**Published at : ** 07 Dec 2023

**Volume :** **IJtech**
Vol 14, No 7 (2023)

**DOI :** https://doi.org/10.14716/ijtech.v14i7.6710

Xu, W., Luis, M., Yuce, B., 2023. A Hybrid Method for The Closed-loop Supply Chain to Minimize Total Logistics Costs.

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Wangyue Xu | Exeter Digital Enterprise Systems (ExDES) Laboratory, Department of Engineering, Faculty of Environment, Science and Economy, University of Exeter, Streatham Campus, Exeter, EX4 4QJ, United Kingdom |

Martino Luis | Exeter Digital Enterprise Systems (ExDES) Laboratory, Department of Engineering, Faculty of Environment, Science and Economy, University of Exeter, Streatham Campus, Exeter, EX4 4QJ, United Kingdom |

Baris Yuce | Exeter Digital Enterprise Systems Laboratory, Department of Engineering, Faculty of Environment, Science and Economy, University of Exeter |

Abstract

Crow search algorithm for binary optimization
(BinCSA) is currently used in some ideal models of the uncapacitated facility
location problem (UFLP), but studies on its use in real-world supply chain
cases remain limited. Therefore, this study aimed to address the gap by
introducing a hybrid method that combined the BinCSA with an exact method to
solve a CLSC problem, including location allocation, transportation, and
supplier selection challenges. The initial sections of the study included
theoretical foundations and experimental results of the BinCSA. Subsequently,
how the BinCSA works in the proposed hybrid method was discussed, and the computational
results were showed to evaluate the performance of the proposed method.

Crow search algorithm; Closed-loop supply chain; Facility location problem; Hybrid method

Introduction

The forward supply chain is a network connecting
facilities and distribution mechanisms to manage the transformation of raw
materials into finished products and deliver them to end customers. In
contrast, the reverse supply chain focuses on the return flow of materials from
customers to suppliers, with the aim of maximizing profits from returned
products or minimizing the total costs of return processes (Kannan *et al.*, 2010). By emphasizing the backward
flow, the reverse supply chain offers significant opportunities for recycling
more materials and promoting environmental friendliness throughout supply chain
activities.

The Closed-loop
Supply Chain
(CLSC) includes both the forward and reverse supply chain. The forward supply
chain facilitates the movement of material flow from upstream suppliers to
downstream customers, while the reverse supply chain manages the return flow
from downstream customers back to upstream suppliers for potential recycling
and reuse. A holistic manifestation of this concept is the CLSC, which requires
a comprehensive assessment of its architectural blueprint. Unlike solely
dissecting the forward and reverse supply chain, the CLSC model demands a
holistic perspective, evaluating not only the performance of the forward supply
chain but also the reverse. The overall performance is considered an entirety,
avoiding a simplistic split into two distinct dimensions.

A
significant increase in scholarly efforts has been on facility location models, addressing questions about the
number and allocation of facilities, locations, and the processing of products,
including recycling centers in the CLSC network (Zhen, Huang,
and Wang, 2019). The significance of
sustainability in CLSC network design is sometimes overlooked while existing
models often prioritize total cost minimization or total profit maximization.
In this study landscape, facility location models for the CLSC network have
been defined by some scholars, reflecting a dedicated effort to optimize
decision variables in both forward and reverse channels (Amin and Zhang, 2012). In similar studies, total cost
minimization or total profit maximization were regarded as fundamental
objective functions. Moreover, the relevance of sustainability was easily
ignored in CLSC network design despite numerous calls for its importance by international
organizations, societies, and governments in recent decades (Pati, Vrat, and
Kumar 2008).
Although sustainability in supply chain has been recently mentioned in the
study, the number of published papers was still limited (Azadi *et al.,* 2015; Brandenburg *et
al.,* 2014; Seuring, 2013).

In
addressing these challenges, this study introduced Crow Search Algorithm (CSA),
a population-based optimization algorithm inspired by the behavior of crow, as
introduced by Askarzadeh (2016). Previous
studies showed the superior efficiency of CSA when compared to established
algorithms such as Genetic Algorithm (GA), Harmony Search (HS), and Particle
Swarm Optimization (PSO) (Askarzadeh, 2016).
Due to the promising capabilities of CSA and the limited literature on
sustainability in supply chain, this study proposed a CLSC network model for a
realistic problem including location-allocation, transportation, and supplier
selection. A novel hybrid method was used to address this problem which
integrated an exact method with CSA for solving the proposed CLSC mathematical
model.

**2. ****Literature Review**

The
concept of a sustainable supply chain includes managing material flows,
information, and funds, as well as collaboration between enterprises along
supply chain while addressing the three aspects of sustainable development,
namely environmental, social, and economic simultaneously (Meixell and Luoma, 2015; Eskandarpour *et al., *2015;
Brandenburg *et al.,* 2014). Adopting sustainability as a strategic
tool can produce various benefits such as improving environmental impacts,
enhancing brand image, generating revenue, customer service, and reducing
production costs (Qiang *et al.,* 2013).

With
advancements in recycling and remanufacturing technologies, scholars are
increasingly focusing on integrating forward and reverse logistics as a CLSC
network (Xie *et al.,* 2017). The CLSC,
a subtype of sustainable supply chain aims to optimize recycling and
refurbishing processes for end-of-life products (Das
and Posinasetti, 2015). A general CLSC has a manufacturer serving for
reverse logistics processes. The returned products and goods are recycled (Ashayeri, Ma, and Sotirov, 2015), and resold in
the primary or secondary market after important processing (Turrisi, Bruccoleri, and Cannella 2013). A
typical CLSC consists of both forward and reverse supply chain channels
including processes like product return, recycling/recovery, remanufacturing,
and resale (He, 2015).

CLSC
network design treats forward and reverse supply chain networks as a cohesive
unit, avoiding local optimality issues associated with separate modelling (Soleimani, Esfahani, and Govindan, 2014).
Sustainable CLSC can be modelled based on its network but additional
complexities, and increasing computational difficulty are introduced (Eskandarpour *et al.,* 2015). Therefore,
capable solution methods are crucial in solving mathematical models.

Meta-heuristic
algorithm, such as swarm-based algorithm, have been applied to various
optimization problems (Utama, Yurifah, and Garside, 2023; Nitnara and Tragangoon, 2023; Zukhruf
*et al.,** *2020). This study focused on a
single-objective MILP model which aimed to minimize total costs in solving
CLSC, location-allocation, transportation, and supplier selection problem. The
proposed hybrid method integrated the Binary Crow Search Algorithm (BinCSA)
with an exact method for efficient problem-solving.

Experimental Methods

This
study proposed a single-objective Mixed-Integer Linear Programming (MILP) model
to address the CLSC problem. The model was solved using a hybrid method that
combined CSA and an exact method. Specifically, CSA for binary optimization
(BinCSA) was adopted to solve the location-allocation problem, which included
selecting the location of distribution centers in a scenario modeled after the
Incapacitated Facility Location Problem (UFLP). The mathematical model was
subsequently solved using the CPLEX solver.

*3.1. Problem Description*

* *The CLSC problem depicted
in Figure 1, incorporated both the forward and reverse supply chain. The
forward supply chain included four distinct echelons, namely ‘supplier’,
‘manufacturers’, ‘distribution centers’, and ‘customers’. This mirrors a
conventional forward supply chain, where manufacturers source components from
suppliers, and finished products are distributed to customers through
distribution centers.

The
reverse supply chain consists of ‘recycling centers’, ‘disposal centers’, and
‘manufacturers’. The recycling centers collect used products from customers,
inspect and disassemble, and segregate the components into ‘usable’ and
‘disposal parts’. Furthermore, the ‘usable parts’ undergo recycling and
refurbishment, while ‘disposal parts’ are sent to 'disposal centers’. The
recycled components are then forwarded to the ‘manufacturer’, combined with new
parts procured from the ‘supplier' and used in the manufacturing process.

The location of the ‘supplier’, ‘plants’,
and ‘customers’ were predetermined while the ‘distribution centers’ and
‘recycling centers’ remained undisclosed. This study operated within a discrete
space, limiting choices for these locations to predefined candidates. (Indonesia).

**Figure 1**
The proposed structure of the proposed CLSC model

This
study introduced a single-objective MILP model for the CLSC. The objective
function aimed to minimize the logistics costs, which included fixed,
transportation, and others. Therefore, fixed costs were defined as the opening
costs of each facility, primarily contingent on the quantity of opened
facility. The transportation costs were influenced by the transportation
expenses between customers’ sites and the opened facilities. Other costs
included the purchasing costs from suppliers and the recycling costs associated
with used products.

*3.2. **Mathematical Model
Description and Explanation*

This section presented the mathematical model for the CLSC, outlined in
Tables 2, 3, and 4. Table 2 shows the model indices, 3 provides information on
model parameters, and Table 4 enumerates the model variables. These components
collectively formed the foundation for understanding the complexities and
intricacies of the CLSC mathematical model presented in this study.

**Table
1** The indices of the CLSC mathematical model

**Table
2** The parameters of the CLSC mathematical model

**Table
3** The decision variables of the CLSC mathematical model

The mathematical model of this CLSC can be formulated as in equation (1). Its objective is to minimize the sum of the opening costs which is the equation (2) the transportation costs is the equation (3), and other costs is equation (4).

The
objective function (1) targets economic impact aimed at minimizing the sum of
total costs. It included fixed costs (equation 2), transportation costs
(equation 3), and other costs (equation 4). Formulation (2) showed the sum of
all fixed costs, which covered the opening costs of distribution and recycling
centers, as well as the purchasing costs of parts from suppliers. Formulation
(3) represented the sum of logistic costs, accounting for transportation costs
between suppliers, plant distribution centers, customers, and recycling
centers. Formulation (4) showed total costs, which comprised purchasing raw
materials and recycling used products.

For the explanation of constraints, constraint (5) endured
the number of acquired parts from suppliers and recycling centers that met
production based on the demands of customers. Constraint (6) limited plant production
to its maximum capacity the plant capacity constraints). (7) and (8) guaranteed
each customer was served by a distribution and recycling center. (9) and (10)
limited the number of products shipped to a distribution center. (11) ensured a
customer was served by only one open distribution center. (12) ensured used
products from a customer were collected by one open recycling center. (13)
limited the number of recycled parts. (14) ensured not all parts were old in
remanufacturing. Constraints (15) and (16) restricted the number of recycled
parts delivered to a plant. (17) set the minimum and maximum purchasing
quantity of parts from a single supplier. Constraints (18), (19), (20), and
(21) were binary and non-negativity restrictions on decision variables.
Constraint (22) represented a large positive number M.

*3.3.** **Inspiration of CSA*

CSA
is a population-based optimization algorithm designed for continuous
optimization (Sonuç, 2021). Inspired by the
intelligent behavior of crows, it mimics characteristics of living in flocks,
remembering hidden food location, following others to steal food, by following
other animals to discover their secret location and protecting their stash from
theft (Askarzadeh, 2016) Recent studies
focused on the behavior and brain function of crow. CSA showed significant
success in addressing these challenges when applied to various optimization
problems. This included but was not limited to studies of Gupta *et al.* (2018) on the healthcare
sector, Sonuç (2021) on facility location
problem, and Panah *et al.* (2021) on
the industrial application. Recent
reviews on applications of CSA refer to Meraihi *et
al.* (2021). This study showed the potential of CSA as the
foundational method to tackle the specific optimization problem under
investigation and marked the pioneering attempt to use CSA for solving this
particular problem, thereby presenting a novel and innovative method in the
field.

*3.4. **Implementation of CSA
for Optimization Problem*

The
number of crows is denoted as N, the total number of dimensions as D, AP refers
to the awareness probability and FL refers to the flight length of crow
traveling. The maximum number of CSA iterations is noted as t_max. For each
iteration, the notation x^(i,t) is used to denote the spatial position of crow
i at iteration t, where i = 1, 2, …, N and t = 1, 2, ..., t_max. m^(i,t)
signifies the most successful position that crows have achieved so far and
symbolizes the position of the crow’s stash. The adjustment of the crow's position
is realized through one of two distinct strategies, each contingent upon the
value of AP, which determines the specific case to be used.

Within the first scenario, crow i adopts
a strategy of shadowing crow j, with the intention of surreptitiously pilfering
sustenance from the cache of crow j. Importantly, crow j doesn’t notice that
crow i is tracking in this case, thereby, the position of crow i is updated
based on the equation (23):

In the alternative scenario, denoted as the second scenario,
it is presumed that crow* j* possesses awareness of crow* i*’s
pursuit. In response, crow *j *will give up on going to its stash, opting instead to
relocate to an alternative spatial position to protect its food. For this case,
the new position of crow *i* is expounded upon as the equation (24):

otherwise: Select a random position as

The notation *r* is a
random numerical value drawn from the continuous interval (0,1) with uniform
distribution. The parameter *AP* is bounded within the interval (0,1) and
establishes a balance between exploration and exploitation. Importantly, the
magnitude of *AP* imparts an influence upon search dynamics, when the
value of *AP* is equal to zero, CSA becomes a local search method, and
when *AP* is set to be one, the search process is performed as a global
search process. The pseudo-code of CSA appears in Figure 2.

**Figure
2** Pseudo-code for CSA

*3.5. **CSA for Binary
Optimization (BinCSA)*

The initialization phase of
BinCSA included generating random binary numbers using a Bernoulli process. A
random number in the range of 0 to 1 was generated, and when it was less than
0.5, it was binarized to 0, otherwise, it was binarized to 1. This process
illiterated repeatedly for each of the D variables till the initialization
stage was complete. This method produced the first feasible solution for the
Uncapacitated Facility Location Problem (ULFP), with the solution size equal to
a total number of possible facility locations. Feasible solutions were
represented as 1 for the potential facility location to be opened and 0
otherwise. The initial fitness values were calculated using the objective
function based on the opening and transportation costs. In the case of discrete
location, BinCSA determined the distribution center location through a series
of steps outlined in Figure 3.

**Figure 3** Flowchart
of the BinCSA

*3.6. **A Two-stage Method to
Solve the Model*

The
conceptual framework for the development of the proposed mathematical model was
previously illustrated in Figure 1 and had equations (1) through (22). It was
planned to be solved with a hybrid method of two stages which integrated both
the exact method and the heuristic algorithm. The BinCSA was used at the
initial stage to optimize facility location for both distribution centers and
recycling centers, subject to uncapacitated constraints. Certain variables
important to facility location problem were determined and treated as fixed
parameters in the simplified version of the mathematical model after the first
stage was completed., The simplified model became more amenable to resolution
through the exact method. In the subsequent stage, the CPLEX solver was used to
obtain solution for the mathematical model.

Results and Discussion

*4.1. **Numerical
Experiment*

A benchmark dataset obtained from both Irawan *et al.* (2022) and ORLIB was used to evaluate the
performance of the proposed model in this study instead of relying on primary
data to evaluate the effectiveness of the proposed model. The dataset included
monetary values in US dollars and distances measured in kilometers. The
evaluation included three main elements performed such as analysis of parameter
settings for BinCSA, presentation of solutions to the uncapacitated location
problem for distribution centers, and a discussion of solutions obtained from
the MILP CLSC model.

BinCSA was executed on ten datasets obtained
from ORLIB. These datasets comprise four sets of data with 25 potential
distribution centers and 50 customers in each set, four sets of data with 50
potential distribution centers and 50 customers in each set, and two sets of
data with 100 potential distribution centers and 1,000 customers in each set.
Each dataset was executed twenty times, and the results of these iterations are
presented in Table 5.

*4.2**. **Parameters
Tuning and Results*

Modifying the parameters
of a metaheuristic algorithm had a direct impact on the quality of the
outcomes. Therefore, fine-tuning them posed a considerable challenge for
scholars because it was a complex process that required conducting numerous
computational experiments to determine the optimal settings specific to a given
problem. In the BinCSA experiment, each parameter was independently assessed
without the influence of other parameters. Optimal configuration could not be
assuredly guaranteed even though several repeated attempts to fine-tune the
parameters were made in such cases.

The practical implementation of the BinCSA identified three key parameters that significantly impacted its performance: population scale (N), awareness probability (AP), and the maximum number of iterations (t_max). Computational time and solution quality were crucially impacted by these parameters. Preliminary experiments suggested that the BinCSA performed relatively well when N = 400 and AP = 0.1. Therefore, for this experiment, N was set at 400 and AP as 0.1, with t_max being the only variable. The results given in Table 4 showed that increasing t_max could improve the solution quality. For datasets that did not reach the optimal solution, they have close gaps. However, in smaller datasets with optimal results, increasing t_max does not affect the values of the results but increases computational time. Determining the most appropriate t_max for each dataset was essential in achieving better performance within reasonable computational time.

In smaller-scale scenarios,
exemplified by ‘cap101’ and ‘cap102’, where problem size was based on a ‘25*50’
matrix, it was viable to adjust the value of ‘t_max’ to a smaller range. This
aimed to enhance the overall performance of result accuracy and computational
efficiency. Conversely, for larger scenarios like ‘capa’ and ‘capb’,
characterized by larger problem dimensions of ‘100*1000’, fine-tuning the ‘t_max’
parameter across a broader range accommodated search for optimal solutions and
maintained computational efficiency. laminates.

**Table 4** Results of 10 instances with t_max = 8,000, t_max = 12,000, and t_max =
30,000

*4.3. **The Results of the
MILP CLSC Model*

After results were
obtained from BinCSA, modifications were made to equations from distribution
centers to customers and customers to recycling centers in the CLSC model.
These equations were deleted, and their values were modified based on BinCSA
results. Parameters and constraints related to these equations were also
removed. The binary results of the opened facility were modified from binary
decision variables to known parameters. This study took the dataset ‘cap101’ as
an example to minimize the total costs of the proposed CLSC mathematical model.
Avoiding the opening of both distribution and recycling centers synchronously
in the same potential location was the rule of facility opening.

The MILP model,
post-modification, comprised 4,137 constraints and 102 variables. The
experiment was conducted on a personal computer with an Intel® Core™ i7-8665U
CPU @1.90GHz 2.11GHz processor with 16GB of RAM. The model was optimally solved
using the IBM ILOG CPLEX optimization studio version 12.11. The CPU time to obtain
the CPLEX result was 0.52 seconds. The minimized total costs that covered both
the forward and reverse supply chain was $95,514,379.54 for one period. In this
scenario, producing one unit of product needed 2 units of part 1, 1 unit of
part 2, and 3 units of part 3. A supplier selection problem was solved.
According to the results, the plant did not purchase any part from supplier 3;
the plant purchased part 1 for 115,636 units, part 2 for 57,818 units, part 3
for 100,000 units from supplier 1; the plant purchased part 3 for 73,454 units
from supplier 2.

Conclusion

In
conclusion, this study successfully applied BinCSA to address the facility
location problem in the proposed MILP model for the CLSC. A hybrid method,
combining the exact method and BinCSA, effectively solved the proposed model.
However, limitations included BinCSA solving impractical ULFP and challenges in
tuning parameters at the initial stage. Future studies can improve parameters
tuning through adaptive learning methodologies, extending BinCSA to capacitated
facility location problem, using simulation-optimization methods, and
incorporating environmental objectives in bi-objective CLSC model. Many
existing experiences were using a hybrid method to address the CLSC-related
problem, which included the amalgamation of two or more distinct
meta-heuristics or exact methods but the body of studies applying CSA in
combination with other methodologies were scarce. Therefore, it is promising to
explore more opportunities to integrate CSA with other meta-heuristics and
exact methods to address problems related to CLSC. One of those future study
opportunities is currently being studied to correspond with cutting-edge
advancements in supply chain study and development.

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