Application of multi-objective optimization based on genetic algorithm for sustainable strategic supplier selection under fuzzy environment
Journal of Industrial Engineering and Management
Application of Multi-Objective Optimization Based on Genetic Algorithm for Sustainable Strategic Supplier Selection under Fuzzy Environment
Muhammad Hashim 2
Muhammad Nazam 1
Liming Yao 0
Sajjad Ahmad Baig 2
Muhammad Abrar 3
Muhammad Zia-ur-Rehman 2
0 Uncertainty Decision-Making Laboratory, Sichuan University Chengdu (China)
1 Institute of Business Management Sciences, University of Agriculture Faisalabad (Pakistan)
2 Department of Management Sciences, National Textile University Faisalabad (Pakistan)
3 Department of Industrial Management, Government College University Faisalabad (Pakistan)
Purpose: The incorporation of environmental objective into the conventional supplier selection practices is crucial for corporations seeking to promote green supply chain management (GSCM). Challenges and risks associated with green supplier selection have been broadly recognized by procurement and supplier management professionals. This paper aims to solve a Tetra “S” (SSSS) problem based on a fuzzy multi-objective optimization with genetic algorithm in a holistic supply chain environment. In this empirical study, a mathematical model with fuzzy coefficients is considered for sustainable strategic supplier selection (SSSS) problem and a corresponding model is developed to tackle this problem. Design/methodology/approach: Sustainable strategic supplier selection (SSSS) decisions are typically multi-objectives in nature and it is an important part of green production and supply chain management for many firms. The proposed uncertain model is transferred into deterministic model by applying the expected value measure (EVM) and genetic algorithm with
hashimscu@gmail; com; nazim_ehsas@yahoo; com; lmyao@scu; edu; cn; sajjad; baig@hotmail; com; abrarphd@gmail; com; mzrehman@ntu; edu; pk
Findings: This study makes a certain contribution by introducing the Tetra ‘S’ concept in both
the theoretical and practical research related to multi-objective optimization as well as in the study
of sustainable strategic supplier selection (SSSS) under uncertain environment. Our results
suggest that decision makers tend to select strategic supplier first then enhance the sustainability.
Research limitations/implications: Although the fuzzy expected value model (EVM) with
fuzzy coefficients constructed in present research should be helpful for solving real world
problems. A detailed comparative analysis by using other algorithms is necessary for solving
similar problems of agriculture, pharmaceutical, chemicals and services sectors in future.
Practical implications: It can help the decision makers for ordering to different supplier for
managing supply chain performance in efficient and effective manner. From the procurement and
engineering perspectives, minimizing cost, sustaining the quality level and meeting production
time line is the main consideration for selecting the supplier. Empirically, this can facilitate
engineers to reduce production costs and at the same time improve the product quality.
Originality/value: In this paper, we developed a novel multi-objective programming model
based on genetic algorithm to select sustainable strategic supplier (SSSS) under fuzzy
environment. The algorithm was tested and applied to solve a real case of textile sector in
Pakistan. The experimental results and comparative sensitivity analysis illustrate the effectiveness
of our proposed model.
Nowadays, sustainable strategic supplier selection (SSSS) is an essential issue for building up a successful
supply chain network in a textile sector due to hygienic concerns. It is a key process of supply chain
management and also the right suppliers selection play a substantial role for improving overall
performance. The process of sustainable manufacturing involves the production of sustainable items and
In these cases, fuzzy set theory is one of the best tool for handling the uncertainty. For example, it is very
difficult for decision maker to determine the demand, cost and quality in advance because the values of
these parameters changed with the passage of time and not remain the same. In this situation, the fuzzy
set theory can be used because of the comportment of unclearness and imprecision of data in the
supplier choice issue. Fuzzy set theory has got the attention of the researchers by Zadeh (1965) and after
that he presented possibility theory and number of scholars are influenced by this theory, such as Dubois
and Prade (1997a, 1997b). It has been employed in a wide assortment of genuine issues. Many scholars
have studied this uncertainty and imprecision by using fuzzy theory (Amid, Ghodsypour & Brien, 2006;
Kumar, Vrat & Shankar, 2006). However, most supplier selection techniques covered in the literature
suppose the studying parameters are deterministic and known (Aissaoui, Haouari & Hassini, 2007). Just a
limited number of studies deal the stochastic and imprecision existed in data associated with supplier
selection decision. Such as Jafar, Songhori and Mohammad (2009) investigated fuzzy group decision
making/linear programming structure for supplier selection issue and order allocating, Liao et al.
presented a comprehensive multi-objective supplier selection framework under stochastic conditions by
considering uncertainties of demand quantity and time. Wen & Chi (2010) investigated a methodology
using fuzzy decisions making and AHP strategy.
Hashim, Yao, Nadeem, Nazim & Nazam (2014) introduced a multi-objective optimization framework to
deal with supplier selection problem under fuzzy environment. Kilic (2013) investigated an integrated
technique to deal with supplier selection in multi-item/multi supplier environment. He researched a
mixed integer liner programming and fuzzy TOPSIS methods to select a suitable supplier in multiples
supplier environment. Liou, Chuang & Tzeng (2013) presented a novel fuzzy integer-based model that
addresses the interdependence among the various criteria and employs the non-additive gap-weighed
analysis. Above all the discussed models to deal with the supplier selection issue played an important role
for solving the real problems.
In the literature there exist a lot of approaches/techniques to solve the problem of sustainable supplier
selection but most of the approaches are based on multi-criteria decision making frameworks (Memon,
Lee & Mari, 2015; Wang-Chen, Chou, Luu & Yu, 2016; You, You, Liu & Zhen, 2015; Banaeian, Mobli,
Fahimnia, Nielsen & Omid, 2016). The fundamental reason for applying the decision making models is
that both alternatives and criteria are fixed a priori and that decision happens once. This basic assumption
definitely limits the accuracy of the results, mostly when the values change with the passage of time and
the pair-wise decision matrix is not fixed or static as in sustainable supplier selection topics. Also, the
fuzzy multi-criteria group decision-making model belief of the supplier selection mainly concentrates on
the cause and effect relationship between the components of systems individually; therefore, it is not
considered as a broader model. Fuzzy Multi-criteria decision making frameworks basically does not
provide a comprehensive understanding of the complicated nature of the (SSSS) problem with respect to
the set of criterion, i.e. political, economic, social and environmental factors (Amin & Zhang, 2012;
Awasthi, Chauhan & Goyal, 2010; Buyukozkan & Cifci, 2011; Chang, Chang & Wu, 2011; Foerstl, Reuter,
Hartmann & Blome, 2010). Therefore, from the above discussion it is revealed that multi-criteria decision
making models cannot be most reliable source for selecting the suppliers for a long time period.
In this research, a fuzzy multi-objective model is presented for the sustainable strategic supplier selection
(SSSS) issue in fuzzy environment. The purchase directors can allot diverse weights for numbers of
criteria with a specific end goal to oversee stream of green supply materials and enhance quality, service
and decreased expense, keeping in mind the end goal to enhance the supply chain performance. This
study contributes to present research in the following ways: first, a multiple objectives technique is
presented which considers multiple and conflicting objective functions for solving supplier selection
problem in better way. Furthermore, demand, costs, service and quality levels are characterized by fuzzy
variables which help decision makers to take more effective and precise decisions in fuzzy environment.
As mentioned previously in the literature review, there is a lack of methodologies which concentrate on
the various sources of uncertainty in an optimization way, and few researches investigate the supplier
selection problem by integrating the objectives including cost, quality and service level in a fuzzy
environment. Hence in this study we developed a sustainable strategic supplier selection model based on
genetic algorithm to solve the real world problem in a textile sector of Pakistan.
The main contributions of this research can be summarized as follows:
Introducing a novel fuzzy multi-objectives model based on genetic algorithm by incorporating
lean cost, sustainable service and greener product quality level in an eco-supply chain network.
Achieving a model which contemplates the different sources of uncertainty affecting supplier
selection in a textile sector by considering the preferences of decision makers in the proposed
Applying the optimization model to a real world textile supply chain dedicated to the issues of
sustainable strategic supplier selection.
The remainder of the paper is organized as follows: part second comprised of sustainable strategic
supplier selection (SSSS) problem under fuzzy environment; part third discuss mathematical
programming model in fuzzy environment and expected value operator to deal with fuzzy parameters for
2. Key Problem Description
For managing supply chain, the manufacturer (Textiles Company) need to purchase green raw materials
or different items from various suppliers and take an assortment of supplier properties, for example,
quality, price and service level into consideration. An individual supplier has diverse execution qualities
because of various criteria. For example, the supplier who can supply a thing at the slightest per unit cost
might not have the best quality or service level than the other contending suppliers. It is clear that there
could be a few deviations in the nature of various items offered by an alternate supplier. That’s, might be
some product of a supplier can have better quality however can be more costly when compare it with
comparable product of alternate suppliers. The sustainable strategic supplier selection (SSSS) problem
manages issues identified with the finding of right suppliers and their portion allocations. A strategic
supplier finding can improve the supply chain performance as well as make a solid framework which can
give an intense backing to purchaser for accomplishing his objectives. It is a complex problem because of
various reasons, by nature, this is a multi-criteria decision making problem. So the managers may be
adopted different criteria for different kinds of material. However, to select right (potential) suppliers
always confuse the managers in case of many kinds of candidates and materials.
The supplier selection problem (SSP) in fuzzy environment can be expressed as follows: assume that the
manager want to choose the supplier from candidates and some differentiations between them are price,
quality and service levels. The manager needs to know which suppliers should be selected and how much
of the quantity Yij should be ordered considering the objectives. However, as to the supplier selection
problem, it is hard to describe the cost and demand as known values because there is not su fficient data
available to analyze, which usually cause uncertainty, imprecise or vague situation (Xu & Yan, 2011;
Jauhar, Pant & Abraham, 2014; Khatie, Bulgak & Segovia, 2010; Lee, Kang, Hsu & Hung, 2009;
Ordoobadi, 2009; Qiang, Hui & Xiao-Dong, 2013; Tako & Robinson, 2012; Alinezad, Seif & Esfandiari,
2013; Baskaran, Nachiappan & Rahman, 2012). Considering this situation, we use fuzzy variable to
describe uncertain, imprecise or ambiguous information in the (SSSS) problem. This research work
concentrates on developing an expected programming method for supplier selection in fuzzy
environment, in which different weights can be allocated to different objectives for showing their
importance in decision making (Chen, Lin & Huang, 2006; Chu & Varma, 2012; Govindan, Khodaverdi
& Jafarian, 2013; Hashemian, Behzadian, Samizadeh & Ignatius, 2014; Rezaei & Ortt, 2012; Rodríguez,
Ortega & Concepción, 2013).
In this problem, a Pakistani vertically integrated textile manufacturing company is chosen for this
research. The proposed firm has approximately 6000 employees per shift; they manufacture garments
products such as sportswear, sleep-wear, underwear, pants and trousers. The chosen firm is one of the
leaders in its product segment in Pakistan; its main customers are major national and international
retailers. This company has enacted various changes in the structure of the final product in order to make
it comfortable, free of harmful chemicals and toxic materials, and to lower its price by providing greener
quality. These changes, in turn, meet both environmental legislation regulations and the demands of their
This problem deals in achieving the following highlighted objectives:
1. To identify and understand the concept of environmental sustain-ability associated with the strategic supplier at industrial context in textile firms.
2. To evaluate the identified criterion to priority by determining and confirming of their relative importance in effective selection of (SSSS).
3. To interpret the fuzzy logic for dominance of one objective over the other for the formulation of
multi-objective optimization based on genetic algorithm for sustainable strategic supplier selection
with sensitivity analysis under fuzzy environment.
In Pakistan, according to the 2016 National Policy on Solid Waste, all industries in the textile sector are
now required to take responsibility for their post-consumer products take-back and environmental
impacts. Because of the Pakistani governments mandate, companies recognize that offering greener
textile products not only meets customer demand but also requires locating good green suppliers to
improve their supply chain management. In this paper, the parameters are characterized by fuzzy variables
that can explain uncertain and imprecise data at the decision time for handling with complex uncertain
problems in practical cases. In real situation, decision makers for taking the decision face an environment
where the information about the study objectives, constraints (parameters) are not available precisely.
Based on the above perspectives, some researchers (Shidpour, Shahrokhi & Bernard, 2013; Singh, 2014;
Soroor, Tarokh, Khoshalhan & Sajjadi, 2012; Iranmanesh & Thomson, 2008; Aissaoui et al., 2007;
Kannan, Khodaverdi, Olfat, Jafarian & Diabat, 2013; Awasthi, Chauhan & Goyal, 2011) pointed out that
in the present reality decision making issues in (SSSS) problems, one often takes place in an uncertain
environment. It is hard to report the problem parameters as known because of the complexity of
environment socially and economically and at the same time some unpredictable factors for example bad
weather and machine or vehicle breakdowns. These disputes expanded the significance of stochastic and
fuzzy programming techniques for solving real issues where information are not known correctly. For
instance, it is not easy for a decision maker to give the accurate information about his needs, however as
indicated by his experience, he can gauge the requirement for one thing as an interval with the possible
values, this explanation is a case of fuzziness. Such a large number of parameters such as time, demand
and cost are normally unverifiable instead of deterministic and it is exceptionally hard to decide accurate
figure of these parameters because of the variance in the values. In real problems, the decision maker
cannot gather the ideal data for every parameter. As various individuals have diverse feeling about the
uncertain variables brought on by the unverifiable environment, and there is no plain meaning of this
change. Consequently in such kind of issues, it can be described by the uncertainty of fuzziness.
Numerous researchers have mentioned this instability and imprecision and deal with them by using fuzzy
theory (Fazlollahtabar, Mahdavi, Ashoori, Kaviani & Mahdavi-Amiri, 2011; Kannan et al., 2013;
Songhori, Tavana, Azadeh & Khakbaz, 2011; Hashemian et al., 2014; Katagiri, Sakawa, Kato & Nishizaki,
2008; Amid et al., 2006; Su, Yang & Pearn, 2011). However, supplier selection issue often times
confronted with environmental uncertainty where fuzziness exist in decision making. In such kind of
situations, fuzzy variables are a best option for describing the uncertainty of decision variables.
In this research, demand, cost, quality level and service level are uncertain parameters and interpreted by
fuzzy variables that can be further described by triangular fuzzy numbers. It is very difficult for a decision
maker to get the accurate data for all uncertain variables. So in this circumstance, the decision maker can
depict the parameters into triangular fuzzy numbers that are more suitable to clarify the instability, for
example, demand is about Dm but emphatically not less than Dl and large than Du.
3. Model Formulation
In this paper, the problem is formulated as a multi-objectives programming problem with fuzzy
coefficients, in which the decision makers have three objectives first minimize the cost and second
maximize greener product quality and third maximize the sustainable service level.
In real life problems, input data is generally imprecise because of incomplete information. In an expert’s
decision making scenario, mostly the usage of fuzzy linguistic variables are preferable instead of
numerical or stochastic data. It is the best options for the decision makers to tackle the subjectivity that
often exist in the process of supplier selection. Therefore, if we want to consider the uncertainty,
especially subjective uncertainty, fuzzy variables can be employed (Xu & Zhou, 2011). In this research, the
parameters used in the proposed model are characterized by fuzzy variables for handling subjective
3.1. Assumptions and Notations
1. Quantity discount is not considered.
2. Purchasing is limited to three kind of goods.
3. Cost, demand, and quality are characterized by fuzzy variables.
4. Each supplier can be selected for more than one product.
Suppose that there is one buyer, i suppliers. The task is to allocate the orders to suppliers for minimizing
cost and maximizing the green material quality.
: aggregate demand of the item over the period from supplier i;
: unit price of the order quantity Yij from the supplier i;
: product quality level of ith supplier for product j;
: product service level of ith supplier for product j;
A: budget allocated to suppliers i;
aij: capacity of ith supplier for greener product j;
3.2. Modeling Formulation
Based on the manager’s objectives in the proposed problem and the notations mentioned above, this
study develop a multi-objective optimization model to attempt it.
In this study, the first objective function is to minimize the total cost for ordering the demand, which will
be counted the basic economic aim to the supplier selection problem in material supply.
Second objective function maximizes the suppliers environment friendly product quality. To make sure that
the production process can be carried through smoothly, the managers require that the quantity of rejected
things ought to be kept at a low level. Since, a textile factory has a limited time to complete a customer
demand in order to cope the penetration of competitors. So, the supplier items quality level should be
considered very carefully when decision makers make the decision on the problem of suppliers selection.
Second constraint states that the total cost should be within expected budget amount.
I J ~
I J ~
Third objective function maximizes the sustainable supplers service level. The late delivery items can
affect the supply chain performance and supply chain visibility. Since a factory or a textile project needs a
lot of manpower and material, the cost can be increased by late delivery. Hence, the supplier effective
service level should be considered seriously when decision makers make the decision on the problem of
strategically fit supplier’s selection.
Generally speaking, some compulsory conditions must be fulfill when the decision maker takes the
decision. In this research, the required conditions are listed below:
The first constraint states that the total supply must be meet the expected demand.
It is generally a very difficult task to solve the optimization problems with multi-objective under
uncertainty (fuzzy environment). For solving the fuzzy model, the first step is to convert the fuzzy values
into certain (deterministic) form. In this study, the expected value model (EVM) is adopted that based on
Me for solving the presented problem. The study parameters are defined in triangular form and for
solving them we used a new fuzzy measure with an optimistic-pessimistic adjusting index. The
explanation of this fuzzy measure Me can be studied in Orji and Wei (2014) and Dubois and Prade
(1994). This is a convex combination of possibility (Pos) and necessity (Nec). The basic information about
these measures can be studied in Wang & Fang (1997). Let D = (b1 + b2 + b3) denotes a triangular fuzzy
variable. According to the definition and properties of expected value operator of fuzzy variable using
measure Me (Xu & Ding, 2011), if there is a fuzzy variable D = (b1 + b2 + b3), where b1, b2, b3 > 0, so the
expected value of D can be written as:
According to the above explanation, by integrating of Equations (1) to (7), multi-objective expected value
model can be formulated as follows:
Third constraint states that order quantity should be less than the suppler capacity.
Fourth constraint states the non-negativity constraints on decision variable.
It is not simple to find an optimal solution for a multi-objective optimization model. In such kind of
problems we need to assign a weight to each objective for normalization. So, in this study, the weighted
sum method is adopted to solve the multi-objective optimization problem. Suppose that wi is a weighted
coefficient for fi(y) objectives functions and the sum of wi will be equal to 1. It expresses the importance
of objective functions in the proposed model. Model can be converted into single objectives using the
The weighted equation can be written as:
min ( f ( y ))=min yY w 1 f 1 ( y )+(−max y Y w 2 f 2 ( y ))+(−max y Y w 3 f 3 ( y ))=∑ w 1 f 1( y )
4. Solution Procedure
Many kinds of evolutionary computation techniques are developed for solving the composite
optimization problems. Genetic algorithm is one of them and a well-known form of evolutionary
algorithms. It does not require the sated information should be in form of gradient about the objective
functions for optimization and it can also provide a number of possible solutions for solving the problem
and the final decision depend on decision makers. From last three decades, it has been gained a significant
success in providing smart solutions to several complicated optimization issues (Jauhar et al., 2014; Khatie
et al., 2010). It belongs to stochastic search methodology that commonly used for the optimization of
objectives for studying problems. It is supported by the mechanics of natural selection and natural
genetics-survival of the fitness function values. The advantage of this approach enables us to obtain the
best optimal solution globally.
Furthermore, it does not required the particular mathematical analysis of optimization issues that makes
it simple coded by users who are not necessarily expert at mathematical and algorithms. It has been
applied for solving different kind of problems, such as transportation problems, facility layout problems,
supplier selection, scheduling, network optimization and so on. Due to the subjective study, development
of genetic algorithm approach is necessary to solve out the supplier selection problem. The proposed
approach to be considered the best option for optimizing fuzzy model. So, GA is a most suited solution
method for getting the good result of the proposed model.
The next section under takes to present GA to solve the multi objective programming model with fuzzy
coefficients. The detail discussion as follows:
Step 1. Initialize the Population: Randomly generated population called chromosomes. These
chromosomes represent the solution of the optimizing objectives. The chromosomes are denoted by
vector y, y = (y1, y2, y3, ..., yNpop).
Step 2. Handling the constraints: Fuzzy simulation is used for checking the chromosome generated by
genetic operator for seeing that the chromosomes are in the feasible region. Generate random vector y
within the possible region till a possible one is accepted as a chromosome. Run the above process for
Npop–size times for getting the initial feasible chromosomes y1, y2, y3, ..., yN–popsize.
Step 3. Evolution function: For the evolution of each chromosomes the following function is applied for
calculating the fitness function values for each chromosomes.
Step 4. Selection: Holland (Lee et al., 2009) developed roulette wheel selection concept for dealing with
selection probability for each chromosome. In this research we apply roulette wheel selection process for
developing selection process. The wheel will roulette Npop–size times and every time a single chromosome is
selected for a new population. The procedure as follows: Calculate the total probability qi for each
chromosome y i
Randomly generate a random number γ in range [0,1] and select the ith chromosome y i. Run the above
procedure Npop–size times for getting the Npop–size pairs of chromosomes.
Step 5. Crossover and mutation operations: These operations are used for updating the chromosomes.
The crossover, operation is started from generating a random number γ from the open interval (0, 1),
chromosomes y i will be selected as a parent if γ < pc, here pc is a parameter which is used defined as the
crossover probability. The selected parents are denoted by y1, y2 ...
After that a random number is generated from open interval (0, 1) and then the crossover operator work
on y1 and y2, in result it produced two children D1 and D2 as follows:
In case of the resulted children are feasible, it will replace the parents with them. Otherwise, redo the
crossover operation with another random number c until the given number of cycles is not over. In
second process named mutation operation, repeat the same process (steps) like crossover process from
chromosomes are expected to be selected after repeating the process Npop–size times. Change each selected
Replace S with S + M.d if S + M.d is feasible, otherwise set M as a random number between 0 and M
until it is feasible or a given number of cycles is finished. Here, M is an appropriately big positive number.
5. Practical Application and Sensitivity Analysis
To demonstrate the applicability of the proposed model, this section presented a numerical case of the
Pakistani Textiles sector. For supplying material to a manufacturing plant of a textile industry, we assume
that there are five suppliers and three kinds of products that need to be managed. In this problem, Cost,
service and quality are the purchasing criteria. The total purchasing cost must be within the given budget
and suppliers capacity. It is supposed that the required information about the supplier’s performance on
the above purchasing criteria is not completely available. It is characterized by fuzzy variables and the
related data are shown in Tables 1 and 2.
5.1. Results and Discussions
Putting the above numerical information into the presented model, we followed GA by using Matlab 7.9
on computer (Pentium 4.2GHz) with 2048 MB memory for testing the effectiveness of the model with
the proposed example. We got the satisfactory solution based on Me fuzzy measure by setting λ = 0.5
(optimistic-pessimistic index), population size is 20 and the probability of crossover and mutation are 0.2
and 0.1 simultaneously, fuzzy simulation based GA based is run at the 60 generations for getting the best
solution. Inertia weight W1 = 0.4, W2 = 0.3, W3 = 0.3. The best results are presented in Table 3. The GA
search process for the optimal solution can be seen in Figure 1. The optimal solution depend on the value
of λ and the different weights assigned to both objects. The decision maker can get the different objective
values by changing these parameters.
5.2. Sensitivity Analysis
The proposed parameters are decided by the estimated data or experts advice to obtain different level
solution. We can make the sensitive analysis by changing the decision makers confidence level based on
optimistic-pessimistic index. Global market is becoming more and more competitive day by day due to
this reason decision maker face rigorous challenges for selecting the supplier in an efficient and cost
effective manner. The comparison of the solution is shown in Figure 2, the red line represents the
solution using parameter λ = 0.8, the green one using parameter λ = 0.5, the blue one using parameter
λ = 0.2. Obviously, the results with the green one showed better results than those with red one presents.
Concurring with real experience, the small value can be a better option than a higher. In this situation, the
decision makers should have a high risk of uncertainty. According to the above discussion, the parameters
value are dependent on decision maker’s attitude, he can select according to his preference. Usually, the
decision makers select the key suppliers first and then consider the rest of partners with respect to other
From the procurement and engineering perspectives, minimizing cost, sustaining the quality level and
meeting the production time-line is always the main consideration for selecting the supplier. This may
facilitate engineers to reduce production costs and at the same time improve their product quality in a
sustainable way by enhancing the R & D capability. Therefore, it is very interesting to hear that when the
engineers ask the key suppliers for sophisticated technology, the buyer will be able to do so. In brief, this
study recommends the buyer to select the suppliers who meet the desired objectives. If the textile
company adopts the minimum cost objective as the most important supplier criteria, it may bring the
holistic supply chain actors into a risky environment. Consequently, the concept of the minimal cost
objective should be replaced by the rest of the strategic sustainable objectives including lead time and
6. Conclusions and Future Directions
Green supplier selection is a major milestone in transition towards the design and management of more
environmentally sustainable supply chains. Most of modeling efforts for sustainable strategic supplier
selection are based on the integration of fuzzy theory with conventional MCDM methods. In this paper,
we developed a novel multi-objective programming model based on genetic algorithm to select
sustainable strategic supplier under fuzzy environment. The model and algorithm are applied to a
practical case in Pakistan. The experimental results and comparative sensitivity analysis illustrate the
effectiveness of our proposed model. The suppliers play very important role in case of managing the
quality, costs and services at desire level, which is affect the purchaser outcomes.
This research mainly investigated a multi-objectives expected value programming model with considering
fuzzy coefficients for giving the solution of proposed problem. Genetic algorithm solution approach is
proposed to get the optimal order allocation to suppliers for minimizing cost, maximizing quality and
service levels. The main contributions of this paper are summarized below.
1. A general fuzzy multi-objective decision making (FMODM) model for sustainable strategic supplier selection based on genetic algorithm was presented. As mentioned, this model allowed for the incorporation of qualitative as well quantitative information expressed in linguistic and numeral terms considered as the aggregation of decision makers preferences.
2. An application example for (SSSS) problem at a Pakistani textile factory was given to verify the
proposed approach. The study demonstrated the distinct characteristics of genetic algorithm. It
was shown that the proposed algorithm could be used to obtain a better understanding of the
complex solutions. The suggested technique is more efficient as compare to deterministic
techniques for solving there all problem under uncertain environment. It can help the decision
maker for ordering to different supplier for managing supply chain performance in efficient and
3. This study provides a single platform for green supplier selection in a fuzzy environment and sets
the stage for additional research in this important and growing knowledge area. The proposed
model and solution approach is examined by a numerical example for checking the effectiveness,
the results showed that it is effective and viable to solve the given numerical illustration. Because
of conflicting nature of the multi-objectives and vagueness in the information related to the
parameters of the decision variables, the deterministic techniques are not suitable to obtain an
Although the fuzzy expected value model with fuzzy coefficients constructed in present study should be
helpful for solving real world problems, detailed analysis and further research is necessary to reveal more
properties of a good method for solving other sector problems like agriculture, pharmaceutical, chemicals
In the future, the researchers and practitioners can compare the results of this study with other fuzzy bi
or tri level multi-objective techniques as well as multi-criteria tools such as fuzzy VIKOR, fuzzy
ELECTRE, and fuzzy PROMETHEE may also be employed. Future researchers should pay more
attention to the environmental objectives of supplier selection for different industries.
The authors would like to thank the Editor (Neslihan Demirel) and the anonymous referees for their very
valuable and helpful suggestions for improving the quality of present research.
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