Designing a new multi-echelon multi-period closed-loop supply chain network by forecasting demand using time series model: a genetic algorithm

Abstract

Demand plays a vital role in designing every closed-loop supply chain network in today's world. The flow of materials and commodities in the opposite direction of the standard supply chain is inevitable. In this way, this study addresses a new multi-echelon multi-period closed-loop supply chain network to minimize the total costs of the network. The echelons include suppliers, manufacturers, distribution centers, customers, and recycling and recovery units of components in the proposed network. Also, a Mixed Integer Linear Programming (MILP) model considering factories' vehicles and rental cars of transportation companies is formulated for the proposed problem. Moreover, for the first time, the demand for the products is estimated using an Auto-Regressive Integrated Moving Average (ARIMA) time series model to decrease the shortage that may happen in the whole supply chain network. Conversely, for solving the proposed model, the GAMS software is utilized in small and medium-size problems, and also, genetic algorithm is applied for large-size problems to obtain initial results of the model. Numerical results show that the proposed model is closer to the actual situation and could reach a reasonable solution in terms of service level, shortage, etc. Accordingly, sensitivity analysis is performed on essential parameters to show the performance of the proposed model. Finally, some potential topics are discussed for future study.

Full text

Vol.:(0123456789)
1 3
Environmental Science and Pollution Research
https://doi.org/10.1007/s11356-022-19341-5
CIRCULAR ECONOMY APPLICATION INDESIGNING SUSTAINABLE MEDICAL WASTE
MANAGEMENT SYSTEMS
Designing anew multi‑echelon multi‑period closed‑loop supply chain
network byforecasting demand using time series model: agenetic
algorithm
ShahabSafaei1· PeimanGhasemi2· FaribaGoodarzian3· MohsenMomenitabar4
Received: 3 December 2021 / Accepted: 17 February 2022
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
Abstract
Demand plays a vital role in designing every closed-loop supply chain network in today’s world. The flow of materials and
commodities in the opposite direction of the standard supply chain is inevitable. In this way, this study addresses a new
multi-echelon multi-period closed-loop supply chain network to minimize the total costs of the network. The echelons include
suppliers, manufacturers, distribution centers, customers, and recycling and recovery units of components in the proposed
network. Also, a Mixed Integer Linear Programming (MILP) model considering factories’ vehicles and rental cars of trans-
portation companies is formulated for the proposed problem. Moreover, for the first time, the demand for the products is
estimated using an Auto-Regressive Integrated Moving Average (ARIMA) time series model to decrease the shortage that
may happen in the whole supply chain network. Conversely, for solving the proposed model, the GAMS software is utilized
in small and medium-size problems, and also, genetic algorithm is applied for large-size problems to obtain initial results
of the model. Numerical results show that the proposed model is closer to the actual situation and could reach a reasonable
solution in terms of service level, shortage, etc. Accordingly, sensitivity analysis is performed on essential parameters to
show the performance of the proposed model. Finally, some potential topics are discussed for future study.
Keywords Closed-loop supply chain network· Demand forecasting· Mathematical model· ARIMA time series model·
Genetic algorithm
Introduction
Designing the transportation network in the supply chain
has attracted much attention in today’s competitive world
(Chan etal. 2016). Providing better services by companies
to satisfy customers, decreasing costs, and increasing net
profit is one of the consequences of this competition (Xu
etal. 2017). Supply chain network design is a strategic issue
that helps to select the best combination of a set of facilities
to achieve an efficient and effective network (Almaraj and
Trafalis 2019). Designing a distribution network is one of
the critical issues in the design of the supply chain network,
which offers a substantial potential factor to reduce costs and
improve service quality (Margolis etal. 2018, Goodarzian
Responsible Editor: Philippe Garrigues
* Peiman Ghasemi
peiman.ghasemi@gutech.edu.om
Shahab Safaei
Ksanan46@yahoo.com
Fariba Goodarzian
Fariba.Goodarzian@mirlabs.org
Mohsen Momenitabar
Mohsen.momenitabar@ndsu.edu
1 Department ofIndustrial Engineering, Faculty ofIndustrial
Engineering, Firoozkooh Branch, Islamic Azad University,
Firoozkooh, Iran
2 Department ofLogistics, Tourism andService Management,
German University ofTechnology inOman (GUtech),
Muscat, Oman
3 Machine Intelligence Research Labs (MIR Labs), Scientific
Network forInnovation andResearch Excellence, 11, 3rd
Street NW, P.O. Box2259, Auburn, WA98071, USA
4 Department ofTransportation, Logistics, andFinance, North
Dakota State University (NDSU), 58105-6050Fargo, ND,
USA

Environmental Science and Pollution Research
1 3
etal. 2021a, 2021b; Mosallanezhad etal. 2021). Therefore,
the design of a supply chain network plays an outstanding
role in long-term strategic decision-making (Wu etal. 2017).
Also, researchers in recent years have paid more attention
to the multi-product nature of such problems (Wang and
Gunasekaran 2017). In this research, modeling the design
of transportation networks in the supply chain and its solu-
tion by meta-heuristic methods are developed and discussed.
Over the past two decades, there have been tremendous
global changes due to advances in technology, the globaliza-
tion of markets, and the new economic-political conditions
(Ghasemi etal. 2017). Due to the growing number of competi-
tors in the global class, organizations were forced to quickly
improve intra-organizational processes to stay in the world-
wide competition. In the 1960s–1970s, organizations tried to
develop detailed market strategies that have mainly focused on
satisfying customers (Mohtashami etal. 2020). They realized
that robust engineering and design and coherent production
operations were the prerequisite for achieving market require-
ments and thus more market share. Therefore, designers were
forced to incorporate the ideals and needs of their customers
into their product design, and in fact, they had to supply a
product with the maximum possible level of quality, at mini-
mum cost considering the customer’s desired ideals (Hassan-
pour etal. 2019; Modibbo etal. 2019, 2021; Ali etal. 2021).
In this research, a new mathematical model for optimizing
the closed-loop supply chain, whose main objectives include
determination of the optimal amount of products and compo-
nents in each segment of the network, minimizing the total
cost of the system, optimizing the amount of transportation
in the entire system has been proposed. This research aims
to design a closed-loop supply chain network that includes
suppliers, manufacturers, distribution centers and customers,
collection and disassembly centers, product, and component
recovery units, as well as a facility for destruction and burial
of damaged and polluting components.
Figure1 shows a closed-loop supply chain network of this
study. Suppliers send components to factories, and factories
produce products based on received demand from custom-
ers. The generated products are sent to distribution centers
by factories’ trucks or transportation companies in order to
be delivered to the customers. In order to increase the speed
of transporting products to meet the customers’ needs with-
out encountering bottlenecks and shortages of vehicles, the
trucks of the factories and the transportation companies have
been used simultaneously. A few products are returned by
consumers and are gathered in the product collection cent-
ers. The collection center divides the products into two
parts, including usable and unusable sections. Some after-
consumption products that have not yet finished their lifetime
can be reused again by some repairing. They are sent to the
product recovery centers from the product collection center
to be recovered. Then, these products are sent to distribution
centers after recovery and repairs. Unusable products are dis-
assembled into components in disassembly centers. The com-
ponents that are usable can be reused after repairing by the
repairing and recovery centers, but some useless components
should be destroyed or buried. These types of components,
such as chemical batteries, chips, various types of chemicals
and plastics, and various types of pollutants, are harmful to
the environment, and they take many years to be recovered.
Therefore, these components have been considered waste and
are gathered in destruction and burial centers for technological
clearing. Because the capacity of the recovery unit for compo-
nents is limited, several recovery centers are needed. After the
recovery phase, the reconstructed components are taken to the
Fig. 1 The schematic view
of closed-loop supply chain
network with multiple manu-
facturers
SupplierManufacturer Distribution centerCustomer
Product Recovery Product Collection
Disassemble &
Separation
Repairing &
Recovering
Components
Destruction
and Burial

Environmental Science and Pollution Research
1 3
warehouse section of the factories to be used as new compo-
nents. Due to the fact that the recovery and collection centers
are limited, new components are purchased from suppliers
based on demand and the number of recovered components.
The autoregressive integrated moving average (ARIMA)
was proposed three decades ago, and it is widely used by
many researchers to forecast the features they need to be
estimated. The ARIMA models can also be used to build
various exponential smoothing techniques. In this study, we
have used the ARIMA time series model to estimate the
value of demand which is the input parameter for the pro-
posed supply chain network. No study in the supply chain
considers forecasting demand by the ARIMA timer series
model, so, in this paper, for the first time, we will estimate
the demand by utilizing this technique as we propose it in
the “Demand forecasting” section separately.
In the present research, for the first time, we will discuss
the issue of service level, the possibility of a shortage, and
other related parameters and variables in the multi-period
closed-loop supply chain network. Therefore, discussing,
modeling, and solving the closed-loop supply chain prob-
lem considering the specific service level to demand, as well
as considering the cost of not satisfying the total amount of
demand in the cost objective function, are one of the contri-
butions of this research.
This research has been compiled into six sections. The
“Literature review” section deals with the literature review.
In the “Problem statement” section, the mathematical model
is presented. The “Solving algorithm” section describes the
solution algorithm, and in the “Computational results” sec-
tion, the computational results are presented, and finally, the
conclusion will be presented in the “Conclusion” section.
Literature review
Meng etal. (2016) developed a simulation-based hierarchi-
cal particle swarm optimization algorithm to solve a multi-
criteria production–distribution program. Their integrated
program included three objectives of minimizing all costs,
including regular labor costs, overtime, outsourcing, inven-
tory maintenance, shortage, recruitment, expulsion, and dis-
tribution costs, reducing the work level changes, and mini-
mizing inefficiency of work levels. Below are the levels of
work. They validated their proposed algorithm with a zero/
one hierarchical genetic algorithm. Phuc etal. (2017) inves-
tigated the reverse logistics of salvage cars. In their model,
the objective functions were fuzzy, and the parameters were
deterministic. The problem included four fuzzy objectives:
minimizing delivering and transportation costs, minimizing
warehouse establishment costs, maximizing reverse service
in return flows. The model’s results indicated a 15% reduc-
tion in total system costs. Zheng etal. (2017) formulated a
multi-objective linear programming model for optimizing
the operations of integrated logistics, reverse logistics, and
returned products in a given supply chain. Factors such as
the return of used products and subsidies by government
agencies were considered in the formulation of the model.
They were considering the model as decentralized and
incomplete information was one of the innovations of this
research. Habibi etal. (2017) designed a three-level sup-
ply chain while simultaneously examining the total cost and
disassembling effects of different commodities. Their model
was a single-product and single-period research, including
manufacturers, distribution centers, and customers. After
defining the model using linearization methods, the opti-
mal solution of the problem was obtained by employing an
interactive method. In this study, tactical decisions on the
selection of transportation systems were also considered.
Li etal. (2017) examined the supply chain network, includ-
ing suppliers, factories, and distribution centers. Decisions
to be made in this network included setting up the factories
and distribution centers, the amount of production, and the
volume of products. The objective function was defined as
the minimization of costs. To solve this model, a genetic
algorithm based on a spanning tree was used, and the valid-
ity of this method was measured by comparing it with the
traditional method of genetic algorithm. Pedram etal. (2017)
presented a multi-period model for maximizing the reverse
supply chain profit of recycled tires. In their proposed model,
the recycling capacity was set to minimize the total cost.
The advantage of this research was considering strategic and
tactical decisions simultaneously. The results indicated the
appropriate performance of the proposed model. Kim etal.
(2018) presented a robust mathematical model for reverse
supply chain management with uncertain demand. Consid-
ering budget constraints and prioritizing suppliers were of
the innovations of this research. To verify the validity of
the proposed model, robust optimization was used, and to
deal with the uncertainty of the problem, and simulation was
used. Sobotka etal. (2017) investigated the reverse supply
chain projects of recycled and resilient materials. Consider-
ing the cost of repairs was one of the issues addressed in this
study. The results of the numerical examples indicated that
the increase in the number of recycled materials leads to a
rise in the cost of repairs to a certain level. Yu and Solvang
(2018) examined the multi-period and multi-product supply
chain. Considering the capacity constraints of facilities and
resilience in the supply chain were of the strengths of this
research. To model this problem, a two-level approach was
used, which in the first level, strategic decisions including
allocation of capacity, and in the second level, operational
decisions including the reduction of supply chain costs were
made. Mota etal. (2018) explored an integrated and resil-
ient supply chain in the chain stores in Europe. Considering
the location of facilities and the prioritization of suppliers

Environmental Science and Pollution Research
1 3
were the most important objectives of this research. The
use of social, economic, and environmental factors in the
constraints made this research different than similar studies.
Flygansvær etal. (2018) presented a mixed-integer non-
linear programming model for the design of a direct and
reversed integrated logistics network for logistics service
providers. Their case study was 102 electronic industry
contractors. To deal with the current uncertainty of the
conditions, the characteristics of the problem were deter-
mined for each period, and in the next period, the model
was again solved for new characteristics. Cheraghalipour
etal. (2018) investigated the logistics of a physical section
of the supply chain, which involved all activities related to
the flow of materials and commodities from the stage of
providing the raw materials to the production of the final
product, including transportation and warehousing. One
of the new trends in logistics management is the recycling
or reuse of products. In this method, products that reach
the end of their useful life will be re-purchased from the
final consumer, and once disassembled, reusable compo-
nents of the product will be recycled in the form of salvage
products. Heydari etal. (2018) presented a zero/one two-
level mixed-integer programming model considering the
direct and inverse flow of recycling of components. The
problem was formulated as an incapacitated mathematical
model. Thinking of the model as decentralized and solv-
ing it with a heuristic method were of the innovations of
this research.
Eydi etal. (2020) proposed a multi-period multi-echelon
forward and reverse supply chain network for product dis-
tribution and collection with transportation mode selection.
In addition, they formulated a new mixed-integer nonlinear
programming model for their problem based on different
levels of facility capacities with the maximum profit objec-
tive function. Finally, a genetic algorithm was used to solve
their model. Antucheviciene etal. (2020) developed sus-
tainable reverse supply chain planning under uncertainty.
Their main aims were to maximize the total profit of opera-
tion, minimize adverse environmental effects, and optimize
customer and supplier service levels. Then, scenario-based
robust planning was used to tackle uncertain parameters. To
solve their model, non-dominated sorting genetic algorithm
II was employed. Finally, they provided actual data from a
case study of the steel industry in Iran. Gao and Cao (2020)
provided a new sustainable reverse logistics supply chain
network by reconstructing the existing facilities into hybrid
processing facilities. They presented a multi-objective sce-
nario-based optimization model to maximize the expected
total monetary profits, minimize the expected total carbon
emission costs, and maximize the expected total created job
opportunities. They used the weighted-sum and augmented-
constraint approaches to solve their model. Eventually, a real
case study in the tire industry was considered to demonstrate
the performance of their model. Sajedi etal. (2020) intro-
duced a two-objective probable mixed integer programming
for the design of a closed-loop supply chain. In their model,
the reverse flow was considered along with the direct flow
as well as strategic decisions along with tactical decisions.
Consideration demand as uncertain was one of the innova-
tions of this research. The results indicated a reduction of
8% in the costs of the system.
Shadkam (2021) designed a complex integer linear
programming model for an integrated direct logistics and
reverse logistic network design considering waste manage-
ment. Their main aims were to minimize the costs related
to the fixed expenses, material flow costs, and the costs
of building potential centers. Eventually, their model was
solved utilizing the cuckoo optimization algorithm. Par-
ast etal. (2021) formulated a bi-objective mixed-integer
linear programming model to design a green forward and
reverse supply chain under uncertainty. They provided a
new location-inventory-routing problem with simultane-
ous pickup and delivery, scheduling of vehicles, and time
window. Their main goals were to minimize total costs
and lost demands simultaneously. Moreover, an approach
according to the fuzzy theory was presented to cope with
uncertain parameters. Finally, they considered a real case
study to show the performance and efficiency of their
model. Another study was done by Gerdrodbari etal.
(2021) presented a bi-objective mixed-integer linear pro-
gramming (MILP) model to design a multi-level, multi-
period, multi-product closed-loop supply chain (CLSC)
for timely production and distribution of perishable prod-
ucts, considering the uncertainty of demand. To face the
model uncertainty, they used the robust optimization (RO)
method to solve and validate the bi-objective model in
small-size problems, and then, they used a non-dominated
sorting genetic algorithm (NSGA-II) for solving large-size
problems.
Only one study considered the time series model when
designing a supply chain network. Ghaderi etal. (2016) uti-
lized auto-regressive moving average (ARMA) time series
models to estimate the number of bioethanol demand in their
network. Then, they used the estimated demand as an input
into their model to design a switchgrass-based bioethanol
supply chain network.
Based on what we have reviewed so far, the issue of ser-
vice level, the possibility of a shortage, and other related
parameters and variables in the multi-period closed-loop
supply chain network have not been considered by research-
ers. More interestingly, the ARIMA time series model has
not been included in any studies in the past, so the main
contribution of this study is as follows:
• Considering service level and the possibility of shortage
in the proposed mathematical model,

Environmental Science and Pollution Research
1 3
• Utilizing the ARIMA time series model to estimate the
demand of supply chain as an input parameter into the
model, and
• We are applying a genetic algorithm to solve the pro-
posed mathematical model for a large-size problem.
On the other hand, the goal of this research is to deter-
mine to identify the optimal number of products and com-
ponents in each section of the network by minimizing the
total costs of the system and optimizing the number of
transporting products in the system. More interestingly,
also, reducing the production costs and using an appropri-
ate producer with lower production costs are other objec-
tives of this model. In the next section, first, we discuss
how to forecast demand using the ARIMA time series
model and then present the problem statement of this
research study by formulating the mathematical model in
the “Problem statement” section.
Demand forecasting
Demand plays a crucial role when designing an efficient sup-
ply chain network. Indeed, the central part of each supply
chain network is to have a reasonable estimation for demand.
In this way, this study has utilized the Auto-Regressive Inte-
grated Moving Average (ARIMA) to forecast the number of
products demands. On the other hand, knowing the excellent
estimation of demand can help us to know the actual costs
of the designed network as well as respond to the customers’
needs in a proper time. The general equation of ARIMA is
brought in Eq.(1) as follows.
To forecast the demand, we have used the demand data-
set between the years 2017 and 2020, which is shown in
Fig.2. As we can see, there are NO seasonality patterns for
the period that we have investigated our data for products.
Therefore, utilizing the ARIMA model can help us to have
good predictions based on our dataset.
Based on Fig.2, it is clearly visible that the trend of
demand of products shows the smooth line that is constant
from one period to another period (month). Furthermore, the
forecasting of demand has been brought in Table1. As we
can see, the demand is predicted for the year 2021 based on
the ARIMA timer series model, so, in this table, we have:
Problem statement
In this section, we aim to state the problem that we are plan-
ning to solve. As we have shown in Fig.1, the suppliers
prepare raw materials for the manufacturers, and then, the
raw materials will be used by manufacturers based on the
Bill of Material (BOM) to produce goods. Then, the gen-
erated goods will be sent to the distribution centers to be
transferred to the customers. The returned products will
be collected by product collection centers. These returned
products will be checked if they are in good condition or
not, and based on that, they will send to either the prod-
uct recovery center or disassemble and separation centers.
If these returned products are sent to the product recovery
center, then they will transfer to the distribution centers to
be distributed in the network again. If the collected products
are disassembled in disassemble and separation centers, they
will have two results. If they are usable, they will send to
repairing recovering components centers for repairing. If
these products cannot be functional, they will be destructed
in destruction and burial centers.
The purpose of the proposed model is to identify the
optimal number of products and components in each sec-
tion of the network by minimizing the total costs of the
system and optimizing the number of transporting prod-
ucts in the system. Also, reducing the production costs
and using an appropriate producer with lower produc-
tion costs are other objectives of this model. Indeed, this
model plans to determine the allocation of orders to the
factories according to the optimal amount of product and
customer demand as well.
(1)
̂
Yt
=𝜇+𝜙
1
.Y
t−1
+𝜙
1
.Y
t−1
+... +𝜙
1
.Y
t−1
−𝜃
1
.e
t−1
−... −𝜃
q
.e
t−q
0
200
400
600
800
1000
1200
Demand of products
Months
Fig. 2 The trend of demand between 2017 and 2020 (48months)
Table 1 Forecasting demands
for the year 2021 (12months) Month 1 2 3 4 5 6 7 8 9 10 11 12
Demand 526 502 645 697 723 576 518 599 464 520 575 608

Environmental Science and Pollution Research
1 3
Before proposing the mathematical model, we have con-
sidered some assumptions that are as follows:
• The mathematical model is assumed to be multi-period,
multi-product, and multi-echelon.
• The demand is estimated by the ARIMA time series
model.
• Recovered components will be taken to the factory ware-
house after rebuilding to be distributed to the network.
• The shortage has been considered in the model and is
allowed in all periods of time.
• The transportation system of factories has two states:
first, the factory’s trucks have been used for shipping
products in the network. Second, the transportation com-
panies are utilized for having some alternatives to the
model to decrease the total costs of transportation in the
system.
Symbols and sets:
Symbols used in the mathematical model of this research
are as follows:
i
index of components
(i∈I
)
j
index of products
(j∈J)
k
index of suppliers
(k∈K)
m
index of manufacturers
(m∈M)
n
index of distribution centers
(n∈N)
l
index of recycling and recovery units of components
(l∈I)
q
index of customers
(q∈Q)
𝛼
index of factories’ vehicles
(𝛼∈V)
𝛼
′
index of rental cars of transportation companies
(
𝛼
�
∈V
�)
t
index of periods
Subsets
Jj
The set of products that have the component j
Parameters
Sjm
Sales price of each unit of the product j by the
manufacturer m
Cjm
The final production cost of each unit of the prod-
uct j by the manufacturer m
Yqt
The service level of customer q in period t
Djqt
Demand for the product j by the customer q in
period t
dj
Disassembly cost for separation of product j
fi
The separation cost of component i
hi
Destruction or burial cost of component i
oil
The cost of recovering the component i at the
recovery center l
rik
The purchase price of component i that is sup-
plied through the supplier k
Coj
The collection cost of product j
O′
j
The recovery cost of product j
Glt
The maximum capacity of recovery center l in
period t
Cap1t
Maximum capacity of the product recovery unit
in period t
Cap2t
Maximum capacity of disassembly and separation
unit in period t
Bk
Maximum capacity of supplier k
𝜐n
Maximum capacity of distribution center n
Hjt
Maximum return percentage of product j in period t
Oit
Maximum percentage of component i that is usa-
ble in period t
Am
Maximum capacity of factory m
O′′
j
Maximum percentage of returned product j that
is recoverable
qijt
The number of components i required to produce
a unit of product j in period t
Trs ikm
The transportation cost of the component i from
the supplier k to the producer m
Trrjq
The transportation cost of product j from cus-
tomer q to the product collection unit
Tr′
jmn𝛼
 The transportation cost of the product j from the
factory m to the distribution center n by the truck
α (owned by the factory m)
Tr′′
jmn
𝛼
′
The transportation cost of the product j from the
factory m to the distribution center n by the truck
𝛼
′
(owned by the transportation companies)
Trd jnq
The transportation cost of product j from distribu-
tion center n to customer q
Tr𝜔j
The transportation cost of the product j from the
product collection unit to the product recovery
unit.
Trf jn
The transportation cost of the product j from the
product recovery unit to distribution center n
Tra j
The transportation cost of the product j from the
collection unit to disassembly and separation unit
Trbil
The transportation cost of the component i from
disassembly and separation unit to the component
recovery center l
Trc ilm
The transportation cost of the component i from
recovery center l to the manufacturer m
scoj
The cost of not meeting the demand for the prod-
uct j
Cap3𝛼t
Maximum number of trucks α in period t
Cap4𝛼
′
t
Maximum number of trucks
𝛼
′
belonging to the
transportation company in period t

Environmental Science and Pollution Research
1 3
Decision variables
Pjmnt
The number of products j produced by the manu-
facturer m and sent to the distribution center n in
the period t
Crpjqt
The number of products j returned by the customer
q in period t
Qikmt
The number of components i to be supplied by the
supplier k and sent to the manufacturer m in period
t
wj
The number of recoverable products j brought from
the collection unit to be recovered.
Tilt
The number of components i disassembled by the
disassembly unit and sent to the component recov-
ery center l in period t
Xilmt
The number of components i that should be rebuilt
by the recovery unit l and sent to the manufacturer
m in period t
V′
i
The number of components i that should be
destroyed.
R′
jt
The number of products j collected to be sent to the
disassembly segment in period t
Y′
jnt
The number of recovered products j sent to the
warehouse of the distribution center n in period t
Yjnqt
The number of products j sent from the distribution
center n to the customer q in period t
nhljqt
The number of product j shortages for customer q
in period t
X′
jmn𝛼t
The number of products j sent by the truck α from
the manufacturer m to the distributor n in period t
X′′
jmn𝛼
′
t
The number of products j sent by the truck
𝛼
′
(owned by the transportation companies) from the
manufacturer m to the distributor n in period t
Mathematical formulation
The proposed mathematical model in this section is formu-
lated as Mixed Integer Linear Programming (MILP) model.
Therefore, We have
The objective function includes minimizing the total cost
of the system which is shown by Eq.(2).
(2)
MinC
=
∑
i
∑
k
∑
m
∑
t
rik∙Qikmt +
∑
j
∑
q
∑
t
Coj∙Crpjqt +
∑
O�
j∙Wj+
∑
dj∙R�
jt
+∑hi∙V�
i+∑
m
∑
l
∑
i
∑
t
Oil∙Xilmt +∑
j
∑
m
∑
n
Cjm∙Pjm +∑
i
∑
l
∑
t
fi∙T
ilt
+∑
a
∑
n
∑
m
∑
j
∑
t
X�
jmnat∙Tr�
jmna +∑
a
∑
n
∑
m
∑
j
Qikmt∙Trs ikm
+∑
a
∑
n
∑
m
∑
j
∑
t
X��
jmnat∙Tr��
jmna +∑
j
∑
n
∑
t
Yjnt∙Tr fjn +∑Wj∙Tr w J
+∑
j
∑
q
∑
t
Crpjqt∙Trrjq +∑
a
∑
n
∑
m
∑
j
Yjnqt∙T rdjnq
Model constraints
(3)
∑
m∈M
Xilmt =Tilt∀i,l,
t
(4)
W
j=O
��
j
∑
q∈Q
Cpjqt∀j,t
(5)
R
�
jt =
(
1−O��
j
)
∑
q∈Q
Crpjqt∀j,t
(6)
∑
q∈Q
Yjnqt =
∑
m∈M
Pjmnt +Y
�
jnt∀j,n,
t
(7)
∑
n∈N
Y
�
jnt =Wj∀j,
t
(8)
Crp
jqt =
∑
n∈N
Hjt.Yjnqt ∀j,q,
t
(9)
D
jqt.γqt =
∑
n∈N
Yjnqt +nhljqt∀j,q,
t
(10)
∑
l∈L
Tilt =Oit
∑
j∈Ji
qij.R
�
jt∀i,t
(11)
V�
i=(1−Oit)
∑
j∈Ji
qij.R
�
jt∀i,
t
(12)
∑
i∈I
∑
m∈M
Qikmt ≤Bk∀k,
t
(13)
∑
𝛼∈𝛼m
Xjmn𝛼t+
∑
𝛼
Xjmn𝛼t=Pjmnt∀j,m,n,
t
(14)
∑
j∈J
∑
n∈N
Pjmnt ≤Am∀m,
t
(15)
∑
j∈J
∑
q∈Q
Yjnqt ≤𝜐n∀n,
t
(16)
∑
j∈J
∑
n∈N
Y
�
jnt ≤Cap1t∀t
(17)
∑
i∈I
∑
l∈L
Tilt ≤Cap2t∀
t

Environmental Science and Pollution Research
1 3
Constraint (3) states that the number of disassembled
components is equal to the number of components recov-
ered by the component recovery centers. Constraint (4)
indicates that the usable products are equal to a percent-
age of returned products. Constraint (5) indicates that
unusable products are equal to a percentage of returned
products. Generally, constraints (4) and (5) show the
percentage of the products recovered by recovery centers
and the percentage of products collected to be sent to the
separation and disassembly units. Constraint (6) states
that the number of products sent to customers is equal
to the sum of recovered products and produced prod-
ucts. Constraint (7) indicates that the number of usable
collected products is equal to the number of recovered
products. Constraint (8) shows that returned products are
equal to a percentage of products purchased by custom-
ers. Constraint (9) ensures that the minimum demand
should be met, and the shortage should be minimized.
Constraints (10) and (11) specify the number of usable
and unusable components in the disassembly unit and
determine the percentage of waste and usable compo-
nents. Constraint (12) specifies the maximum capacity
of supplier k. Constraint (13) states that the number
of produced components sent to distribution centers
is equal to the number of products sent by the factory
and rental trucks. The constraints (14) and (15) show,
respectively, the capacity constraints of the factories and
the distribution centers. Constraints (16) and (17) indi-
cate, respectively, the capacity constraints of the product
recovery unit and disassembly section. Constraint (18)
shows the capacity constraints for component recovery
units. Constraints (19) and (20) also indicate the capac-
ity constraints of containers. Constraint (21) states that
the number of produced components is equal to the total
number of recovered components and purchased compo-
nents from suppliers. Finally, constraint (22) shows the
nature of decision variables in the model.
(18)
∑
i∈I
∑
m∈M
Xilmt ≤Glt∀l,
t
(19)
∑
j∈J
∑
m∈M
∑
n∈N
X
�
jmn𝛼t≤Cap3t∀𝛼,
t
(20)
∑
j∈J
∑
m∈M
∑
n∈N
X
��
jmn𝛼
�t≤Cap4t∀𝛼
�
,
t
(21)
∑
n∈N
∑
j∈Ji
qij.Pjmnt ≤
∑
l∈L
Xilmt +
∑
k∈K
Qikmt∀i,m,t
(22)
P
jmnt,Crpjqt ,Qikmt ,Wj,Tilt ,Xilmt,V
′
i,R
′
jt,Y
′
jnt,Yjnqt ,nhljqt ,X
′
jmn𝛼t,X
′′
jmn
𝛼
′
t
≥
0
Solving algorithm
In this study, the exact solution algorithm is used to solve the
model on a small and medium scale, and the genetic algo-
rithm (GA) is applied to solve the model on a large scale.
The flowchart of the GA, which displays an overview of how
the algorithm is executed, is shown in Fig.3. The selection
of the fittest individuals from a population begins the natural
selection process. They generate offspring who inherit the
parents’ qualities and are passed down to the next genera-
tion. If parents are physically active, their children will be
fitter than they are and have a better chance of surviving.
This procedure will continue to iterate until a generation of
the fittest individuals is discovered.
Display ofthechromosome
The first step after determining the technique used to convert
each solution to a chromosome is to create an initial popu-
lation of chromosomes. At this stage, the initial solution is
usually generated by a random function. Here, for example,
the chromosome of the variable nhljqt is shown in Fig.4 as
follows:
As we defined earlier, the variable nhljqt is the number of
shortages of product j for customer q in period t. The two
indices of q and t are considered columns, and the index of
j is regarded as a row to generate the initial chromosome of
this problem. For instance, the number 96 shows the value
of product 2, customer 2 in time period 2. This number will
go through GA procedure as we defined in Fig.4 to generate
its optimal number at the end of the maximum iteration of
the algorithm, so this number is not an optimal number at
this stage for the variable nhljqt.
Genetic operations
Genetic operations imitate the inherited gene transfer pro-
cess for the creation of new children in each generation.
An essential part of the genetic algorithm is the creation of
new chromosomes called children through some of the old
chromosomes called parents. In general, this operation is
performed by two major operators: mutation operator and
crossover operator.
Crossover operators
There are the operators that select one or more points from
two or more solutions and change their values. These opera-
tors consider a solution and exchange some locations of the
solution with other solutions for creating new solutions.
These operators are called crossover operators. In fact, on
the remaining chromosomes of the initial population, a

Environmental Science and Pollution Research
1 3
crossover is performed. Here in Fig.5, a two-point crosso-
ver is used.
Mutation operators
There are the operators that select one or more genes from
a chromosome and change their values. In these operators,
one or more locations of a character string with a specific
length are considered, and the values of the characters in
those locations are changed. In this type of operator, the
solution information is used to create another answer. This
change may be too little or too much, and too little or too
much information is used based on the amount of change. In
other words, the more the differences are, the solution will
be more random; and this randomness is helpful for enter-
ing the new genetic materials into the population. When the
population converges towards a particular solution, the prob-
ability of a mutation must be increased to prevent this, and
vice versa; if the population has non-identical solutions, the
Fig. 3 Flowchart of the genetic
algorithm Start
Parameter tuning
Generate primary population
Stopping
CriteriaSelect best solutionEnd
Generation/copy Selection
Cross over
Mutation
Calculation objective functions
Fig. 4 Chromosome representation

Environmental Science and Pollution Research
1 3
probability of mutation must be reduced (Fig.6). Here, for a
mutation operator, a row is randomly selected and reversed.
Stopping criteria
After the birth of children generating a new generation and
calculating its fitness function, there is a need for a criterion
to end the algorithm that we refer to as some of the most
common ones.
• Implementation of the program is often carried out for
a predetermined number of generations. For example, at
the beginning of the program, the number of generations
is 50 for repetition.
• Sometimes, computing time is considered a criterion to
stop the algorithm.
• Sometimes, this criterion is based on the extent of the
dispersion of genes within the population.
In the problem-solving approach of some algorithms,
time, and in some others, a maximum number of genera-
tions is used.
For statistical analysis, we use the least significant differ-
ence method (LSD) to find significant differences (Chouhan
etal. 2021, Arani etal. 2021, Dehdari Ebrahimi etal. 2017,
Ahmed etal. 2020). Figure7 shows the output of the LSD
method using the MINITAB statistical software. According
to the results, it can be concluded that the genetic algorithm
has a better performance in a discrete state than the rest of
the algorithms.
Computational results
After determining the optimal parameters of the algorithms,
for evaluating the performance of the meta-heuristic method,
the exact solution is considered. Due to the high solution
time of the exact methods for large-scale problems, prob-
lem solution is not possible with the GAMS software, so
the meta-heuristic method has been applied in this study.
According to the complexity of solving the mathematical
model by increasing the scale of the problem, calculating the
optimal amount is a complicated task. Therefore, the judg-
ment criterion is the solution of the GAMS software, which
is a solution close to optimal. Table2 shows the scale of the
test problems at a small level.
Table3 shows the results of the model solution on a
small and medium scale. The first column of the table is
Fig. 5 Two-point crossover operator
Fig. 6 Mutation operator
0.16
0.15
0.14
0.13
0.12
0.11
0.10
RDIfor GA
Interval Plot of GA
95%CIfor theMean
Fig. 7 95% confidence interval for the RDI objective function

Environmental Science and Pollution Research
1 3
the problem number. The first five problems are on a small
scale, and the next five are on a medium scale. According
to the results obtained from the problem-solving algorithms
and the GAMS software, we found that on a small scale and
in most cases, the solution obtained from algorithms was
better than the solution proposed by the GAMS software
which shows the efficiency of the algorithms. By increasing
the scale of the problem, the GAMS software cannot solve
the problem at a reasonable time, but other algorithms give
a near-optimal solution at a very appropriate time. As shown
in Table3, the average error is 0.7%. Also, the problem-
solving time of the exact solution is significantly increased
by increasing the scale of the problem, while this time for
the genetic algorithm is much lower and has a lower rate, so
given the above explanations, the genetic algorithm can be
trusted to solve large-scale problems.
To solve the problem in large scale, there are 30 product
types, 35 customers, 2 periods, 4 suppliers, 2 manufactur-
ers, 2 distributors, and 3 recycling centers. Table4 shows
the results of a large-scale model solution. This table shows
the shortage of product j for the customer q in the period t,
which is the result of the variable
nhljqt
.
Table5 shows the number of returned products j in period
t by customer q. This table is the result of the variable
crpjpt
.
Figure8 shows the value of objective functions calculated
by the genetic algorithm in terms of various parameters. As
can be seen, the calculated values have a reasonable con-
vergence, so we can also rely on the results of a large-scale
model solution that can also be trusted.
Figure9 shows the relationship between the rates of
returned products in each period with the value of the objec-
tive function. It is evident that increasing the rate of return
could increase the cost. For example, an increase in the rate
of return up to 94 units has resulted in a cost of 434,418
$ and growing it to 100 units leads to result in a cost of
482,687 units.
Figure10 shows the relationship between the service lev-
els in each period with the value of the objective function.
As it is evident, increasing service level leads to reductions
in costs. For example, an increase in service level up to 1.7
units has resulted in a cost of 490,318 units, and an increase
of up to 2 units leads to result in a cost of 438,789 units.
Conclusion
To design an efficient supply chain network, organizations
need to design an efficient transportation network. In gen-
eral, the design of the supply chain network is considered
one of the essential issues in the field of optimization. In this
research, a closed-loop supply chain network was studied
and modeled in the form of a MILP model. The objective
of this study was to minimize the total costs considering a
specific service level to demand, as well as considering the
cost of not satisfying the total amount of demand. There-
fore, demand points have a certain amount of demand that
its certain level must be supplied and, in proportion to the
non-satisfied amount of demand, the related cost is added to
the objective function. Also, since this problem has a high
computational complexity, it is categorized as NP-hard, so
the genetic algorithm was used to solve the proposed model.
The results of the sensitivity analysis indicated that increas-
ing the rate of return could increase the total costs of the
whole network.
One of the most important management insights that we
can pinpoint for this study is that the proposed model has
been solved by GA that has wide applicability to solve vari-
ous large-size problems in reality. Indeed, the managers and
decision-makers can get benefit by applying the proposed
Table 2 Small scale selected
problems No Supplier no Factory no Distribution
center no
Customer no Product no Factor
multipli-
cation
1 1 2 2 3 1 12
2 1 2 3 3 2 36
3 2 2 2 4 2 64
4 2 3 3 4 2 144
5 3 2 3 5 3 270
Table 3 Results of model solving in small and medium scale
No GAMS GA Error %
f1
Time(s)
f1
Time(s)
f1
1 8150.2 1 8150.2 1 0
2 8342.4 50 8343.5 5 0.01
3 8609.4 88 8701.1 7 1
4 8972.5 112 9036.1 12 0.7
5 9385.0 215 9432.0 13 0.4
6 12,321.1 1018 12,511.6 27 1.5
7 14,159.2 3293 14,160.8 30 0
8 16,774.9 3892 17,023.3 37 1.4
9 17,819.7 5826 18,005.5 50 1.0
10 19,218.8 8797 19,588.8 63 1.8

Environmental Science and Pollution Research
1 3
methodology in their industry by minimizing costs of the
supply chain network as well as decreasing the shortage of
their products during transmission of goods in the network.
Therefore, the results of this research can be useful and
efficient for industries such as wood and paper, petrochemi-
cal industries, and medical equipment. The main limitation
of this research are as follows:
• The ARIMA time series model utilized in this study can
be used for data with constant trends overall. If someone
has a database without a stable trend, they cannot use the
ARIMA model. In this way, it is highly suggested to use
some other techniques like the Long Short-Term Memory
(LSTM) to estimate demand.
Table 4 Shortage level of
product j for customer q in
period t
nhljqt
Value
nhljqt
Value
nhljqt
Value
nhljqt
Value
nhl1,13,1
208
nhl16,6,1
736
nhl1,13,2
569
nhl17,33,2
807
nhl
1
,
5
,1
720
nhl
17
,
5
,1
786
nhl
2
,
27
,2
439
nhl
18
,
2
,2
377
nhl1,22,1
746
nhl17,7,1
718
nhl3,19,2
261
nhl19,22,2
596
nhl
2
,
28
,1
488
nhl
18
,
10
,1
745
nhl
4
,
11
,2
207
nhl
19
,
24
,2
190
nhl
3
,
5
,1
669
nhl
19
,
12
,1
181
nhl
5
,
30
,2
137
nhl
20
,
23
,2
616
nhl
3
,
14
,1
529
nhl
20
,
13
,1
411
nhl
6
,
23
,2
724
nhl
20
,
8
,2
496
nhl
4
,
11
,1
737
nhl
21
,
32
,1
397
nhl
7
,
9
,2
811
nhl
20
,
29
,2
528
nhl
5
,
34
,1
585
nhl
21
,
16
,1
365
nhl
7
,
6
,2
203
nhl
21
,
33
,2
778
nhl
6
,
29
,1
688
nhl
22
,
20
,1
280
nhl
7
,
7
,2
299
nhl
22
,
34
,2
378
nhl
6
,
30
,1
822
nhl
23
,
29
,1
788
nhl
8
,
35
,2
154
nhl
23
,
4
,2
264
nhl
7
,
25
,1
139
nhl
24
,
19
,1
746
nhl
9
,
1
,2
726
nhl
24
,
26
,2
304
nhl
8,8
,1
145
nhl
24,2
,1
277
nhl
10,10,
2
822
nhl
25,28,
2
831
nhl
9
,
32
,1
434
nhl
25
,
32
,1
499
nhl
10
,
12
,2
726
nhl
26
,
32
,2
310
nhl10,9,1
591
nhl25,17,1
183
nhl11,25,2
700
nhl27,28,2
219
nhl
11
,
2
,1
182
nhl
26
,
18
,1
154
nhl
11
,
18
,2
787
nhl
27
,
14
,2
696
nhl12,35,1
520
nhl26,21,1
665
nhl11,17,2
442
nhl28,17,2
176
nhl
13
,
1
,1
857
nhl
26
,
26
,1
690
nhl
12
,
10
,2
851
nhl
29
,
28
,2
364
nhl13,33,1
718
nhl27,24,1
835
nhl13,16,2
341
nhl30,19,2
100
nhl
14
,
27
,1
223
nhl
28
,
21
,1
453
nhl
14
,
21
,2
847
nhl
30
,
21
,2
140
nhl15,25,1
424
nhl29,23,1
136
nhl15,3,2
420
nhl
15
,
4
,1
804
nhl
30
,
6
,1
435
nhl
16
,
5
,2
464
Table 5 The number of returned
products j in period t by the
customer q
crpjpt
Value
crpjqt
Value
crpjqt
Value
crpjqt
Value
crp
1
,
15
,1
464
crp
16
,
5
,1
671
crp
1
,
13
,2
108
crp
16
,
6
,2
836
crp2,2,1
693
crp17,2,1
592
crp2,10,2
566
crp17,4,2
489
crp
3
,
13
,1
344
crp
18
,
14
,1
720
crp
3
,
19
,2
376
crp
18
,
18
,2
347
crp4,9,1
520
crp19,11,1
230
crp4,1,2
702
crp19,11,2
579
crp
5
,
9
,1
258
crp
20
,
11
,1
415
crp
5
,
11
,2
407
crp
20
,
8
,2
359
crp6,20,1
165
crp20,4,1
470
crp6,20,2
757
crp20,9,2
862
crp
6
,
15
,1
203
crp
21
,
7
,1
493
crp
6
,
15
,2
350
crp
21
,
9
,2
615
crp6,15,1
533
crp21,7,1
896
crp7,7,2
445
crp22,16,2
478
crp
7
,
1
,1
221
crp
22
,
12
,1
137
crp
8
,
12
,2
625
crp
23
,
14
,2
431
crp8,10,1
235
crp23,16,1
261
crp9,19,2
655
crp24,5,2
363
crp
9
,
19
,1
117
crp
24
,
8
,1
250
crp
10
,
6
,2
237
crp
25
,
8
,2
787
crp10,6,1
108
crp25,8,1
192
crp10,11,2
466
crp26,17,2
717
crp
11
,
18
,1
163
crp
26
,
17
,1
342
crp
11
,
17
,2
107
crp
27
,
3
,2
376
crp
12
,
3
,1
863
crp
27
,
3
,1
791
crp
12
,
3
,2
321
crp
28
,
3
,2
161
crp
13
,
2
,1
712
crp
28
,
20
,1
495
crp
13
,
2
,2
534
crp
29
,
13
,2
633
crp
14
,
3
,1
164
crp
29
,
13
,1
196
crp
14
,
3
,2
836
crp
30
,
15
,2
196
crp
15
,
12
,1
144
crp
30
,
15
,1
895
crp
15
,
12
,2
183
crp
30
,
17
,2
582

Environmental Science and Pollution Research
1 3
• The proposed model can be tested on other meta-heuris-
tics algorithms like Particle Swarm Optimization (PSO)
and Ant Colony Optimization (ACO) and then compared
together to find the best algorithm in terms of their per-
formances.
Several aspects can be considered for future research,
which is as follows:
• Considering the capacity constraint for inventory storage
in factories, warehouses, and distribution centers,
• Considering the facility location problem for factories
and distribution centers,
• Considering a variety of sales policies such as gradual
discounts and incremental discounts for production costs,
• Considering the single-source state to meet demands, it
means that each customer is only connected with one
distribution center, and
• Fuzzification of numbers of the problem and getting
closer to the real world.
Author contribution Shahab Safaei: conceptualization. Peiman Gha-
semi: mathematical model, software, investigation, methodology. Far-
iba Goodarzian: data curation, writing—reviewing and editing. Mohsen
Momenitabar: data curation, writing—reviewing and editing.
Availability of data and materials The data that support the findings
of this study are available from the corresponding author upon reason-
able request.
Declarations
Ethical approval and competing interests All authors have participated
in (a) conception and design, or analysis and interpretation of the data;
(b) drafting the article or revising it critically for important intellec-
Fig. 8 Convergence of the
genetic algorithm
80
82
84
86
88
90
92
94
96
98
100
350000 370000 390000 410000 430000 450000 470000 490000
the number of returned products
value of the objective function
Fig. 9 Changes in the number of costs based on returned products
400000
420000
440000
460000
480000
500000
520000
540000
1.51.6 1.71.8 1.
92
optimal cost
service level
Fig. 10 Changes in the number of costs based on service level

Environmental Science and Pollution Research
1 3
tual content; and (c) approval of the final version. This manuscript
has not been submitted to, nor is under review at, another journal or
other publishing venue and has not self-plagiarism. The authors have
no affiliation with any organization with a direct or indirect financial
interest in the subject matter discussed in the manuscript.
Consent to participate and consent to publish Furthermore, we hereby
transfer the unlimited rights of publication of the above-mentioned
paper in whole to “Environmental science and pollution research.” The
corresponding author signs for and accepts responsibility for releasing
this material on behalf of any and all co-authors. This agreement is to
be signed by at least one of the authors who have obtained the assent of
the co-author(s) where applicable. After submission of this agreement
signed by the corresponding author, changes of authorship or in the
order of the authors listed will not be accepted.
Competing interests The authors declare no competing interests.
References
Ahmed, M. M., Iqbal, S. S., Priyanka, T. J., Arani, M., Momenitabar,
M., & Billal, M. M. (2020, August). An environmentally sustain-
able closed-loop supply chain network design under uncertainty:
application of optimization. InInternational Online Conference
on Intelligent Decision Science(pp. 343–358). Springer, Cham.
Ali I, Modibbo UM, Chauhan J, Meraj M (2021) An integrated multi-
objective optimization modelling for sustainable development
goals of India. Environ Dev Sustain 23(3):3811–3831
Almaraj II, Trafalis TB (2019) An integrated multi-echelon robust
closed-loop supply chain under imperfect quality production. Int
J Prod Econ 218:212–227
Antucheviciene J, Jafarnejad A, Amoozad Mahdiraji H, Razavi Hajia-
gha SH, Kargar A (2020) Robust multi-objective sustainable
reverse supply chain planning: an application in the steel industry.
Symmetry 12(4):594
Arani M, Chan Y, Liu X, Momenitabar M (2021) A lateral resup-
ply blood supply chain network design under uncertainties. Appl
Math Model 93:165–187
Chan FT, Jha A, Tiwari MK (2016) Bi-objective optimization of
three echelon supply chain involving truck selection and load-
ing using NSGA-II with heuristics algorithm. Appl Soft Comput
38:978–987
Cheraghalipour A, Paydar MM, Hajiaghaei-Keshteli M (2018) A bi-
objective optimization for citrus closed-loop supply chain using
Pareto-based algorithms. Appl Soft Comput 69:33–59
Chouhan VK, Khan SH, Hajiaghaei-Keshteli M (2021) Metaheuristic
approaches to design and address multi-echelon sugarcane closed-
loop supply chain network. Soft Comput 25(16):11377–11404
Dehdari Ebrahimi Z, Momeni Tabar M (2017) Design of mathematical
modeling in a green supply chain network by collection centers in
the environment. Environmental Energy and Economic Research
1(2):153–162
Eydi A, Fazayeli S, Ghafouri H (2020) Multi-period configuration of
forward and reverse integrated supply chain networks through
transport mode. Scientia Iranica 27(2):935–955
Flygansvær B, Dahlstrom R, Nygaard A (2018) Exploring the pursuit
of sustainability in reverse supply chains for electronics. J Clean
Prod 189:472–484
Gao X, Cao C (2020) A novel multi-objective scenario-based optimiza-
tion model for sustainable reverse logistics supply chain network
redesign considering facility reconstruction.J Cleaner Prod,270,
122405
Gerdrodbari MA, Harsej F, Sadeghpour M, Aghdam MM (2021) A
robust multi-objective model for managing the distribution of
perishable products within a green closed-loop supply chain. J
Industr Manag Opt
Ghaderi H, Asadi M, Shavalpour S (2016) A switchgrass-based bioeth-
anol supply chain network design model under auto-regressive
moving average demand. J Renew Energy Environ 3(3):1–10
Ghasemi P, Khalili-Damghani K, Hafezolkotob A, Raissi S (2017) A
decentralized supply chain planning model: a case study of hard-
board industry. The International Journal of Advanced Manufac-
turing Technology 93(9):3813–3836
Goodarzian, F., Kumar, V., & Ghasemi, P. (2021b). A set of efficient
heuristics and meta-heuristics to solve a multi-objective pharma-
ceutical supply chain network.Computers & Industrial Engineer-
ing,158, 107389.
Goodarzian F, Taleizadeh AA, Ghasemi P, Abraham A (2021a)
An integrated sustainable medical supply chain network dur-
ing COVID-19.Engineering Applications of Artificial Intelli-
gence,100, 104188
Habibi MK, Battaïa O, Cung VD, Dolgui A (2017) Collection-
disassembly problem in reverse supply chain. Int J Prod Econ
183:334–344
Hassanpour A, Bagherinejad J, Bashiri M (2019) A robust leader-
follower approach for closed loop supply chain network design
considering returns quality levels. Comput Ind Eng 136:293–304
Heydari J, Govindan K, Sadeghi R (2018) Reverse supply chain coor-
dination under stochastic remanufacturing capacity. Int J Prod
Econ 202:1–11
Kim J, Do Chung B, Kang Y, Jeong B (2018) Robust optimization
model for closed-loop supply chain planning under reverse logis-
tics flow and demand uncertainty. J Clean Prod 196:1314–1328
Li J, Wang Z, Jiang B, Kim T (2017) Coordination strategies in a
three-echelon reverse supply chain for economic and social ben-
efit. Appl Math Model 49:599–611
Margolis JT, Sullivan KM, Mason SJ, Magagnotti M (2018) A multi-
objective optimization model for designing resilient supply chain
networks. Int J Prod Econ 204:174–185
Meng K, Lou P, Peng X, Prybutok V (2016) A hybrid approach for
performance evaluation and optimized selection of recoverable
end-of-life products in the reverse supply chain. Comput Ind Eng
98:171–184
Modibbo, U. M., Arshad, M., Abdalghani, O., & Ali, I. (2021). Opti-
mization and estimation in system reliability allocation prob-
lem.Reliability Engineering & System Safety,212, 107620.
Modibbo UM, Umar I, Mijinyawa M, Hafisu R (2019) Genetic algo-
rithm for solving university timetabling problem. Amity Journal
of Computational Sciences (AJCS) 3(1):43–50
Mohtashami Z, Aghsami A, Jolai F (2020) A green closed loop supply
chain design using queuing system for reducing environmental
impact and energy consumption.Journal of cleaner produc-
tion,242, 118452
Mosallanezhad B, Chouhan VK, Paydar MM, Hajiaghaei-Keshteli M
(2021) Disaster relief supply chain design for personal protection
equipment during the COVID-19 pandemic.Applied Soft Com-
puting,112, 107809.
Mota B, Gomes MI, Carvalho A, Barbosa-Povoa AP (2018) Sustain-
able supply chains: an integrated modeling approach under uncer-
tainty. Omega 77:32–57
Parast ZZD, Haleh H, Darestani SA, Amin-Tahmasbi H (2021) Green
reverse supply chain network design considering location-routing-
inventory decisions with simultaneous pickup and delivery.Envi-
ronmental Science and Pollution Research, 1–22
Pedram A, Yusoff NB, Udoncy OE, Mahat AB, Pedram P, Babalola A
(2017) Integrated forward and reverse supply chain: A tire case
study. Waste Manage 60:460–470

Environmental Science and Pollution Research
1 3
Phuc PNK, Vincent FY, Tsao YC (2017) Optimizing fuzzy reverse sup-
ply chain for end-of-life vehicles. Comput Ind Eng 113:757–765
Sajedi S, Sarfaraz AH, Bamdad S, Khalili-Damghani K (2020) Design-
ing a sustainable reverse logistics network considering the con-
ditional value at risk and uncertainty of demand under different
quality and market scenarios. Int J Eng 33(11):2252–2271
Shadkam E (2021) Cuckoo optimization algorithm in reverse logistics:
a network design for COVID-19 waste management.Waste Man-
agement & Research, 0734242X211003947
Sobotka A, Sagan J, Baranowska M, Mazur E (2017) Management of
reverse logistics supply chains in construction projects. Procedia
Engineering 208:151–159
Wang G, Gunasekaran A (2017) Operations scheduling in reverse sup-
ply chains: Identical demand and delivery deadlines. Int J Prod
Econ 183:375–381
Wu Z, Kwong CK, Aydin R, Tang J (2017) A cooperative negotiation
embedded NSGA-II for solving an integrated product family and
supply chain design problem with remanufacturing consideration.
Appl Soft Comput 57:19–34
Xu Z, Elomri A, Pokharel S, Zhang Q, Ming XG, Liu W (2017)
Global reverse supply chain design for solid waste recycling
under uncertainties and carbon emission constraint. Waste Man-
age 64:358–370
Yu H, Solvang WD (2018) Incorporating flexible capacity in the plan-
ning of a multi-product multi-echelon sustainable reverse logistics
network under uncertainty. J Clean Prod 198:285–303
Zheng B, Yang C, Yang J, Zhang M (2017) Pricing, collecting and con-
tract design in a reverse supply chain with incomplete information.
Comput Ind Eng 111:109–122
Publisher's note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.