
to transport larger quantities in order to reduce their
xed costs. These issues were neglected in the referenced
papers. Thus, a research opportunity is to better eval-
uate these cost structure assumptions in the integrated
models.
AnimportantissueinLNPisthelocationproblemthat
is NP-hard, and is integrated with other problems that
can result in a greater number of constraints and com-
plicating variables, consequently more dicult to solve.
Most of the articles studied present non-exact solution
approaches, as is presented in Figure 11.Manystud-
ies which use the single-level models, use decomposi-
tion strategies for solving them. In fact, most heuris-
tics methods in the sample were based on the decom-
positionidea,thusseveralpapersproposedcustomised
sequential heuristics and Lagrangian relaxation-based
heuristics.
Regarding the relation between the integration strate-
gies and the types of solution methods, to solve these
single models were used non-exact methods; while multi-
levelmodelsweresolvedwithbothexactandnon-exact
methods; and models with interconnected timescales
were solved with general-purpose solvers. Regarding the
relation between the decisions and the type of solution
methods, models with product ow, inventory levels and
production quantity are often solved by purpose general
solvers. However, models with decisions like inventory
policies and routing decisions, are addressed mainly
through meta-heuristics.
In the current business environment aected by
uncertainties, LNP is a complex decision-making pro-
cess. Important information for decision-making such as
customer demand, lead times, sales prices, availability,
and capacities are uncertain and could vary consid-
erably along the planning horizon (Amiri-Aref, Klibi,
and Babai 2018). A few articles cope with stochastic/
uncertain parameters through techniques such as rep-
resentative scenarios, stochastic programming, robust
optimisation, and fuzzy programming.
Most articles have a single economic objective mainly
minimising total cost or maximising prot. Few papers
propose multi-objective models, considering environ-
mental and social objectives. The environmental objec-
tives aim to reduce the impacts of the decisions on the
environment, and are measured through indicators such
as gas emission. The social objectives aim to maximise the
social benet measured through indicators like the num-
berofjobscreated,andtheyaremorediculttomeasure,
dene and use.
Thereby, there are research gaps in the integrated plan-
ning of the logistics network, as pointed out in Figure 11.
First, there is a gap in the consideration of some char-
acteristics of the integrated problems, mainly parameter
uncertainty. Thus, studies that propose appropriate tech-
niques to address uncertainties in the problem parame-
ters, as well as approaches to solving these problems can
be interesting and promising. Other practical character-
istics that could be regarded in the problem modelling
would be multiple products and multiple transportation
alternatives. Depending on the practical context, it would
be interesting to look at environmental and social objec-
tives, in addition to economic objectives. According to
the product type, and responding to government legis-
lation and social pressure, reverse logistics for the proper
disposal or the re-manufacturing of used products should
be also considered. blackThus, there are important issues
that decision-makers in LNP have to manage in the prac-
tice,whichareneglectedintheliterature.Atthesame
time, the studies presented elaborated models and solu-
tion methods. However, few studies applied the mathe-
maticalmodelsinrealcases.Thus,thequestionsraisedby
Bertrand and Fransoo in 2002 about the ‘gaps’ between
theory and practice in operation research remain as a gap
in the literature.
Regarding the integration, there are gaps in the
integration of relevant decisions, in particular the
transportation mode selection. Moreover, there are
opportunities to properly develop integration strategies
for aggregate decisions, as well as propose represen-
tative mathematical models considering adequate time
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 21
structure for decisions. It is also interesting to compare
dierent strategies to address the integration of decisions.
Most solution approaches of the articles are heuristic,
thus there is an opportunity to develop exact methods
exploring the characteristics of the models and the inte-
gration of decisions.
8. Final remarks
Managers and researchers of the operations manage-
ment/operation research community have noticed the
importance of integrated planning in logistics network
design and planning, mainly because of the potential ben-
ets obtained when addressing dierent decision levels.
This paper used a systematic literature review to better
understand how decision level integration was devel-
oped in the optimisation models of the literature. A set
of articles on integrated planning of logistics networks
published from 2000 to 2020 was reviewed. The grow-
ingnumberofpublicationsinrecentyearsindicatesan
increasing trend of research activities on this topic.
Based on this literature survey, we present a concep-
tual framework to highlight the challenges and benets of
integrated planning, and also the main characteristics of
the reference papers regarding the integrated decisions,
integrating strategies, and solution methods. We also dis-
cuss some research gaps in the literature. There are some
interesting opportunities for future research in dierent
directions, such as the development of integrated deci-
sion levels, development of integrating approaches, pro-
cessing and aggregation data, incorporation of parameter
uncertainties, development of exact solution methods, as
well as applications to industrial and service settings.
Despite the growing literature in LNP integrated deci-
sions, many studies do not dierentiate the timing of
the decisions. There is a predominance of simple data
aggregation in the problem modelling, considering only
a single period in the planning horizon with all decisions
aggregated. Thus, a promising line of research would
be to develop models for LNP carefully dening proper
planning horizons, the time structure and the frequency
in which decisions should be made or revised. Modeling
assumptions should include the dynamism and variabil-
ity presented in the current business contexts.
These research opportunities encourage collaboration
and partnership between academia and organisations,
particularly the industry. It can help to propose bet-
ter problem descriptions and formulations, and better
optimisation approaches and tools, to eectively support
decision-making in logistics network planning. These
tools can be useful in practice, contributing to the devel-
opment of collaborative research.
In SC networks, organisations should cooperate with
each other to improve the performance of the whole SC,
and this type of integration could be addressed in future
studies.
Acknowledgments
Theauthorswouldliketothanktheanonymousreviewersfor
their useful comments and suggestions or revision.
Disclosure statement
No potential conict of interest was reported by the
author(s).
Funding
ThisstudywaspartiallynancedbytheCoordenaçãodeAper-
feiçoamento de Pessoal de Nível Superior - Brasil (CAPES) -
Finance Code 001; São Paulo Research Foundation (FAPESP)
[grant number 2016/01860-1], [grant number 2017/07236-0],
[grant number 2018/09563-1].
Notes on contributors
Aura Jalal, MSc, is a doctoral student at
Department of Production Engineering,
Federal University of São Carlos, in Brazil.
Her research interests are focused on loca-
tion and distribution problems, inven-
tory management, robust optimisation,
stochastic programming, reverse logistics,
and exact and heuristic solution meth-
ods such as Bender’s decomposition, matheuristic, and hybrid
methods.
Eli Angela Vitor Toso is an associated
professor at the Production Engineering
Department of the Federal University of
São Carlos – campus Sorocaba, in Brazil.
She received her BSc’s degree, master’s
degree, and doctorate, all in production
engineering from the Federal University of
SãoCarlos.Also,sheattendedasplitPHD
programatUniversityoftheWestofEngland,inBristol,UK.Eli
Toso has developed projects with companies and public insti-
tutions focusing on applied operations research. Her research
interests comprise logistics network design and production
planning problems, mainly to understand how to address these
problems in practical contexts. Her other scientic interests rely
on optimisation models and solution methods applied to the
integration of strategic, tactical, and operational decisions.
Reinaldo Morabito isaprofessoratthe
Production Engineering Department of
the Federal University of São Carlos, in
Brazil. He earned a B.S. in Civil Engineer-
ing from the State University of Camp-
inas, an M.Sc. in Computer Science and
Computational Mathematics and a Ph.D.
in Transportation Engineering, both from
22 A. M. JALAL ET AL.
the University of Sao Paulo, Brazil. He was a visiting scholar
at the Sloan School of Management, M.I.T., Cambridge, MA.
Prof. Morabito has coordinated many grants from funding
agencies and has developed applied projects with several com-
panies in Brazil, with a focus on Operations Research, Service
and Operations Management, Production and Logistics Plan-
ning and Control. His research interests include logistics and
transportation planning including vehicle routing problems,
probabilistic location problems, cutting and packing problems,
lot sizing, and scheduling problems, and queueing networks
applied to manufacturing systems. Additionally, he has worked
on combinatorial optimisation, stochastic programming, and
robust optimisation.
ORCID
Aura Maria Jalal http://orcid.org/0000-0002-1092-5002
Eli Angela Vitor Toso http://orcid.org/0000-0001-7531-0300
Reinaldo Morabito http://orcid.org/0000-0002-3948-305X
References
Adulyasak, Yossiri, Jean François Cordeau, and Raf Jans.
2015. “The Production Routing Problem: A Review of
Formulations and Solution Algorithms.” Computers and
Operations Research 55: 141–152. doi:10.1016/j.cor.2014.
01.011
Ahmadi, Ghazaleh, S. Ali Torabi, and Reza Tavakkoli-
Moghaddam. 2016. “A Bi-objective Location-inventory
Model with Capacitated Transportation and Lateral Trans-
shipments.” International Journal of Production Research 54
(7): 2035–2056.
Ahmadi-Javid, Amir, Elahe Amiri, and Mahla Meskar. 2018.“A
Prot-Maximization Location-Routing-Pricing Problem : A
Branch-and-Price Algorithm.” European Journal of Opera-
tional Research 271 (3): 866–881.
Ahmadi-Javid, Amir, and Nader Azad. 2010.“Incorporating
Location, Routing and Inventory Decisions in Supply Chain
Network Design.” Transportation Research Part E: Logistics
and Transportation Review 46 (5): 582–597.
Ahmadi-Javid, Amir, and Pooya Hoseinpour. 2015a.“A
Location-inventory-pricing Model in a Supply Chain Distri-
bution Network with Price-sensitive Demands and
Inventory-capacity Constraints.” Transportation Research
Part E 82: 238–255.
Ahmadi-Javid, Amir, and Pooya Hoseinpour. 2015b.“Incorpo-
ratingLocation,InventoryandPriceDecisionsIntoaSupply
Chain Distribution Network Design Problem.” Computers
and Operations Research 56: 110–119.
Ahmadi-Javid, Amir, and Amir Hossein Seddighi. 2012.“A
Location-routing-inventory Model for Designing Multi-
source Distribution Networks.” Engineering Optimization 44
(6): 637–656.
Akbari, Ali Akbar, and Behrooz Karimi. 2015.“ANewRobust
Optimization Approach for Integrated Multi-echelon, Multi-
product, Multi-period Supply Chain Network Design Under
Process Uncertainty.” International Journal of Advanced
Manufacturing Technology 79: 229–244.
Alavi, Sepideh, Nader Azad, Mojtaba Heydar, and Hamid
Davoudpour. 2016. “Integrated Production, Inventory, and
Location-Allocation Decisions in Designing Supply Chain
Networks.” International Journal of Information Systems and
Supply Chain Management 9 (4): 22–42.
Alenezi, Abdulrahman R., and Mohammed A. Darwish. 2014.
“Integrated Location Model with Risk Pooling and Trans-
portation Mode Selection.” International Journal Industrial
and System Engineering 16 (2): 200–222.
Alshamsi,Ahmed,andAliDiabat.2018. “Large-scale Reverse
Supply Chain Network Design: An Accelerated Benders
Decomposition Algorithm.” Computers and Industrial Engi-
neering 124 (2017): 545–559.
Amiri-Aref, Mehdi, Walid Klibi, and M. Zied Babai. 2018.“The
Multi-sourcing Location Inventory Problem with Stochastic
Demand.” European Journal of Operational Research 266 (1):
72–87.
Angazi, Hojat. 2016. “An Integrated Location Inventory Rout-
ing Model in Supply Chain Network Designing Under
Uncertainty.” Decision Science Letters 5: 551–568.
Arabzad, S. Mohammad, Mazaher Ghorbani, and Reza
Tav ak ko li - Mo g h ad da m . 2014. “An Evolutionary Algorithm
for a New Multi-objective Location-inventory Model in
a Distribution Network with Transportation Modes and
Third-party Logistics Providers.” International Journal of
Production Research 53 (4): 1038–1050.
Aryanezhad, Mir-bahador, Seyed Gholamreza Jalali, and
Armin Jabbarzadeh. 2010.“AnIntegratedSupplyChain
Design Model with Random Disruptions Consideration.”
African Journal of Business Management 4 (12): 2393–2401.
Azizi, Vahid, and Guiping Hu. 2020. “Multi-product Pickup
and Delivery Supply Chain Design with Location-routing
and Direct Shipment.” International Journal of Production
Economics 226 (2019): 107648.
Azizi, Vahid, Guiping Hu, and Mahsa Mokari. 2020.“A
Two-stage Stochastic Programming Model for Multi-period
Reverse Logistics Network Design with Lot-sizing.” Com-
puters and Industrial Engineering 143 (2019): 106397.
Badri, Hossein, Mahdi Bashiri, and Taha Hossein. 2013.“Inte-
grated Strategic and Tactical Planning in a Supply Chain Net-
work Design with a Heuristic Solution Method.” Computers
and Operations Research 40 (4): 1143–1154.
Ballou, Ronald H., and James M. Masters. 1993.“Commer-
cial Software for Locating Warehouses and Other Facilities.”
Journal of Business Logistics 14 (2): 71–108.
Barbosa-Póvoa, Ana Paula, Cátia da Silva, and Ana Carvalho.
2018. “Opportunities and Challenges in Sustainable Sup-
ply Chain: An Operations Research Perspective.” European
Journal of Operational Research 268: 399–431.
Bashiri, Mahdi, Hossein Badri, and Jafar Talebi. 2012.“ANew
Approach to Tactical and Strategic Planning in Production –
Distribution Networks.” Applied Mathematical Modelling 36
(4): 1703–1717.
Benders, J. F. 1962.“PartitioningProceduresforSolvingMixed-
variables Programming Problems.” Numerische Mathematik
4: 238–252.
Bertrand, J. Will M., and Jan C. Fransoo. 2002. “Operations
Management Research Methodologies Using Quantitative
Modeling.” International Journal of Operations and Produc-
tion Management 22 (2): 241–264.
Bertsimas, Dimitris, and Melvyn Sim. 2004.“ThePriceof
Robustness.” Operations Research 52 (1): 35–53.
Biuki,Mehdi,AbolfazlKazemi,andAlirezaAlinezhad.2020.
“An Integrated Location-routing-inventory Model for Sus-
tainable Design of a Perishable Products Supply Chain Net-
work.” Journal of Cleaner Production 260: 120842.
Brahimi, Nadjib, and Sharfuddin A Khan. 2014.“Warehouse
Location with Production, Inventory, and Distribution
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 23
Decisions: a Case Study in the Lube Oil.” Journal of the
Operational Research Society 12 (2): 175–197.
Brunaud, Braulio, and Ignacio E. Grossmann. 2017.“Perspec-
tivesinMultilevelDecision-makingintheProcessIndustry.”
Frontiers of Engineering Management 4 (3): 256–270.
Cabrera, Guillermo, Stefanie Niklander, Enrique Cabrera, and
Franklin Johnson. 2016. “Solving a Distribution Network
Design Problem by Means of Evolutionary Algorithms.”
Studies in Informatics and Control 25 (1): 21–28.
Calvete, Herminia I., Carmen Galé, and José A. Iranzo. 2014.
“Planning of a Decentralized Distribution Network Using.”
Omega 49: 30–41.
Candas, Mehmet Ferhat, and Erhan Kutanoglu. 2007.“Benets
of Considering Inventory in Service Parts Logistics Network
Design Problems with Time-based Service Constraints.” IIE
Transacti ons 39 (2): 159–176.
Candas, Mehmet Ferhat, and Erhan Kutanoglu. 2020.“Inte-
grated Location and Inventory Planning in Service Parts
Logistics with Customer-based Service Levels.” European
Journal of Operational Research 285 (1): 279–295.
Cardoso, Sónia R., Ana Paula F. D. Barbosa-Póvoa, and Susana
Relvas. 2013. “Design and Planning of Supply Chains with
Integration of Reverse Logistics Activities Under Demand
Uncertainty.” European Journal of Operational Research 226
(3): 436–451.
Cordeau, Jean François, Federico Pasin, and Marius M.
Solomon. 2006. “An Integrated Model for Logistics Network
Design.” Annals of Operations Research 144 (1): 59–82.
Dai, Zhuo, Faisal Aqlan, Xiaoting Zheng, and Kuo Gao. 2018.
“A Location-inventory Supply Chain Network Model Using
Two Heuristic Algorithms for Perishable Products with
Fuzzy Constraints.” Computers and Industrial Engineering
119: 338–352.
Darvish, Maryam, Claudia Archetti, Leandro C. Coelho, and
M. Grazia Speranza. 2019. “Flexible Two-echelon Location
Routing Problem.” European Journal of Operational Research
277 (3): 1124–1136.
Darvish, Maryam, and Leandro C. Coelho. 2018.“Sequen-
tial Versus Integrated Optimization: Production, Location,
Inventory Control, and Distribution.” European Journal of
Operational Research 268 (1): 203–214.
Das, K., and S. Sengupta. 2009. “A Hierarchical Process Indus-
try Production-distribution Planning Model.” International
Journal of Production Economics 117 (2): 402–419.
Denyer,David,andDavidTraneld.2009. “Producing a Sys-
tematic Literature Review.” In TheSageHandbookofOrga-
nizational Research Methods,editedbyBuchananDavidand
Bryman Alan, 671–689. London: Sage Publications Ltd.
Diabat, Ali. 2016. “A Capacitated Facility Location and Inven-
tory Management Problem with Single Sourcing.” Optimiza-
tion Letters 10 (7): 1577–1592.
Diabat, Ali, Olga Battaïa, and Dima Nazzal. 2015.“An
Improved Lagrangian Relaxation-based Heuristic for a Joint
Location-inventory Problem.” Computers and Operations
Research 61: 170–178.
Diabat, Ali, and Rany Deskoores. 2016. “A Hybrid Genetic
AlgorithmBasedHeuristicforAnIntegratedSupplyChain
Problem.” Journal of Manufacturing Systems 38: 172–180.
Diabat,Ali,andJean-philippeRichard.2015.“AnIntegrated
Supply Chain Problem: a Nested Lagrangian Relaxation
Approach.” Annals of Operations Research 229: 303–323.
Diabat, Ali, Jean-philippe Richard, and Craig W Codrington.
2013.“ALagrangianRelaxationApproachtoSimultaneous
Strategic and Tactical Planning in Supply Chain Design.”
Annals of Operations Research 203: 55–80.
Drexl, Michael, and Michael Schneider. 2015.“ASurveyof
Variants and Extensions of the Location-routing Problem.”
European Journal of Operational Research 241 (2): 283–
308.
Engebrethsen, Erna, and Stéphane Dauzère-Pérès. 2018.
“Transportation Mode Selection in Inventory Models: A Lit-
erature Review.” European Journal of Operational Research
279 (1): 1–29.
Etebari, Farhad. 2019. “A Simultaneous Facility Location, Vehi-
cle Routing and Dynamic Pricing in a Distribution Net-
work.” Applied Soft Computing Journal 83: 105647.
Farahani, Reza Zanjirani, Hannaneh Rashidi Bajgan, Behnam
Fahimnia, and Mohamadreza Kaviani. 2014.“Location-
inventory Problem in Supply Chains: a Modelling Review.”
International Journal of Production Research 53 (12): 3769–
3788.
Farahani,RezaZanjirani,SamiraFallah,RubénRuiz,SaraHos-
seini,andNasrinAsgari.2018.“ORModelsinUrbanSer-
vice Facility Location: A Critical Review of Applications
and Future Developments.” European Journal of Operational
Research 276 (1): 1–27.
Fattahi, Mohammad, and Kannan Govindan. 2017.“Integrated
Forward/reverse Logistics Network Design Under Uncer-
tainty with Pricing for Collection of Used Products.” Annals
of Operations Research 253 (1): 193–225.
Fattahi, M., M. Mahootchi, and S. M. Moattar Husseini.
2016. “Integrated Strategic and Tactical Supply Chain Plan-
ning with Price-sensitive Demands.” Annals of Operations
Research 242 (2): 423–456.
Firoozi,Z.,N.Ismail,S.Ariafar,S.H.Tang,M.K.M.A.Arif-
n, and A Memariani. 2014.“EectsofIntegrationonthe
Cost Reduction in Distribution Network Design for Perish-
able Products.” Mathematical Problems in Engineering 2014:
1–10.
Fleischmann, Bernhard, and Herbert Meyr. 1997. “The General
Lotsizing and Scheduling Problem.” OR Spektrum 19: 11–21.
Fleischmann, Bernhard, Herbert Meyr, and Michael Wagner.
2002. “Advanced Planning.” In Supply Chain Management
and Advanced Planning, 71–96. Berlin, Heidelberg: Springer
Berlin Heidelberg. http://link.springer.com/10.1007/978-3-
662-10142-1_5
Forouzanfar, F., R. Tavakkoli-Moghaddam, M. Bashiri, A.
Baboli, and S. M. Hadji Molana. 2018.“NewMathemati-
cal Modeling for a Location-routing-inventory Problem in
aMulti-periodClosed-loopSupplyChaininaCarIndus-
try.” Journal of Industrial Engineering International 14 (3):
537–553.
Gebennini, Elisa, Rita Gamberini, and Riccardo Manzini.
2009. “An Integrated Production-distribution Model for
the Dynamic Location and Allocation Problem with Safety
Stock Optimization.” International Journal of Production
Economics 122 (1): 286–304.
Ghaderi, Abdolsalam, and Robert L. Burdett. 2019.“AnInte-
grated Location and Routing Approach for Transporting
Hazardous Materials in a Bi-modal Transportation Net-
work.” Transportation Research Part E: Logistics and Trans-
portation Review 127: 49–65.
Ghezavati,V.R.,M.S.Jabal-Ameli,andA.Makui.2009.“A
New Heuristic Method for Distribution Networks Consider-
ing Service Level Constraint and Coverage Radius.” Expert
Systems with Applications 36 (3 Part 1): 5620–5629.
24 A. M. JALAL ET AL.
Gholamian, M. R., and M. Heydari. 2017.“AnInventoryModel
with METRIC Approach in Location-routing-inventory
Problem.” Advances in Production Engineering and Manage-
ment 12 (2): 115–126.
Ghomi-Avili, Morteza, Seyed Gholamreza Jalali Naeini, Reza
Tavakkoli-Moghaddam, and Armin Jabbarzadeh. 2018.“A
Fuzzy Pricing Model for a Green Competitive Closed-loop
Supply Chain Network Design in the Presence of Disrup-
tions.” Journal of Cleaner Production 188: 425–442.
Ghomi-Avili, Morteza, Reza Tavakkoli-Moghaddam, Seyed
Gholamreza Jalali Naeini, and Armin Jabbarzadeh. 2021.
“Competitive Green Supply Chain Network Design Model
Considering Inventory Decisions Under Uncertainty: A Real
Case of a Filter Company.” International Journal of Pro-
duction Research 59 (14): 4248–4267. doi:10.1080/00207543.
2020.1760391.
Ghorbani, Atiye, and Mohammad Reza Akbari Jokar. 2016.
“A Hybrid Imperialist Competitive-simulated Annealing
Algorithm for a Multisource Multi-product Location-
routing-inventory Problem.” Computers and Industrial Engi-
neering 101: 116–127.
Govindan, K., A. Jafarian, R. Khodaverdi, and K. Devika. 2014.
“Two-echelon Multiple-vehicle Location – Routing Problem
with Time Windows for Optimization of Sustainable Sup-
plyChainNetworkofPerishableFood.”Intern. Journal of
Production Economics 152: 9–28.
Govindan, Kannan, Ahmad Jafarian, and Vahid Nourbakhsh.
2015. “Bi-objective Integrating Sustainable Order Alloca-
tion and Sustainable Supply Chain Network Strategic Design
with Stochastic Demand Using a Novel Robust Hybrid
Multi-objective Metaheuristic.” Computers and Operations
Research 62: 112–130.
Govindan, Kannan, Ahmad Jafarian, and Vahid Nourbakhsh.
2019. “Designing a Sustainable Supply Chain Network Inte-
grated with Vehicle Routing: A Comparison of Hybrid
Swarm Intelligence Metaheuristics.” Computers and Opera-
tions Research 110: 220–235.
Govindan, Kannan, P. C. Jha, and Kiran Garg. 2016.“Prod-
uct Recovery Optimization in Closed-loop Supply Chain
to Improve Sustainability in Manufacturing.” International
Journal of Production Research 54 (5): 1463–1486.
Govindan, Kannan, Hassan Mina, Ali Esmaeili, and Seyed
Mohammad Gholami-Zanjani. 2020.“AnIntegratedHybrid
ApproachforCircularSupplierSelectionandClosedLoop
Supply Chain Network Design Under Uncertainty.” Journal
of Cleaner Production 242: 118317.
Govindan, Kannan, Hamed Soleimani, and Devika Kannan.
2015. “Reverse Logistics and Closed-loop Supply Chain: A
Comprehensive Review to Explore the Future.” European
Journal of Operational Research 240 (3): 603–626.
Guerrero,W.J.,C.Prodhon,N.Velasco,andC.A.Amaya.2015.
“A Relax-and-price Heuristic for the Inventory-Location-
Routing Problem.” International Transactions in Operational
Research 22 (1): 129–148.
Guo, Hao, Congdong Li, Ying Zhang, Chunnan Zhang, and Yu
Wang. 2018. “A Nonlinear Integer Programming Model for
Integrated Location, Inventory, and Routing Decisions in a
Closed-Loop Supply Chain.” Complexity 2018: 2726070.
Guo, Hao, Ying Zhang, Chunnan Zhang, Yidong Zhang, and
Zixin Han. 2020. “A Multi-commodity Location-inventory
Problem in a Closed-loop Supply Chain with Commer-
cial Product Returns.” International Journal of Production
Research 58 (22): 6899–6916. doi:10.1080/00207543.2019.
1686186.
Hammami, Ramzi, Yannick Frein, and Bouchaib Bahli. 2017.
“Supply Chain Design to Guarantee Quoted Lead Time
and Inventory Replenishment: Model and Insights.” Interna-
tional Journal of Production Research 55 (12): 3431–3450.
Hiassat, Abdelhalim, Ali Diabat, and Iyad Rahwan. 2017.
“A Genetic Algorithm Approach for Location-inventory-
routing Problem with Perishable Products.” Journal of Man-
ufacturing Systems 42: 93–103.
Jeet, Vishv, and Erhan Kutanoglu. 2018.“PartCommonality
Eects on Integrated NetworkDesign and Inventory Models
for Low-demand Service Parts Logistics Systems.” Interna-
tional Journal of Production Economics 206: 46–58.
Jesson, Jill, Lydia Matheson, and Fiona M. Lacey. 2011.Doing
Your Literature Review: Traditional and Sistematic Tech-
niques. London: SAGE Publications.
Kabadurmus, Ozgur, and Mehmet S. Erdogan. 2020.“Sustain-
able, Multimodal and Reliable Supply Chain Design.” Annals
of Operations Research 292: 47–70.
Karakostas, Panagiotis, Angelo Sifaleras, and Michael C. Geor-
giadis. 2019. “A General Variable Neighborhood Search-
based Solution Approach for the Location-inventory-
routing Problem with Distribution Outsourcing.” Comput-
ers and Chemical Engineering 126 (1): 263–279.
Kaya, Onur, and Busra Urek. 2016.“AMixedIntegerNonlinear
Programming Model and Heuristic Solutions for Location,
Inventory and Pricing Decisions in a Closed Loop Supply
Chain.” Computers and Operations Research 65: 93–103.
Keskin, Burcu B., and Halit Üster. 2012.“Production/
Distribut ion System Design with Inventory Considerations.”
Naval Research Logistics.59: 172–1950.
Khatami, Maryam, Masoud Mahootchi, and Reza Zanjirani
Farahani. 2015. “Benders’ Decomposition for Concurrent
Redesign of Forward and Closed-loop Supply Chain Net-
work with Demand and Return Uncertainties.” Transporta-
tion Research Part E: Logistics and Transportation Review 79:
1–21.
Kim, Ji Su, and Dong Ho Lee. 2015.“AnIntegratedApproach
for Collection Network Design, Capacity Planning and Vehi-
cleRoutinginReverseLogistics.”Journal of the Operational
Research Society 66 (1): 76–85.
Lagos, Carolina, Fernando Paredes, Stefanie Niklander, and
Enrique Cabrera. 2015. “Solving a Distribution Network
DesignProblembyCombiningAntColonySystemsand
Lagrangian Relaxation 1.” Studies in Informatics and Control
24 (3): 251–260.
Li, Yanhui, Hao Guo, Lin Wang, and Jing Fu. 2013.“AHybrid
Genetic-simulated Annealing Algorithm for the Location-
inventory- Routing Problem Considering Returns Under
E-supply Chain Environment.” The Scientic World Journal
2013: 125893.
Liao, Shu-hsien, Chia-lin Hsieh, and Peng-jen Lai. 2011.“An
Evolutionary Approach for Multi-objective Optimization of
the Integrated Location – Inventory Distribution Network
Problem in Vendor-managed Inventory.” Expert Systems
With Applications 38 (6): 6768–6776.
Liao, Shu Hsien, Chia Lin Hsieh, and Yu Siang Lin. 2011.
“A Multi-objective Evolutionary Optimization Approach
for An Integrated Location-inventory Distribution Net-
work Problem Under Vendor-managed Inventory Systems.”
Annals of Operations Research 186: 213–229.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 25
Lin, Lin, Mitsuo Gen, and Xiaoguang Wang. 2009.“Inte-
grated Multistage Logistics Network Design by UsingHybrid
Evolutionary Algorithm.” Computers and Industrial Engi-
neering 56 (3): 854–873.
Liu, Yunhua, Ehsan Dehghani, Mohammad Saeed Jabal-
ameli, Ali Diabat, and Chung Cheng Lu. 2020.“ACoor-
dinated Location-inventory Problem with Supply Disrup-
tions: A Two-phase Queuing Theory–optimization Model
Approach.” Computers and Industrial Engineering 142:
106326.
Manzini, Riccardo. 2012.“ATop-downApproachandaDeci-
sion Support System for the Design and Management of
Logistic Networks.” Transportation Research Part E 48:
1185–1204.
Manzini, Riccardo, Riccardo Accorsi, and Marco Bortolini.
2014. “Operational Planning Models for Distribution Net-
works.” International Journal of Production Research 52 (1):
89–116.
Manzini, Riccardo, Mauro Gamberi, Elisa Gebennini, and
Alberto Regattieri. 2008. “An Integrated Approach to the
Design and Management of a Supply Chain System.” Inter-
national Journal of Advanced Manufacturing Technology 37:
625–640.
Manzini, Riccardo, and Elisa Gebennini. 2008. “Optimization
ModelsfortheDynamicFacilityLocationandAllocation
Problem.” International Journal of Production Research 46
(8): 2061–2086.
Martins, Sara, Pedro Amorim, Gonçalo Figueira, and Bernardo
Almada-lobo. 2017. “An Optimization-simulation Approach
totheNetworkRedesignProblemofPharmaceutical
Wholesalers.” Computers and Industrial Engineering 106:
315–328.
Melo, M. Teresa, Stefan Nickel, and Francisco Saldanha-da
Gama. 2009.“FacilityLocationandSupplyChainManage-
ment – A Review.” European Journal of Operational Research
196 (2): 401–412.
Miranda, Pablo, and Rodrigo Garrido. 2004.“Incorporat-
ing Inventory Control Decisions Into a Strategic Distri-
bution Network Design Model with Stochastic Demand.”
Transportation Research Part E: Logistics and Transportation
Review 40 (3): 183–207.
Miranda, Pablo A., and Rodrigo A. Garrido. 2006.“ASimulta-
neous Inventory Control and Facility Location Model with
Stochastic Capacity Constraints.” Networks and Spatial Eco-
nomics 6 (1): 39–53.
Miranda, Pablo A., Rodrigo A. Garrido, and José A. Ceroni.
2009. “e-Work Based Collaborative Optimization Approach
for Strategic Logistic Network Design Problem.” Computers
and Industrial Engineering 57 (1): 3–13.
Mogale, D. G., Naoufel Cheikhrouhou, and Manoj Kumar
Tiwari. 2020. “Modelling of Sustainable Food Grain Supply
Chain Distribution System: a Bi-objective Approach.” Inter-
national Journal of Production Research 58 (18): 5521–5544.
doi:10.1080/00207543.2019.1669840.
Monteiro, M. M., J. E. Leal, and F. M. P. Raupp. 2010.“AFour-
Type Decision-Variable MINLP Model for a Supply Chain
Network Design.” Mathematical Problems in Engineering
2010: 450612.
Mota, Bruna, Maria Isabel Gomes, Ana Carvalho, and Ana
Paula Barbosa-Povoa. 2018. “Sustainable Supply Chains: An
Integrated Modeling Approach Under Uncertainty.” Omega
(United Kingdom) 77: 32–57.
Motaghedi-Larijani, Arash, Mohammad-Saied Jabalameli, and
Reza Tavakkoli. 2012. “A Network Design Model Consider-
ing Inventory Cost From a Third Party Logistics Perspective
A Network Design Model Considering Inventory Cost From
a Third Party Logistics Perspective.” International Journal
of Management Science and Engineering Management 7(1):
29–35.
Mousavi, S. Meysam, Reza Tavakkoli-Moghaddam, and Fari-
borz Jolai. 2013. “A Possibilistic Programming Approach for
the Location Problem of Multiple Cross-docks and Vehicle
Routing Scheduling Under Uncertainty.” Engineering Opti-
mization 45 (10): 1223–1249.
Mousavi, Seyed Mohsen, Ardeshir Bahreininejad, S. Nur-
maya Musa, and Farazila Yusof. 2017. “A Modied Particle
Swarm Optimization for Solving the Integrated Location and
Inventory Control Problems in a Two-echelon Supply Chain
Network.” Journal of Intelligent Manufacturing 28: 191–206.
Mousavi, S. Meysam, Behnam Vahdani, R Tavakkoli-
moghaddam, and H Hashemi. 2014. “Location of Cross-
docking Centers and Vehicle Routing Scheduling Under
Uncertainty: A Fuzzy Possibilistic – Stochastic Program-
ming Model.” Applied Mathematical Modelling 38 (7–8):
2249–2264.
Naimi Sadigh, Ali, Hamed Fallah, and Nasim Nahavandi. 2013.
“A Multi-objective Supply Chain Model Integrated with
Location of Distribution Centers and Supplier Selection
Decisions.” International Journal of Advanced Manufactur-
ing Technology 69 (1–4): 225–235.
Nakhjirkan, Sara, and Farimah Mokhatab Raei. 2017.“An
Integrated Multi-Echelon Supply Chain Network Design
Considering Stochastic Demand: A Genetic Algorithm
Based Solution.” Promet-Trac and Transportation 29 (4):
391–400.
Nakhjirkan, Sara, Farimah Mokhatab Raei, and Ali Hussein-
zadeh Kashan. 2019. “Developing An Integrated Decision
Making Model in Supply Chain Under Demand Uncertainty
Using Genetic Algorithm and Network Data Envelopment
Analysis.” International Journal of Mathematics in Opera-
tional Research 14 (1): 53–81.
Nasiri,G.Reza,andHamidDavoudpour.2012.“Coordinated
Location, Distribution and Inventory Decisions in Sup-
ply Chain Network Design: A Multi-objective Approach.”
South African Journal of Industrial Engineering 23 (2):
159–175.
Nasiri, G. Reza, Hamid Davoudpour, and Behrooz Karimi.
2010.“TheImpactofIntegratedAnalysisonSupplyChain
Management: A Coordinated Approach for Inventory Con-
trol Policy.” Supply Chain Management 15 (4): 277–289.
Nasiri,G.Reza,NasimGhaari,andHamidDavoudpour.2015.
“Location-inventory and Shipment Decisions in An Inte-
grated Distribution System: An Ecient Heuristic Solution.”
European Journal Industrial Engineering 9 (5): 613–637.
Nekooghadirli, N., R. Tavakkoli-Moghaddam, V. R. Gheza-
vati, and S. Javanmard. 2014.“SolvingaNewBi-objective
Location-routing-inventory Problem in a Distribution Net-
work by Meta-heuristics.” Computers and Industrial Engi-
neering 76 (1): 204–221.
Prodhon, Caroline, and Christian Prins. 2014.“ASurveyof
Recent Research on Location-routing Problems.” European
Journal of Operational Research 238 (1): 1–17.
Puga,MatíasSchuster,andJean-sébastienTancrez.2017.“A
Heuristic Algorithm for Solving Large Location – Inventory
26 A. M. JALAL ET AL.
Problems with Demand Uncertainty.” European Journal of
Operational Research 259: 413–423.
Qazvini, Zahra Ebrahimi, Mohsen Sadegh Amalnick, and Has-
san Mina. 2016. “A Green Multi-depot Location Routing
Model with Split-delivery and Time Window.” International
Journal of Management Concepts and Philosophy 9 (4): 271.
Rabbani,M.,R.Heidari,andR.Yazdanparast.2019.“A
Stochastic Multi-period Industrial Hazardous Waste
Location-routing Problem: Integrating NSGA-II and Monte
Carlo Simulation.” European Journal of Operational Research
272 (3): 945–961.
Rae-Majd, Zahra, Seyed Hamid Reza Pasandideh, and Bah-
man Naderi. 2018. “Modelling and Solving the Integrated
Inventory-location-routing Problem in a Multi-period and
Multi-perishable Product Supply Chain with Uncertainty:
Lagrangian Relaxation Algorithm.” Computers and Chemi-
cal Engineering 109: 9–22.
Rahmaniani, Ragheb, Teodor Gabriel Crainic, Michel Gen-
dreau, and Walter Rei. 2017. “The Benders Decomposition
Algorithm: A Literature Review.” European Journal of Oper-
ational Research 259 (3): 801–817. doi:10.1016/j.ejor.2016.
12.005
Ramezani, Majid, and Ali Mohammad Kimiagari. 2016.
“Simultaneous Optimization of Operational and Financial
DecisionstoClosed-loopSupplyChainNetworkUnder
Uncertainty.” Proceedings of the Institution of Mechanical
Engineers, Part B: Journal of Engineering Manufacture 230
(10): 1910–1924.
Rappold,JamesA.,andBenD.VanRoo.2009.“Designing
Multi-echelon Service Parts Networks with Finite Repair
Capacity.” European Journal of Operational Research 199 (3):
781–792.
Sabri, Ehap H., and Benita M. Beamon. 2000.“AMulti-
objective Approach to Simultaneous Strategic and Opera-
tional Planning in Supply Chain Design.” Omega 28 (5):
581–598.
Sadeghi Rad, Reza, and Nasim Nahavandi. 2018.“ANovel
Multi-objective Optimization Model for Integrated Prob-
lem of Green Closed Loop Supply Chain Network Design
and Quantity Discount.” Journal of Cleaner Production 196:
1549–1565.
Sadjadi, Seyed Jafar, Ahmad Makui, Ehsan Dehghani, and Mag-
soud Pourmohammad. 2016.“ApplyingQueuingApproach
for a Stochastic Location-inventory Problem with Two Dif-
ferent Mean Inventory Considerations.” Applied Mathemat-
ical Modelling 40: 578–596.
Sadjady, Hannan, and Hamid Davoudpour. 2012.“Two-
echelon, Multi-commodity Supply Chain Network Design
with Mode Selection, Lead-times and Inventory Costs.”
Computers and Operations Research 39 (7): 1345–1354.
Salema, Maria Isabel Gomes, Ana Paula Barbosa-Povoa, and
Augusto Q. Novais. 2010. “Simultaneous Design and Plan-
ning of Supply Chains with Reverse Flows: A Generic
Modelling Framework.” European Journal of Operational
Research 203 (2): 336–349.
Salema, Maria Isabel Gomes, Ana Paula Barbosa Póvoa, and
Augusto Q. Novais. 2009. “A Strategic and Tactical Model for
Closed-loop Supply Chains.” OR Spectrum 31 (3): 573–599.
Saragih, Nova Indah, Senator Nur Bahagia, Suprayogi, and Ibnu
Syabri. 2019. “A Heuristic Method for Location-inventory-
routing Problem in a Three-echelon Supply Chain System.”
Computers and Industrial Engineering 127: 875–886.
Savelsbergh, Martin. 2008. “A Branch-and-Price Algorithm for
the Generalized Assignment Problem.” Operations Research
45 (6): 831–841.
Schuster Puga, Matías, Stefan Minner, and Jean-Sébastien Tan-
crez. 2019. “Two-stage Supply Chain Design with Safety
Stock Placement Decisions.” International Journal of Produc-
tion Economics 209: 183–193.
Schwardt, Martin, and Jan Dethlo. 2005. “Solving a Contin-
uous Location-routing Problem by Use of a Self-organizing
Map.” International Journal of Physical Distribution and
Logistics Management 35 (6): 390–408.
Shahabi, Mehrdad, Shirin Akbarinasaji, Avinash Unnikrish-
nan, and Rachel James. 2013. “Integrated Inventory Control
and Facility Location Decisions in a Multi-Echelon Supply
Chain Network with Hubs.” Networks and Spatial Economics
13: 497–514.
Shavandi, Hassan, and Bita Bozorgi. 2012.“Developinga
Location-inventory Model Under Fuzzy Environment.” The
International Journal of Advanced Manufacturing Technology
63 (1–4): 191–200.
Sherafati, Mahtab, and Mahdi Bashiri. 2016.“ClosedLoopSup-
ply Chain Network Design with Fuzzy Tactical Decisions.”
Journal of Industrial Engineering International 12: 255–
269.
Shu, Jia, Qiang Ma, and Sijie Li. 2010.“IntegratedLocation
and Two-echelon Inventory Network Design Under Uncer-
tainty.” Annals of Operations Research 181 (1): 233–247.
Singh, Tejinder Pal, Nicoleta Neagu, Michele Quattrone, and
Philippe Briet. 2015. “Network Design for Cylinder Gas
Distribution.” Journal of Industrial Engineering and Manage-
ment 8 (1): 85–109.
Solak, Senay, Christina Scherrer, and Ahmed Ghoniem. 2014.
“The Stop-and-drop Problem in Nonprot Food Distri-
bution Networks.” Annals of Operations Research 221 (1):
407–426.
Soleimani, Hamed, Yusof Chaharlang, and Hadi Ghaderi. 2018.
“Collection and Distribution of Returned-remanufactured
Products in a Vehicle Routing Problem with Pickup and
Delivery Considering Sustainable and Green Criteria.” Jour-
nal of Cleaner Production 172: 960–970.
Soleimani, Hamed, Mirmehdi Seyyed-Esfahani, and Mohsen
Akbarpour Shirazi. 2016. “A New Multi-criteria Scenario-
based Solution Approach for Stochastic Forward/reverse
Supply Chain Network Design.” Annals of Operations
Research 242 (2): 399–421.
Tancrez, Jean-Sébastien, Jean-Charles Lange, and Pierre Semal.
2012. “A Location-inventory Model for Large Three-level
Supply Chains.” Transportation Research Part E: Logistics
and Transportation Review 48 (2): 485–502.
Tang, Kai, and Chao Yang. 2008.“
ADistributionNetwork
Design Model for Deteriorating Item.” International Journal
of Logistics Systems and Management 4 (3): 366.
Tapia-Ubeda, Francisco J., Pablo A. Miranda, and Marco Mac-
chi. 2018. “Discrete Optimization A Generalized Benders
Decomposition Based Algorithm for An Inventory Location
Problem with Stochastic Inventory Capacity Constraints.”
European Journal of Operational Research 267 (3): 806–817.
Tapia-Ubeda, Francisco J., Pablo A. Miranda, Irene Roda,
MarcoMacchi,andOrlandoDurán.2020.“Modellingand
Solving Spare Parts Supply Chain Network Design Prob-
lems.” International Journal of Production Research 58:
5299–5319.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 27
Tavakkoli-Moghaddam, R., A. Makui, and Z. Mazloomi. 2010.
“A New Integrated Mathematical Model for a Bi-objective
Multi-depot Location-routing Problem Solved by a Multi-
objective Scatter Search Algorithm.” Journal of Manufactur-
ing Systems 29 (2–3): 111–119.
Tiwari, M. K., N. Raghavendra, Shubham Agrawal, and S.
K. Goyal. 2010. “A Hybrid Taguchi – Immune Approach
to Optimize an Integrated Supply Chain Design Problem
with Multiple Shipping.” European Journal of Operational
Research 203 (1): 95–106.
Traneld, D., D. Denyer, and P. Smart. 2003.“Towardsa
Methodology for Developing Evidence-Informed Manage-
ment Knowledge by Means of Systematic Review.” British
Journal of Management 14: 207–222.
Tsao, Yu Chung, Divya Mangotra, Jye Chyi Lu, and Ming
Dong. 2012. “A Continuous Approximation Approach for
the Integrated Facility-inventory Allocation Problem.” Euro-
pean Journal of Operational Research 222 (2): 216–228.
Tsiakis,P.,N.Shah,andC.C.Pantelides.2001.“Design
of Multi-echelon Supply Chain Networks Under Demand
Uncertainty.” Industrial and Engineering Chemistry Research
40 (16): 3585–3604.
Üster, Halit, Burcu B. Keskin, and Sila Çetinkaya. 2008.“Inte-
grated Warehouse Location and Inventory Decisions in a
Three-tier Distribution System.” IIE Transactions 40 (8):
718–732.
van Eck, Nees Jan, and Ludo Waltman. 2010.“SoftwareSur-
vey: VOSviewer, a Computer Program for Bibliometric Map-
ping.” Scientometrics 84 (2): 523–538.
Wang,Lin,HuiQu,TaoChen,andFang-PingYan.2013.
“An Eective Hybrid Self-Adapting Dierential Evolu-
tion Algorithm for the Joint Replenishment and Location-
InventoryProbleminaThree-LevelSupplyChain.”The
Scientic World Journal 2013: 270249.
Wheatley, David, Fatma Gzara, and Elizabeth Jewkes. 2015.
“Logic-based Benders Decomposition for An Inventory-
location Problem with Service Constraints.” Omega (United
Kingdom) 55: 10–23.
You,Fengqi,andIgnacioE.Grossmann.2008.“Mixed-Integer
NonlinearProgrammingModelsandAlgorithmsforLarge-
Scale Supply Chain Design with Stochastic Inventory Man-
agement.” Industrial and Engineering Chemistry Research 47:
7802–7817.
Yu, Vincent F., Nur Mayke Eka Normasari, and Huynh Trung
Luong. 2015. “Integrated Location-Production-Distribution
Planning in a Multiproducts Supply Chain Network Design
Model.” Mathematical Problems in Engineering 2015: 1–13.
Yuchi, Qunli, Zhengwen He, Zhen Yang, and Nengmin Wang.
2016. “A Location-Inventory-Routing Problem in Forward
and Reverse Logistics Network Design.” Discrete Dynamics
in Nature and Society 2016: 3475369.
Zeballos, Luis J., Carlos A. Méndez, and Ana P. Barbosa-Povoa.
2018. “Integrating Decisions of Product and Closed-loop
SupplyChainDesignUnderUncertainReturnFlows.”Com-
puters and Chemical Engineering 112: 211–238.
Zeballos, Luis J., Carlos A. Méndez, Ana P. Barbosa-Povoa,
and Augusto Q. Novais. 2014.“
Multi-periodDesignand
Planning of Closed-loop Supply Chains with Uncertain Sup-
ply and Demand.” Computers and Chemical Engineering 66:
151–164.
Zhalechian, M., R. Tavakkoli-Moghaddam, B. Zahiri, and M.
Mohammadi. 2016.“SustainableDesignofaClosed-loop
Location-routing-inventory Supply Chain Network Under
Mixed Uncertainty.” Transportation Research Part E: Logis-
tics and Transportation Review 89: 182–214.
Zhang, Wei, and Di Xu. 2014. “Integrating the Logistics Net-
work Design with Order Quantity Determination Under
Uncertain Customer Demands.” Expert Systems with Appli-
cations 41 (1): 168–175.
Zheng, Xiaojin, Meixia Yin, and Yanxia Zhang. 2019.“Inte-
grated Optimization of Location, Inventory and Routing
in Supply Chain Network Design.” Transportation Research
Part B: Methodological 121: 1–20.
28 A. M. JALAL ET AL.
Appendix. Sample articles
Table A1. Sample articles.
No. Authors No. Authors
Ahmadi, Torabi, and Tavakkoli-
Moghaddam (2016)
Ahmadi, Torabi, and Tavakkoli-
Moghaddam (2016)
Liao, Hsieh, and Lin (2011) Liao, Hsieh, and Lin (2011)
Ahmadi-Javid and Azad (2010) Ahmadi-Javid and Azad (2010) Liao, Hsieh, and Lai (2011) Liao, Hsieh, and Lai (2011)
Ahmadi-Javid and Hossein
Seddighi (2012)
Ahmadi-Javid and Hossein
Seddighi (2012)
Lin, Gen, and Wang (2009) Lin, Gen, and Wang (2009)
Ahmadi-Javid and
Hoseinpour (2015b)
Ahmadi-Javid and
Hoseinpour (2015b)
Liu et al. (2020)Liuetal.(2020)
Ahmadi-Javid, Amiri, and
Meskar (2018)
Ahmadi-Javid, Amiri, and
Meskar (2018)
Manzini et al. (2008) Manzini et al. (2008)
Ahmadi-Javid and
Hoseinpour (2015a)
Ahmadi-Javid and
Hoseinpour (2015a)
Manzini (2012) Manzini (2012)
Akbari and Karimi (2015) Akbari and Karimi (2015) Manzini, Accorsi, and
Bortolini (2014)
Manzini, Accorsi, and
Bortolini (2014)
Alavi et al. (2016) Alavi et al. (2016) Manzini and Gebennini (2008) Manzini and Gebennini (2008)
Alenezi and Darwish (2014) Alenezi and Darwish (2014) Martins et al. (2017) Martins et al. (2017)
Alshamsi and Diabat (2018) Alshamsi and Diabat (2018) Miranda and Garrido (2004) Miranda and Garrido (2004)
Amiri-Aref, Klibi, and Babai (2018) Amiri-Aref, Klibi, and Babai (2018) Miranda, Garrido, and Ceroni (2009) Miranda, Garrido, and Ceroni (2009)
Angazi (2016) Angazi (2016) Miranda and Garrido (2006) Miranda and Garrido (2006)
Arabzad, Ghorbani, and Tavakkoli-
Moghaddam (2014)
Arabzad, Ghorbani, and Tavakkoli-
Moghaddam (2014)
Mogale, Cheikhrouhou, and
Tiwari (2020)
Mogale, Cheikhrouhou, and
Tiwari (2020)
Aryanezhad, Jalali, and
Jabbarzadeh (2010)
Aryanezhad, Jalali, and
Jabbarzadeh (2010)
Monteiro, Leal, and Raupp (2010) Monteiro, Leal, and Raupp (2010)
Azizi and Hu (2020) Azizi and Hu (2020)Motaetal.(2018)Motaetal.(2018)
Azizi, Hu, and Mokari (2020) Azizi, Hu, and Mokari (2020) Motaghedi-Larijani, Jabalameli,
and Tavakkoli (2012)
Motaghedi-Larijani, Jabalameli,
and Tavakkoli (2012)
Badri, Bashiri, and Hossein (2013) Badri, Bashiri, and Hossein (2013) Mousavi, Tavakkoli-Moghaddam,
and Jolai (2013)
Mousavi, Tavakkoli-Moghaddam,
and Jolai (2013)
Bashiri, Badri, and Talebi (2012) Bashiri, Badri, and Talebi (2012) Mousavi et al. (2014) Mousavi et al. (2014)
Biuki, Kazemi, and Alinezhad (2020)Biuki, Kazemi, and Alinezhad (2020) Mousavi et al. (2017) Mousavi et al. (2017)
Brahimi and Khan (2014) Brahimi and Khan (2014) Naimi Sadigh, Fallah, and
Nahavandi (2013)
Naimi Sadigh, Fallah, and
Nahavandi (2013)
Cabrera et al. (2016) Cabrera et al. (2016) Nakhjirkan and Rafiei (2017) Nakhjirkan and Rafiei (2017)
Calvete, Galé, and Iranzo (2014) Calvete, Galé, and Iranzo (2014) Nakhjirkan, Rafiei, and
Kashan (2019)
Nakhjirkan, Rafiei, and
Kashan (2019)
Candas and Kutanoglu (2007) Candas and Kutanoglu (2007) Nasiri, Davoudpour, and
Karimi (2010)
Nasiri, Davoudpour, and
Karimi (2010)
Candas and Kutanoglu (2020) Candas and Kutanoglu (2020) Nasiri, Ghaffari, and
Davoudpour (2015)
Nasiri, Ghaffari, and
Davoudpour (2015)
Cardoso, Barbosa-Póvoa, and
Relvas (2013)
Cardoso, Barbosa-Póvoa, and
Relvas (2013)
Nekooghadirli et al. (2014) Nekooghadirli et al. (2014)
Dai et al. (2018) Dai et al. (2018) Puga and Tancrez (2017) Puga and Tancrez (2017)
Darvish and Coelho (2018) Darvish and Coelho (2018) Schuster Puga, Minner and
Tancrez (2019)
Schuster Puga, Minner and
Tancrez (2019)
Darvish et al. (2019)Darvish et al. (2019) Qazvini, Amalnick, and M ina (2016) Qazvini, Amalnick, and Mina (2016)
Das and Sengupta (2009) Das and Sengupta (2009) Rabbani, Heidari, and
Yazdanparast (2019)
Rabbani, Heidari, and
Yazdanparast (2019)
Wheatley, Gzara, and Jewkes (2015) Wheatley, Gzara, and Jewkes (2015) Sadeghi Rad and Nahavandi (2018) Sadeghi Rad and Nahavandi (2018)
Diabat, Richard, and
Codrington (2013)
Diabat, Richard, and
Codrington (2013)
Rafie-Majd, Pasandideh, and
Naderi (2018)
Rafie-Majd, Pasandideh, and
Naderi (2018)
Diabat and Richard (2015) Diabat and Richard (2015) Rappold and Van Roo (2009) Rappold and Van Roo (2009)
Diabat (2016)Diabat(2016) Sabri and Beamon (2000) Sabri and Beamon (2000)
Diabat, Battaïa, and Nazzal (2015) Diabat, Battaïa, and Nazzal (2015) Sadjadi et al. (2016) Sadjadi et al. (2016)
Diabat and Deskoores (2016) Diabat and Deskoores (2016) Sadjady and Davoudpour (2012) Sadjady and Davoudpour (2012)
Etebari (2019) Etebari (2019) Salema, Póvoa, and Novais (2009) Salema, Póvoa, and Novais (2009)
Fattahi, Mahootchi, and
Husseini (2016)
Fattahi, Mahootchi, and
Husseini (2016)
Salema, Barbosa-Povoa, and
Novais (2010)
Salema, Barbosa-Povoa, and
Novais (2010)
Fattahi and Govindan (2017) Fattahi and Govindan (2017) Saragih et al. (2019) Saragih et al. (2019)
Firoozi et al. (2014) Firoozi et al. (2014) Schwardt and Dethloff (2005) Schwardt and Dethloff (2005)
Forouzanfar et al. (2018) Forouzanfar et al. (2018) Shahabi et al. (2013) Shahabi et al. (2013)
Gebennini, Gamberini, and
Manzini (2009)
Gebennini, Gamberini, and
Manzini (2009)
Shavandi and Bozorgi (2012) Shavandi and Bozorgi (2012)
Ghaderi and Burdett (2019) Ghaderi and Burdett (2019) Sherafati and Bashiri (2016) Sherafati and Bashiri (2016)
Ghezavati, Jabal-Ameli, and
Makui (2009)
Ghezavati, Jabal-Ameli, and
Makui (2009)
Shu, Ma, and Li (2010) Shu, Ma, and Li (2010)
Gholamian and Heydari (2017) Gholamian and Heydari (2017) Singh et al. (2015) Singh et al. (2015)
Ghomi-Avili et al. (2018) Ghomi-Avili et al. (2018) Solak, Scherrer, and
Ghoniem (2014)
Solak, Scherrer, and
Ghoniem (2014)
(continued).
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 29
Table A1. Continued
No. Authors No. Authors
Ghomi-Avili et al. (2021) Ghomi-Avili et al. (2021) Soleimani, Seyyed-Esfahani, and
Shirazi (2016)
Soleimani, Seyyed-Esfahani, and
Shirazi (2016)
Ghorbani and Akbari Jokar (2016) Ghorbani and Akbari Jokar (2016) Soleimani, Chaharlang, and
Ghaderi (2018)
Soleimani, Chaharlang, and
Ghaderi (2018)
Govindan et al. (2014)Govindanetal.(2014) Tancrez, Lange, and Semal (2012) Tancrez, Lange, and Semal (2012)
Govindan, Jafarian, and
Nourbakhsh (2015)
Govindan, Jafarian, and
Nourbakhsh (2015)
Tang and Yang (2008) Tang and Yang (2008)
Govindan, Jha, and Garg (2016) Govindan, Jha, and Garg (2016) Tapia-Ubeda, Miranda, and
Macchi (2018)
Tapia-Ubeda, Miranda, and
Macchi (2018)
Govindan, Jafarian, and
Nourbakhsh (2019)
Govindan, Jafarian, and
Nourbakhsh (2019)
Tapia-Ubeda et al. (2020) Tapia-Ubeda et al. (2020)
Govindan et al. (2020)Govindanetal.(2020) Tavakkoli-Moghaddam, Makui, and
Mazloomi (2010)
Tavakkoli-Moghaddam, Makui, and
Mazloomi (2010)
Guerrero et al. (2015) Guerrero et al. (2015) Tiwari et al. (2010) Tiwari et al. (2010)
Guo et al. (2018) Guo et al. (2018)Tsaoetal.(2012)Tsaoetal.(2012)
Guo et al. (2020)Guo et al. (2020) Tsiakis, Shah, and Pantelides (2001) Tsiakis, Shah, and Pantelides (2001)
Hammami, Frein, and Bahli (2017) Hammami, Frein, and Bahli (2017) Halit, Keskin and Çetinkaya (2008) Halit, Keskin and Çetinkaya (2008)
Hiassat, Diabat, and Rahwan (2017) Hiassat, Diabat, and Rahwan (2017) Wang et al. (2013) Wang et al. (2013)
Jeet and Kutanoglu (2018) Jeet and Kutanoglu (2018) You and Grossmann (2008) You and Grossmann (2008)
Kabadurmus and Erdogan (2020) Kabadurmus and Erdogan (2020) Yu, Normasari, and Luong (2015) Yu, Normasari, and Luong (2015)
Karakostas, Sifaleras, and
Georgiadis (2019)
Karakostas, Sifaleras, and
Georgiadis (2019)
Yuchi et al. (2016) Yuchi et al. (2016)
Kaya and Urek (2016) Kaya and Urek (2016) Zeballos et al. (2014) Zeballos et al. (2014)
Keskin and Üster (2012) Kesk in and Üster (2012) Zeballos, Méndez, and Barbosa-
Povoa (2018)
Zeballos, Méndez, and Barbosa-
Povoa (2018)
Khatami, Mahootchi, and
Farahani (2015)
Khatami, Mahootchi, and
Farahani (2015)
Zhalechian et al. (2016) Zhalechian et al. (2016)
Kim and Lee (2015) Kim and Lee (2015) Zhang and Xu (2014) Zhang and Xu (2014)
Lagos et al. (2015)Lagos et al. (2015) Zheng, Yin, and Zhang (2019) Zheng, Yin, and Zhang (2019)
Li et al. (2013)Lietal.(2013)
