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RESEARCH ARTICLE
Resilience and sustainable supply chain network design by
considering renewable energy
Reza Lotfi
1,2
| Bahareh Kargar
3
| Seyed Hosein Hoseini
4
| Sima Nazari
5
|
Soroush Safavi
6
| Gerhard-Wilhelm Weber
7,8
1
Department of Industrial Engineering,
Yazd University, Yazd, Iran
2
Department of Industrial Engineering,
Behineh Gostar Sanaye Arman,
Tehran, Iran
3
School of Industrial Engineering, Iran
University of Science and Technology,
Tehran, Iran
4
Department of Project and Construction,
Tehran, Iran
5
Department of Business Management,
Zanjan Branch, Islamic Azad University,
Zanjan, Iran
6
Department of Industrial Engineering,
Dalhousie University, Halifax, Nova
Scotia, Canada
7
Faculty of Engineering Management,
Poznan University of Technology, Poznan,
Poland
8
Institute of Applied Mathematics (UME),
METU, Ankara, Turkey
Correspondence
Reza Lotfi, Department of Industrial
Engineering, Yazd University, Yazd, Iran.
Email: reza.lotfi.ieng@gmail.com;
rezalotfi@stu.yazd.ac.ir
Summary
Nowadays, using renewable energy (RE) is faster growing by each country.
The managerial and designer of supply chain network design (SCND) have to
plan to apply RE in pillars of supply chain (SC). This research indicates resil-
ience and sustainable SCND by considering RE (RSSCNDRE) for the first time.
A two-stage new robust stochastic optimization is embedded for RSSCNDRE.
The first stage locates facility location and RE and the second stage defines
flow quantity between SC components. We solve the model by GAMS-CPLEX
solver to locate components of SC and RE. Effects of changing conservative
coefficient and demand are investigated and by increasing 20% for conservative
coefficient, the cost function increase by 0.5%. Also, when demand is high,
activating RE is economically feasible and we cannot buy and supply energy
by the government power network and have to supply energy by RE. After
activating RE, by increasing 20% for demand, the cost function increases by
6%. We contribute fix-and-optimize strategy to define the upper bound for a
large-scale problem. The proposed upper bound for the main model is less
than 10% and appropriate for estimating the cost of large-scale problems. This
research suggested to equip SC by RE that SC becomes resilient against
demand fluctuation and sustainable energy resource compatible with sustain-
able development goal (SGD7).
KEYWORDS
renewable energy, resilience, robust optimization, supply chain network design,
sustainability
1|INTRODUCTION
One of the vital requirements for a supply chain (SC) is
energy supply. Energy supply on time makes SC resilient
against disruption. One of the best methods for energy
supply is receiving energy by renewable energy (RE) in
SC.
1
RE is clean energy and makes SC sustainable, and
has no pollution to the environment.
2
Therefore, RE
makes SC resilient and sustainable, which plays a vital
role in SC's flexibility to disrupt demand. Nowadays, we
are in coronavirus disease 2019 (COVID-19) condition
and face demand fluctuation. We have problems in sup-
plying goods, services in global and local SC, chaos, and
resonance effects all over SC.
3
When RE can increase the
resiliency of SC by decreasing costs and removing to buy
energy from the government, managers of SC change
his/her procedure of energy supply and move to
RE. Using RE grows up in all countries (in Figure 1) so
Received: 3 April 2021 Revised: 8 May 2021 Accepted: 12 May 2021
DOI: 10.1002/er.6943
Int J Energy Res. 2021;1–18. wileyonlinelibrary.com/journal/er © 2021 John Wiley & Sons Ltd. 1
that governments should plan and help SC that wants to
apply it. Iran government gives subsidies to organizations
that want to use RE in the production cycle. In the
United States, growing RE is very fast, and we are wit-
nessing 100% growth from 2000 to 2018 and 17% of
United States energies is providing by RE. Hydropower
and wind power are the main RE of the United States
and we predict that solar energy is increased from 11% in
2017 to 48% in 2025.
5
Hence, governments should focus
on RE, and managers of SC need to pay more attention
to supply energy by RE. The government encouragement
can able SC to go fast to the RE. Therefore, we need to
design and configure a resilience and sustainable SC with
RE supply. A research gap in using SC with RE equip-
ment is required and is not considered in the literature
review. We, as a researcher, should encourage to remove
using fossil energy and present a model that applies clean
energy for SC.
As a result, the innovation of this research and the
main objective of the work is as follows:
1. Designing a resilience and sustainable SC with R
energy supply by RE.
2. Components of SC can select supply energy through
RE or buy energy from governments.
3. To cope with current disruptions like COVID-19 and
natural disasters, the resiliency and robustness of the
facility have been suggested.
The paper is organized as follows. In Section 2, we
describe models in the field of resilience and sustainable
SC in the literature. In Section 3, the problem description
is stated. In Section 4, the findings of research and sensi-
tivity analysis for numerical examples are presented. In
Section 5, the managerial insights and practical implica-
tions are discussed. In Section 6, the conclusion is
summarized.
2|SURVEY ON RELATED WORK
Since the concept of SC network design (SCND)
defines until now, many researchers presented differ-
enttoolsintheSCNDareaforresiliencyandsustain-
ability. Some researchers used several tools to improve
the performance of SCND and others developed in
solution approach. Also, applying a management sys-
tem (MS) as a part of an integrated MS can help to
improve and corporate sustainability for SCND
(Muhammad
6
;M
7
).
Recent research that focused on energy problem,
resiliency, and sustainability are as follows:
Neto, Walther, Bloemhof, Van Nunen, and Spengler
8
presented a reverse SC that computes cost and environ-
mental impact. Environmental impact includes minimiz-
ing CO
2
emission and cumulative energy demand (CED).
Their model used energy and did not generate it by them-
selves. The case study of this research was waste electri-
cal and electronic.
One of the authors that suggested integration sustain-
ability and resiliency were Fahimnia and Jabbarzadeh.
9
They emphasized that resiliency by the flexible capacity
of facilities and regarding sustainability by environmental
and social objectives. The flexible capacity of facilities
FIGURE 1 Renewable capacity additions by country/region 2019–2021
4
[Colour figure can be viewed at wileyonlinelibrary.com]
2LOTFI ET AL.
can help the model to encounter disruption and adopt
the model.
Zahiri, Zhuang, and Mohammadi
10
investigated an
integrated sustainable-resilient for a pharmaceutical
SCND. A new fuzzy possibilistic-stochastic programming
approach has been presented to deal with uncertainty.
Measures of resilience were node criticality, flow com-
plexity, node complexity, multiple assignments, and cus-
tomer de-service level.
Jabbarzadeh, Fahimnia, and Sabouhi
11
investigated a
resilient and sustainable SCND in a plastic pipes industry
in partial disruption. They embedded a fuzzy c-means
clustering method for assessing the sustainability of sup-
pliers. After that, they develop a stochastic bi-objective
optimization model and using ε-constraint for solving the
model. In their model, they minimized the expected total
cost and maximized the expected sustainability perfor-
mance. They added backup suppliers, extra supply/pro-
duction capacities, and multiple sourcing to the model to
deal with resiliency.
Disruption in the electric power system network for
perishable products is considered by Yavari and Zaker.
12
They investigated a resilient green closed-loop SCND
(CLSCND) for perishable products with disruption in the
electric power system network. Integration between
power system network and SCND were as the suggestion
of authors as resiliency policy. Also, for a green approach,
they used the assessment of carbon emission. They found
that the integration between two-layer reduces cost and
carbon emission. They embedded Lp-metric as a solution
approach.
Pavlov, Ivanov, Pavlov, and Slinko
13
surveyed redun-
dancy and contingency planning in resource manage-
ment of a resilient and sustainable SCND. They
coordinated between sustainable resource utilization and
SC resilience in their model. They expressed that the
designer of the SC network should create a balance
between redundancy of the network and resiliency and
sustainability. If redundancy of network becomes high,
cost of the network and environmental impact grows up
but the resiliency of network against disruption is
increased. They suggested Dantzig and Wolfe for solving
the model.
Souza, Bloemhof-Ruwaard, and Borsato
14
designed a
sustainable SCND by resiliency in environmental impact.
They maximized profit while minimizing ecological
impact. Ecosystem network analysis is applied to assess
resiliency. The ε-constraint was embedded to solve the
model. The case study of this research was the sugar
beet SC.
Kaur and Singh
15
focused on minimizing carbon
emissions and the cap-and-trade method. They proposed
a sustainable-resilience SCND in disaster conditions.
Their model was mixed-integer nonlinear programming
(MINLP) and used flexible capacity against demand fluc-
tuation and increase the resiliency of the model.
Mohammed, Harris, Soroka, and Nujoom
16
presented
a hybrid fuzzy multi-objective and multiple-criteria deci-
sion analysis (MCDM) for a green and resilience SCND.
They applied three objectives: cost, environmental impact
(green approach), and the value of SC resilience. They
handled ε-constraint to produce Pareto frontier for objec-
tives. They applied the MCDM approach (Technique for
Order of Preference by Similarity to Ideal Solution
(TOPSIS) and fuzzy Analytic Hierarchy Process (AHP))
to weight objectives.
Fazli-Khalaf, Naderi, Mohammadi, and Pishvaee
17
designed a resilient and sustainable CLSCND in the tire
industry. They proposed maximum coverage demand as a
resiliency strategy. Also, using CO
2
emission and social
responsibility were the sustainable objectives of the
authors. They found that by increasing cost, the amount
of greenness, social responsibility, and reliability
decrease. They applied flexible fuzzy to handle uncer-
tainty in the model. Finally, they solve the model by Lp-
metrics.
Rajesh
18
surveyed on resiliency SC with three indica-
tors. Node density, node complexity, and node criticality
was suggested as resiliency indicators. Regarding the
nonlinear model, they contribute to teaching learning-
based optimization for solving the model.
Zamanian, Sadeh, Amini Sabegh, and Ehtesham
Rasi
19
suggested a resilience and sustainable SC for the
gas and oil industry. They applied service level and pen-
alty per underutilized capacity for considering resiliency
in their model. Maximizing the total revenue include rev-
enue, cost, and environmental costs, the penalty per
underutilized capacity, and maximizing service level
were objectives of the model. To solve the model, they
applied ε-constraint.
Hosseini-Motlagh, Samani, and Shahbazbegian
20
designed SCND for the electricity industry. They consider
sustainability and resiliency in network design. For con-
ducting sustainability and resiliency in their model, they
added maximizing social impact and minimizing de-
resiliency as an objective function. To cope with uncer-
tainty, a fuzzy robust optimizing was a tool that they
assemble to their model. Applying fuzzy robust optimiz-
ing indicate that costs increase by 50%, but the amount of
sustainability and resiliency increases to 50% and 20%.
Sabouhi, Jabalameli, Jabbarzadeh, and Fahimnia
21
presented a resilient and responsive SCND, and they
applied six resilience strategies that are the contribution
of this research. These strategies include multiple sourc-
ing and transport routes, backup suppliers, adding extra
production capacities, lateral transshipment, and direct
LOTFI ET AL.3
shipment. They utilized stochastic programming and
employed the L-shaped Benders decomposition to solve
the model.
Lotfi et al
22
designed a resilient and sustainable
CLSCND with flexibility in capacities and robustness
against demand disruption. This model used minimizing
CO
2
emission and CED and maximizing employment.
They applied robust stochastic programming to cope with
uncertainty by considering Conditional Value at Risk
(CVaR). They compared the proposed model with
another risk method. The results indicate that the perfor-
mance of the proposed model is better than other
methods.
Hasani, Mokhtari, and Fattahi
23
presented a green
and resilient SCND under disruption. The objectives of
the model are minimizing cost, centralization, and CO
2
emission. They used a mitigation strategy for the resil-
iency of SC. Their resiliency strategy included facility for-
tification, geographical facility dispersion, semi-finished
goods production, and multi-sourcing strategies. To solve
the model, they applied improved Strength Pareto Evolu-
tionary Algorithm 2.
Mehrjerdi and Shafiee
24
investigated the effect of
multiple sourcing and information-sharing as resilience
strategies in a CLSCND. They considered sustainability
in designing the network. They used data from the tire
industry to validate their model and solved the model by
improved augmented ε-constraint (AUGMECON2).
Jouzdani and Govindan
25
designed a sustainable
SCND for perishable dairy food. They drew a multi-
objective model to optimize costs, energy consumption,
and the traffic congestion related to SCND. Also, they
considered revised multi-choice goal programming to
solve the model. Finally, they suggested and a trade-off
between costs, energy consumption, and traffic of SC.
One of the new concepts that are proposed by
26
is via-
ble SC. In this approach, the authors integrated agility,
resilience, and sustainability in SCND. The pillar of via-
ble SC include organizational (backup supplier and sub-
contractor, facility fortification, and workplace
resilience), informational (digital twins, data analytics,
visibility, supplier portals, and Blockchain), technological
(additive manufacturing, robotics, smart manufacturing
and warehousing, and industry 4.0), financial (liquidity
reserves, business-government, and revenue manage-
ment), and process-functional (inventory and capacity
buffers, flexible capacity and sourcing, omnichannel,
product diversification, and substitution) structure. They
embedded dynamic systems theory and approach to the
proposed structural model.
Guo, Yu, Boulaksil, Allaoui, and Hu
27
considered a
sustainable SCND that focused on environmental foot-
print and social responsibilities as sustainability pillars.
They presented the Multi-Neighborhood Descent Tra-
versal Algorithm (MNDTA) to produce and introduce a
lower bound for evaluating the proposed method. They
showed that MNDTA could have high-quality solutions
and close to near-optimal for large scale. They found that
running their model costs grows up negligibility, while
the environmental impact decreases and social responsi-
bility increases.
The list of classifications of the literature is addressed
in Table 1 that are extracted based on.
22
Energy supply,
resiliency strategy, kind of SC, sustainability objectives,
solution approach, kind of uncertainty, and industry are
considered for classifications in this list. It can be shown
that SCND and energy supply with RE are not studied in
previous research. This study investigates the application
of energy supply with RE for SCND as a sustainability
strategy and flexible capacity as resiliency against uncer-
tainty recommended. The research gap, innovation, and
the main objective of the work are to design a resilient
and sustainable SC with establishing RE supply. The
components of SC can select supply energy through RE
or buy energy from governments. To cope with current
disruptions like COVID-19 and natural disasters, the
resiliency of the facility include flexible capacity and sup-
ply of energy by RE is suggested. We defined a new form
of the objective function for conservatives decision-
makers for robustness and risk-aware of the model.
3|PROBLEM DESCRIPTION
One of the problems that SC encounters in this situation
like COVID-19 because of demand disruption, is energy
supply. We try to solve this problem by suggesting a new
resilient and sustainable SC equipped with RE. We apply
a flexible capacity strategy for facilities to prepare model
resiliency. Our suggested SC includes suppliers, manufac-
turers, distributing centers, and retailers that are shown
in Figure 2 that can have RE. When the resilience and
sustainable facility is activated, RE can be activated or
not activated and supply energy for them or supply
energy by the government. In our model decision vari-
ables are facilities location (SC and RE facilities) and are
flow variables between facilities. We define a new form
of cost objective function, including the coefficient of
expected value and the minimax of the cost function for
all scenarios. We suggest this form of the cost function to
robust model against disruption and worst case that pay
more attention to risk-averse and conservative decision-
makers.
Assumption:
•All demands should be satisfied.
4LOTFI ET AL.
TABLE 1 Survey of resilience and sustainable SCND
References
Energy
supply Resiliency strategy Kind of SC
Sustainability goal
Solution approach Uncertainty IndustryEconomic Environmental Energy Social Others
8 Buy energy - SCND ✓✓ ✓- - Pareto-efficient - Waste electrical and
electronic
9 - Flexible capacity SCND ✓✓ -✓- Fuzzy goal
programming
Stochastic
fuzzy
Sportswear clothing
10 - Node criticality, flow
complexity, node
complexity,
multiple
assignments, and
customer de-service
level
SCND ✓✓ -✓✓DVG (Differential
Evolution (DE)
algorithm,
Variable
Neighborhood
Search (VNS))
NSGA-II (Non-
dominated Sorting
Genetic Algorithm
II)
MOICA (Multi-
objective imperialist
competitive
algorithm)
Fuzzy-robust Pharmaceutical
11 - Backup, multiple
suppliers, and extra
capacity
SCND ✓---✓ε-constraint Stochastic Plastic pipes
12 Buy Energy Integration of two
layers of networks
CLSCND ✓✓ - - - LP-metrics Stochastic Dairy
13 - Redundancy of
network
SCND ✓---✓Dantzig and Wolfe Stochastic Seaport
14 - Environmental impact SCND ✓✓ ---ε-constraint - Sugar beet
15 - Flexible capacity SCND ✓✓ - - - Lingo - Numerical example
(NE)
16 - Resilience objective
function
SCND ✓✓ --✓ε-constraint, Fuzzy
AHP, TOPSIS
Fuzzy NE
17 - Maximal coverage,
reliable
CLSCND ✓✓ ✓-✓Lp-metric Fuzzy flexible Tire
(Continues)
LOTFI ET AL.5
TABLE 1 (Continued)
References
Energy
supply Resiliency strategy Kind of SC
Sustainability goal
Solution approach Uncertainty IndustryEconomic Environmental Energy Social Others
18 - Node density, node
complexity, node
criticality
SCND ✓---✓TLBO - Electronic
19 - Service level, penalty
per underutilized
capacity
SCND ✓✓ --✓ε-constraint - Gas and oil
20 - Service level, number
of facilities
SCND ✓---✓Fuzzy multi-objective
goal programming
Fuzzy-robust Electricity
26 - Viable supply chain SCND ✓---✓Dynamic systems - -
21 - Seven strategies
a
SCND ✓LBD Stochastic Paint
22 Buy energy Flexible capacity and
reliability
CLSCND ✓✓ ✓✓- Lp-metric Stochastic Automobile
23 - Mitigation SCND ✓✓ --✓SPEA2 Robust Medical devices
24 - Multiple sourcing and
information sharing
CLSCND ✓✓ -✓- AUGMECON2 Stochastic Tire
25 - - SCND ✓-✓-✓RMCGP Stochastic Dairy food
27 - - SCND ✓✓ -✓- MNDTA - NE
Present
study
Using
renewable
energy
Flexible capacity
+energy resiliency
SCND ✓Constraint Constraint - - GAMS and fix-and-opt Robust
stochastic
NE
Abbreviations: CLSCND, closed-loop SCND; LBD, L-shaped Benders decomposition; LP, linear programming; SC, supply chain; SCND, supply chain network design; TLBO, teaching learning-based optimization.
a
Seven strategies: multiple sourcing and transport routes, backup suppliers, adding extra production capacities, lateral transshipment, and direct shipment.
6LOTFI ET AL.
•The shortage is not allowed.
•All forward SC constraint include flow and capacity
constraint is active.
•Flexible capacity strategy is resilience strategy.
•When the resilience facility is activated, RE can be
activated or not activated and supply energy for the
facility or supply energy by the government power
network.
•Using scenario-based robust optimization against risks.
•Sustainability constraints (maximum allowed emission
and energy consumption) are activated.
The objective function (1) indicates minimizing cost
function and includes the expected value and minimax of
the cost function for each scenario. We suggest this form of
the cost function to robust model against disruption and
worst case. Constraints (2) to (6) show fix-costs that include
fixed-cost activating facilities, REs, and maintenance cost of
REs for all periods. Constraints (7) to (9) show the variable
cost of facilities (considering energy) and variable cost of
energy that supply by REs or buying energy. Constraint
(10) shows demand satisfaction. Constraints (11) to (13) are
flow constraints in forwarding SC. Constraints (14) to
FIGURE 2 Resilience and
sustainable supply chain network
design by considering renewable
energy (RSSCNDRE) [Colour figure
can be viewed at
wileyonlinelibrary.com]
Model 1: Resilience and sustainable SCND by considering RE (RSSCNDRE)
minZ¼1λðÞ
P
s
psΓsþλmax Γs
ðÞ, (1)
Subject to:
Γs¼FC þVCs, (2)
FC ¼FC1þFC2þFC3, (3)
FC1¼P
s0
fss0xss0þP
m
fmmxmmþP
d
fcdxddþP
r
frrxrr, (4)
FC2¼P
s0
fress0xress0þP
m
fremmxremmþP
d
freddxreddþP
r
frerrxrerr, (5)
FC3¼X
t
X
s
ðX
s0
mress0tsxress0þX
m
mremmtsxremm
þX
d
mreddtsxreddþX
r
mrerrts xrerrÞ,
(6)
VCs¼VC1sþVC2s,8s(7)
VC1s¼X
pX
t
ðX
s0
X
m
vsms0mptsqsms0mpts þX
mX
d
vmcmdptsqmdmdpts
þX
d
X
r
vdrdrpts qdrdrpts þX
rX
c
vrcrcptsqrcrcpts Þ,
8s(8)
(Continues)
LOTFI ET AL.7
(17) are capacity constraints and the amount of output of
each facility should be less than the capacity of each facility.
Constraints (18) to (21) guarantee that each RE is
established if the facility is installed in the same location.
Constraint (22) guarantee that total environmental emis-
sions of SC system are less than allowed emission. Con-
straint (23) guarantee that the total energy consumption of
SC system is less than the allowed energy consumption.
Constraints (24) and (25) are decision variables, and
Constraint (24) are facilities location (SC and RE facilities)
and binary variables and Constraint (25) are flow variables
that are positive between facilities.
3.1 |Linearization of the problem
As regards the objective function (1) and Equation (9) are
MINLP, we need to change them to mixed-integer
VC2s¼X
pX
t
ðX
s0
X
m
esms0mptsqsms0mpts 1xress0
ðÞþ
X
mX
d
emcmdptsqmdmdpts 1fremm
ðÞþ
X
d
X
r
edrdrpts qdrdrpts 1fredd
ðÞþ
X
rX
c
ercrcptsqrcrcpts 1frerr
ðÞÞ
,
8s(9)
Flow constraints:
P
r
qrcrcpts ≥dcpts,8c,p,t,s(10)
P
d
qdrdrpts ¼P
c
qrcrcpts,8r,p,t,s(11)
P
m
qmdmdpts ¼P
r
qdrdrpts ,8d,p,t,s(12)
P
s0
qsms0mpts ¼P
d
qmdmdpts,8m,p,t,s(13)
Resiliency constraints (flexible and scenario-based capacity)
P
c
qrcrcpts ≤ρrCaprrpts xrr,8r,p,t,s(14)
P
r
qdrdrpts ≤ρdCapddpts xdd,8d,p,t,s(15)
P
d
qmdmdpts ≤ρmCapmmptsxmm,8m,p,t,s(16)
P
m
qsms0mpts ≤ρs0Capss0ptsxss0,8s0,p,t,s(17)
RE and energy resiliency constraints:
xress0≤xss0,8s0(18)
xremm≤xmm,8m(19)
xredd≤xdd,8d(20)
xrerr≤xrr,8r(21)
Sustainability constraints (Maximum allowed emission and energy consumption):
X
pX
t
X
s
ðX
s0
X
m
emsms0mptsqsms0mpts þX
mX
d
emmcmdptsqmdmdpts
þX
d
X
r
emdrdrpts qdrdrpts þX
rX
c
emrcrcptsqrcrcpts Þ≤EMSC,
(22)
X
pX
t
X
s
ðX
s0
X
m
ensms0mptsqsms0mpts þX
mX
d
enmcmdptsqmdmdpts
þX
d
X
r
endrdrpts qdrdrpts þX
rX
c
enrcrcptsqrcrcpts Þ≤ENSC,
(23)
Decision variables:
xss0,xmm,xdd,xrr,xress0,xremm,xredd,xrerr0, 1
fg 8s0,m,d,r(24)
qsms0mpts,qmdmdpts ,qdrdrpts ,qrcrcpts ≥08s0,m,d,r,
p,t,s
(25)
(Continued)
8LOTFI ET AL.
programming (MIP) by operational research method for
time solution decrease.
28,29
Linearizing max function:
If t¼max Ωs
ðÞ, then we can change t≥Ωs,8s.
Linearizing the product of a binary and a continuous
variable:
We suppose that the expression is z¼Ax , where Ais
a continuous variable and xis a binary variable. If Ais
greater than zero, then we can show
30
:
z≤Mx ð26Þ
z≤Að27Þ
z≥A1xðÞMð28Þ
z≥0ð29Þ
If xis zero, zfinally be zero based on
Equations (26) and (29). If xis 1, zfinally be Abased on
Equations (27) and (28). As a result, we can linearize model
(1) to model (2):
We linearize model (1) to model (2) for changing
MINLP to MIP. By changing MINLP to MIP, solving the
model is more straightforward than MINLP in solver,
and we reduce the complexity of the model.
Also, the complexity of model (2) includes numbers
of binary, positive, free variables, and constraints are
shown in Equations (50) to (53). As can be seen, one of
the essential factors for constraints, positive and free vari-
ables, is scenario sets. When the number of scenario
increase, the scale of the model grows up. Therefore,
using scenario reduction or novel algorithms to reduce
binary variables or constraints can be helpful for solving
minimum time.
Binary variables ¼2s0
jj
þm
jj
þd
jj
þr
jj
ðÞ,ð50Þ
Positive variables ¼2p
jj
:t
jj
:s
jj s0
jj
:m
jj
þm
jj
:d
jj
þd
jj
:r
jj
ð
Model 2: Linearizing of RSSCNDRE
minZ¼1λðÞ
P
s
psΓsþλt, (30)
subject to:
t≥Γs8s(31)
VC2s¼X
pX
t
ðX
s0
X
m
esms0mptsηs0mpts þX
mX
d
emcmdptsμmdpts þ
X
d
X
r
edrdrpts φdrpts þX
rX
c
ercrcptsγrcpts Þ,
8s(32)
ηs0mpts ≤qsms0mpts 8s0,m,p,t,s(33)
ηs0mpts ≥qsms0mpts M:xress08s0,m,p,t,s(34)
ηs0mpts ≥08s0,m,p,t,s(35)
ηs0mpts ≤M:1xress0
ðÞ 8s0,m,p,t,s(36)
μmdpts ≤qmdmdpts 8m,d,p,t,s(37)
μmdpts ≥qmdmdpts M:xremm8m,d,p,t,s(38)
μmdpts ≥08m,d,p,t,s(39)
μmdpts ≤M:1xremm
ðÞ 8m,d,p,t,s(40)
φdrpts ≤qdrdrpts 8d,r,p,t,s(41)
φdrpts ≥qdrdrpts M:xredd8d,r,p,t,s(42)
φdrpts ≥08d,r,p,t,s(43)
φdrpts ≤M:1xredd
ðÞ 8d,r,p,t,s(45)
γrcpts ≤qrcrcpts 8r,c,p,t,s(46)
γrcpts ≥qrcrcpts M:xrerr8r,c,p,t,s(47)
γrcpts ≥08r,c,p,t,s(48)
γrcpts ≤M:1xrerr
ðÞ 8r,c,p,t,s(49)
Constraints (2)–(8), (10)-(25).
LOTFI ET AL.9
þr
jj
:c
jjÞ
,ð51Þ
Free variables ¼6þ4s
jj
,ð52Þ
Constraints ¼4þ5s
jj
þp
jj
:t
jj
:s
jjð
3r
jj
:c
jj
þ3:d
jj
:r
jj
þ3m
jj
:d
jj
þ3s0
jj
:m
jj
þc
jj
þ2r
jj
þ2d
jj
þ2m
jj
þs0
jjÞ
þr
jj
þd
jj
þm
jj
þs0
jj
,
ð53Þ
3.2 |A proposed approach for large scale
fix-and-optimize (upper bound)
Regarding the number of scenarios, we need an algo-
rithm to solve in minimum time and give us the appro-
priate bound. Our new algorithm gives us an upper
bound as follows (Figure 3). When we relax each con-
straint, the result of the objective function always
equal to or less than the main model in linear pro-
gramming (LP).
22
After that, when we fix the binary
variable by the fix-and-optimize method, we receive
the upper bound, and the objective function is equal
and bigger than the main model. The validation and
defining upper bound of this technique approved in all
references of SC.
31
We define our new approach based on these
steps:
1. Solve the model by relaxing binary decision variables
and change to between zero and one (relax con-
straint (24)).
2. As regard, we produce LP solution and receive a lower
bound.
TABLE 2 Number of indices, constraints, and variables for the numerical example
Problem s0
jj
:m
jj
:d
jj
:r
jj
:c
jj
:p
jj
:t
jj
:s
jj Constraints
Single variables
(Free and positive) Discrete variables Cost function Time solution
P1-main 3.3.3.3.3.3.3.3 4568 1986 24 2 057 598.20 1.71
FIGURE 3 Solution approach for upper bound fix-and-optimize [Colour figure can be viewed at wileyonlinelibrary.com]
10 LOTFI ET AL.
3. Loop:
a. We do summation on binary variables for every
index that now positive variables and round to up.
b. Run and solve the model with a number of fixed
summation binary variable based on the previ-
ous step.
c. If the model solve and optimize, we take the upper
bound, and save it.
d. If the model satisfies stop criteria (the difference
between two steps is less than 0.001), then the
model stops the loop.
4. Report objective function (sort output based on kind
of objective).
4|RESULTS AND DISCUSSION
Due to the lack of data and inaccessibility to data on RE,
a numerical example has been taken and estimated based
on the overall information of managers of Iran's Renew-
able Energy and Energy Efficiency Organization.
32
In this
section, we define problems that show the performance
TABLE 3 Parameters of the numerical example
Parameters Value Unit Parameters Value Unit
ddcpts [U (2000, 2100)].1000. (s-1)/( s
jj
-1).0.2 +0.9) Num. frr[U (30,40)].1000; $
vsms0mpts U (0.002,0.003); $/Num. fress0[U (160,170)].100; $
vmdmdpts U (0.004,0.005); $/Num. fremm[U (600,700)].100; $
vdrdrpts U (0.002,0.003); $/Num. fredd[U (80,85)].100; $
vrcrcpts U (0.001,0.002); $/Num. frerr[U (30,40)].100; $
esms0mpts U (0.004,0.005); $/Num. pps1/ s
jj %
emdmdpts U (0.004,0.005); $/Num. λ85 %
edrdrpts U (0.004,0.005); $/Num. M10
500
-
ercrcpts U (0.004,0.005); $/Num. emsms0mpts U (0.0004,0.0005); Ton/Num.
Capss0pts [U (5500,6600)].1000; Num. emmdmdpts U (0.0004,0.0005); Ton/Num.
Capmmpts [U (55 000,66 000)].1000; Num. emdrdrpts U (0.0004,0.0005); Ton/Num.
Capddpts [U (3300,4400)].1000; Num. emrcrcpts U (0.0004,0.0005); Ton/Num.
Caprrpts [U (3300,4400)].1000; Num. ensms0mpts U (0.0001,0.0002); MJ/Num.
mress0ts [U (3,4)].100; $ enmdmdpts U (0.0001,0.0002); MJ/Num.
mremmts [U (3,4)].100; $ endrdrpts U (0.0001,0.0002); MJ/Num.
mreddts [U (3,4)].100; $ enrcrcpts U (0.0001,0.0002); MJ/Num.
mrerrts [U (3,4)].100; $ EMSC 50000:s0
jj:mjj:djj:rjj:sjj Ton
fss0[U (160,170)].1000; $ ENSC 70000:s0
jj
:m
jj
:d
jj
:r
jj
:s
jj MJ
fmm[U (600,700)].1000; $ ρs0¼ρm¼ρd¼ρr¼0:9
fdd[U (80,85)].1000; $
FIGURE 4 Potential location for the facility supply chain (SC)
[Colour figure can be viewed at wileyonlinelibrary.com]
LOTFI ET AL.11
of the mathematical model. The number of sets (indices)
is shown in Tables 2 and 3. We have three optimistic, pes-
simistic, and possible scenarios.
We applied GAMS 24.1.2 software with CPLEX Solver
for solving mathematical models with Processor Core
i3-3210, CPU 3.2 GHz, 8.00 GB RAM, operating system
type 64-bit.
We show the potential of location for selecting sup-
pliers, manufacturers, DC, retailers in Figure 4. The
potential of sites is in the city of Iran. After solving the
model, the model selects suitable locations for compo-
nents of SC, RE, and the amount of flow and amount of
objective function is 2 057 598.20 based on Table 2. The
mathematical model is calculated and shows that where
to locate SC components and RE in Figure 5 and
Table 4.
4.1 |Changing scale of the main model
We define several problems in medium-scale in
Table 5. As can be seen, by the increasing scale
FIGURE 5 Final location of the facility with solar energy
[Colour figure can be viewed at wileyonlinelibrary.com]
TABLE 4 Comparing main model
and proposed algorithm for upper
bound
Problem: P1 Variables
City
Behbahan Nayriz Iranshahr
Supplier xss0,1 01
RE for supplier xress0101
Naein Khoramdareh Zahedan
Manufacturer xmm,1 0 0
RE for manufacturer xremm10 0
Sanandaj Kashan Kashmar
Distributing center (DC) xdd,1 1 1
RE for DC xredd111
Tabriz Tehran Mashhad
Retailer xrr,1 1 1
RE for retailer xrerr11 1
Abbreviation: RE, renewable energy.
TABLE 5 Cost function and time solution for different problems
Problem s0
jj
:m
jj
:d
jj
:r
jj
:c
jj
:p
jj
:t
jj
:s
jj Constraints Single variables Discrete variables Cost function Time solution
P1 3.3.3.3.3.3.3.3 4570 1986 24 2 057 598.20 1.71
P2 3.3.3.3.3.3.3.5 7604 3290 24 2 071 137.05 2.56
P3 4.4.4.4.4.4.4.3 13 862 6194 32 2 967 646.92 15.55
P4 4.4.4.6.4.4.4.4 22 829 10 298 36 2 978 674.33 45.53
P5 5.5.5.6.5.5.5.3 36 192 16 560 42 4 819 795.31 168.33
12 LOTFI ET AL.
of problems, the cost function and time solution
grow up in Figures 6 and 7. Time solution shows
that model behavior is exponential in large scale
and Non-deterministic Polynomial-time hard
(NP-hard).
4.2 |Effects of changing the
conservative coefficient
Also, we exam on a conservative coefficient (λ).
By changing the conservative coefficient (λ) for Problem
P1 that varied between 0.1 and 1 that the amount of con-
servation of decision-maker has been changed. However,
if λclose to 1, the amount of conservation increases and
the cost function grows up and it can consider in Table 6
and Figures 8 and 9. By increasing 20% for the conser-
vative coefficient, the cost function increase by 0.5%.
4.3 |Effects of changing demand
As it is evident in Table 7, decreasing demand, defiantly,
amount of using RE decrease and is not feasible eco-
nomic. In Figure 10, we can see that when demand
increases, the cost function will increase, and activating
RE is needed and we cannot buy and supply energy from
the government power network and have to provide
energy by RE. By growing 20% for demand, the cost func-
tion increase by 6%.
4.4 |Producing upper bound for the
main model
We compare the main model and proposed algorithm
for upper bound by a new fix-and-optimize strategy
based on the solution approach in Section 3.2 (C) and
validate results in Table 8. Also, we generate a lower
bound based on LP model (A) by relaxing constraint
(24). In Figures 11,12 and 13, the comparison of the
two methods and the main model is drawn. We see
that the proposed upper bound for the main model is
less than 10%. This approach is appropriate for large-
scale problems because we receive a near-optimal solu-
tion in minimum time.
FIGURE 6 Cost function for different problems [Colour figure
can be viewed at wileyonlinelibrary.com]
FIGURE 7 Time solution for different problems [Colour figure
can be viewed at wileyonlinelibrary.com]
TABLE 6 Effects of changing
conservative coefficient Problem Conservative coefficient (λ) Cost function Time solution
P1 0.80 2 052 425.45 1.51
P1 0.85 2 055 011.82 1.73
P1-main model 0.9 2 057 598.20 1.71
P1 0.95 2 060 185.68 1.55
P1 1.00 2 062 770.95 1.31
LOTFI ET AL.13
5|MANAGERIAL INSIGHTS AND
PRACTICAL IMPLICATIONS
Resilience against disruption and sustainability by RE
is one of the subjects that need more attention for
managers of SC. Attention to sustainable development
goal (SDG) is grown every day, and people want to
receive products and services based on SDG require-
ments. Therefore, people want to buy products and
services from SC that observe SDG requirements.
There are many tools and pillars of resiliency and sus-
tainably of SC is suggested in the survey review. In
this research, embedding RE is suggested for resil-
iency and sustainability tools for SCs with high
demand. Appling RE needs high fix-cost and having
maintenance costs that only support by increasing
sales and demands. But what is certain that all SCs
graduallygotoembedREinSCND,becausethe
energy of RE is free and clean and it is necessary for
decreasing costs and environmental impact and
increasing sustainability. We, as managerial SC, have
to accept and equip SC by RE. How much we go
faster,amountofflourishing,comparative,andresil-
ience is more. Using RE decreases cost, we can inves-
tigate and develop the research and development
(R&D) of products and increase social welfare.
Increasing day by day variety of products and trans-
shipment of demand from one SC to another SC, we
have to think about comparative benefits. Clean RE
like solar energy that has a minimum cost to establish
than other RE. It can help the SC and government
until energy supply and use many suppliers that can
produce products with minimum cost and far from
SCs and SCs does not need to buy energy from the
government power network with high cost. We survey
changing demand and we can see that when demand
increases, the cost function will increase, and activat-
ing RE is economically feasible. Finally, we try to
draw a model for managers to observe RE in design-
ing SCND or reconfigure SCND, if their SCND is
active now and not applied RE.
FIGURE 8 Cost function for different Lambda [Colour figure
can be viewed at wileyonlinelibrary.com]
FIGURE 9 Time solution for different Lambda [Colour figure
can be viewed at wileyonlinelibrary.com]
TABLE 7 Effects of changing demand
Problem Changing demand Cost function
P1 50% 1 438 129.13
P1 30% 1 562 744.06
P1 20% 1 806 072.84
P1-main model 0% 2 057 598.20
P1 +20% 2 191 494.53
P1 +50% 2 255 581.33
FIGURE 10 Effects of changing demand [Colour figure can be
viewed at wileyonlinelibrary.com]
14 LOTFI ET AL.
6|CONCLUSIONS
The necessity and importance of RE are not hidden
from anyone. As a result, we suggested a novel SCND
that wants to pay more attention to resiliency and sus-
tainability by considering RE. This SCND has suppliers,
manufacturers, distributing centers, retailers, and cus-
tomers. Each component of SC wants to add RE like
solar energy to supply energy. We defined a new form of
the objective function to all range of decision-makers
for robustness and risk-aware of the model. We embed-
ded a new robust two-stage stochastic optimization that
the objective function combine of mean and minimax
method. The first stage locates facility location and RE,
TABLE 8 Comparing the main model and proposed algorithm for the upper bound
Problem
LP model-Lower bound (A) Main model (B)
Proposed upper bound
for main model (C)
Gap
1
Gap
2
Cost function
Time
solution Cost function
Time
solution Cost function
Time
solution
P1 1 141 581.85 0.34 2 057 598.20 1.71 2 060 135.56 1.33 45% 0%
P2 1 151 157.95 0.62 2 071 137.05 2.56 2 115 827.02 2.13 44% 2%
P3 2 158 239.37 1.11 2 967 646.92 15.55 3 021 472.47 2.83 27% 2%
P4 2 151 378.75 3.53 2 978 674.33 45.53 3 008 598.19 6.30 28% 1%
P5 3 665 043.79 10.03 4 819 795.31 168.33 5 412 121.02 15.85 24% 12%
Abbreviation: LP, linear programming.
FIGURE 11 Attaining upper bound for problem P5 [Colour
figure can be viewed at wileyonlinelibrary.com]
FIGURE 12 The cost function for three model algorithm
[Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 13 Time solution for three model algorithm [Colour
figure can be viewed at wileyonlinelibrary.com]
LOTFI ET AL.15
and the second stage defines flow quantity between SC
components.
The results of this research and managerial insights
are as follows:
1. The mathematical model is calculated and shows how
to locate components of SC, RE in Iran and determine
flow quantity well in Figure 5.
2. Also, we can see that, by increasing the scale of prob-
lems, the cost function and time solution grow up in
Figures 6 and 7. Time solution shows that the behavior
of the model is exponential on large-scale and NP-hard.
3. Effects of changing conservative coefficient are sur-
veyed and indicate that when the amount of conserva-
tion increases, the cost function grows up, and it can
consider in Table 6 and Figures 8 and 9. By increasing
20% for the conservative coefficient, the cost function
increase by 0.5%.
4. Effects of changing demand are investigated and
when demand is high, activating RE is economically
feasible and we cannot buy and supply energy by the
government power network and have to supply
energy by RE. After activating RE, by increasing 20%
for demand, the cost function increases by 6%.
5. We compare the main model and proposed algorithm
for upper bound by a novel fix-and-optimize strategy.
Also, we generate a lower bound based on LP by
relaxing constraint (24). In Figures 12 and 13, the
comparison of the two methods and main models is
drawn and we see that the proposed upper bound for
the main model is less than 10%.
6. This research proposed to equip SC by RE, as it is resil-
ient against demand fluctuation and sustainable about
energy resource. This SC is compatible with SGD7.
Regarding research constraints for solving the main model
on a large scale, we suggest embedding heuristic and
meta-heuristic algorithms to solve models and add other
objectives for future research.
33,34
Also, we recommend
other coherent risk criteria like CVaR
35
and entropic value
at risk,
36
and robust CVaR
37
for considering risk and other
method uncertainty like robust convex and robust stochas-
tic.
38
Appling data-driven robust optimization is an advan-
tage for a conservative decision-maker. Also, we propose
to employ Blockchain as an innovative technology for the
sustainability and resiliency of SC.
NOTATIONS
Indices
s0index of supplier
mindex of manufacturer
dindex of distributing center (DC)
rindex of retailer
cindex of customer
pindex of product
tindex of time period
sindex of scenario
Parameters
ddcpts demand customer cfor product ptime period
tunder scenario s
vsms0mpts cost transshipment from supplier s0to manu-
facturer mfor product ptime period tunder
scenario s(without energy)
vmdmdpts cost transshipment from manufacturer mto
DC dfor product ptime period tunder sce-
nario s(without energy)
vdrdrpts cost transshipment from DC dto retailer rfor
product ptime period tunder scenario s
(without energy)
vrcrcpts cost transshipment from retailer rto customer
cfor product ptime period tunder scenario s
(without energy)
esms0mpts cost energy consumption from supplier s0to
manufacturer mfor product ptime period t
under scenario s
emdmdpts cost energy consumption from manufacturer
mto DC dfor product ptime period tunder
scenario s
edrdrpts cost energy consumption from DC dto
retailer rfor product ptime period tunder
scenario s
ercrcpts cost energy consumption from retailer rto
customer cfor product ptime period tunder
scenario s
mress0ts cost of RE maintenance at supplier s0for time
period tunder scenario s
mremmts cost of RE maintenance at manufacturer m
for time period tunder scenario s
mreddts cost of RE maintenance at DC dfor time
period tunder scenario s
mrerrts cost of RE maintenance at retailer rfor time
period tunder scenario s
fss0cost of activation supplier s0
fmmcost of activation manufacturer m
fddcost of activation DC d
frrcost of activation retailer r
fress0cost of activation RE at supplier s0
fremmcost of activation RE at manufacturer m
freddcost of activation RE at DC d
frerrcost of activation RE at retailer r
emsms0mpts emission CO
2
for transshipment from sup-
plier s0to manufacturer mfor product p
time period tunder scenario s
16 LOTFI ET AL.
emmdmdpts emission CO
2
for transshipment from man-
ufacturer mto DC dfor product ptime
period tunder scenario s
emdrdrpts emission CO
2
for transshipment from DC d
to retailer rfor product ptime period t
under scenario s
emrcrcpts emission CO
2
for transshipment from
retailer rto customer cfor product ptime
period tunder scenario s
ensms0mpts energy consumption for transshipment from
supplier s0to manufacturer mfor product p
time period tunder scenario s
enmdmdpts energy consumption for transshipment from
manufacturer mto DC dfor product ptime
period tunder scenario s
endrdrpts energy consumption for transshipment from
DC dto retailer rfor product ptime period
tunder scenario s
enrcrcpts energy consumption for transshipment from
retailer rto customer cfor product ptime
period tunder scenario s
Capss0pts capacity supplier s0for product ptime
period tunder scenario s
Capmmpts capacity manufacturer mfor product ptime
period tunder scenario s
Capddpts capacity DC dfor product ptime period t
under scenario s
Caprrpts capacity retailer rfor product ptime period
tunder scenario s
ppsprobably of scenario s
λcoefficient of conservative
Mbig number
EMSC maximum allowed emission for SC
ENSC maximum allowed energy consumption for SC
ρs0coefficient of availability of supplier s0
ρmcoefficient of availability of manufacturer m
ρdcoefficient of availability of DC d
ρrcoefficient of availability of retailer r
DECISION VARIABLES
Binary variables
xss0if supplier s0is activated, equal 1 otherwise 0
xmmif manufacturer mis activated, equal 1 other-
wise 0
xddif DC dis activated, equal 1 otherwise 0
xrrif retailer ris activated, equal 1 otherwise 0
xress0if RE in supplier s0is activated, equal 1 other-
wise 0
xremmif RE in manufacturer mis activated, equal
1 otherwise 0
xreddif RE in DC dis activated, equal 1 otherwise 0
xrerrif RE in retailer ris activated, equal 1 other-
wise 0
Continues variables
qsms0mpts quantity transshipment from supplier s0to
manufacturer mfor product ptime period t
under scenario s
qmdmdpts quantity transshipment from manufacturer m
to DC dfor product ptime period tunder sce-
nario s
qdrdrpts quantity transshipment from DC dto retailer
rfor product ptime period tunder scenario s
qrcrcpts quantity transshipment from retailer rto cus-
tomer cfor product ptime period tunder sce-
nario s
Auxiliary variables
ηs0mpts auxiliary variable from supplier s0to manufac-
turer mfor product ptime period tunder sce-
nario s
μmdpts auxiliary variable from manufacturer mto DC
dfor product ptime period tunder scenario s
φdrpts auxiliary variable from DC dto retailer rfor
product ptime period tunder scenario s
γrcpts auxiliary variable from retailer rto customer c
for product ptime period tunder scenario s
FC fix cost include FC1, FC2,FC3,
VCsvariable cost includes VC1s,VC2sfor scenario s
Γsfix cost and variable cost for scenario s
tauxiliary variable for minimax function
ORCID
Reza Lotfi https://orcid.org/0000-0001-5868-8467
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How to cite this article: Lotfi R, Kargar B,
Hoseini SH, Nazari S, Safavi S, Weber G-W.
Resilience and sustainable supply chain network
design by considering renewable energy. Int
J Energy Res. 2021;1–18. https://doi.org/10.1002/
er.6943
18 LOTFI ET AL.
