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ORIGINAL ARTICLE
A hybrid model for supplier selection: integration of AHP
and multi expression programming (MEP)
Alireza Fallahpour
1
•Ezutah Udoncy Olugu
1
•Siti Nurmaya Musa
1
Received: 11 May 2015 / Accepted: 11 October 2015
The Natural Computing Applications Forum 2015
Abstract Supplier evaluation and selection is a compli-
cated process which deals with conflicting attributes such
as quality, cost. To mitigate the computational complexity,
intelligent-based techniques have gained much popularity.
But the main shortcoming of the existing models in this
regard is to be a black box system. In this paper, we aim to
combine analytical hierarchy process with multi-expression
programming to both introduce a new evolutionary
approach in the field of supplier evaluation and selection
and cope with the earlier problem. To show the validity of
the model, statistical test was carried out. The finding
showed that the proposed model is accurate and accept-
able for using in the evaluation process.
Keywords Supplier selection Black box
Multi-expression programming AHP Supply chain
management
1 Introduction
Supplier evaluation and selection is a critical issue for
achieving success in any manufacturing industry. Multi-
criteria decision making (MCDM) as the main approach of
decision-making theory has been successfully used to solve
this problem [1,2]. Due to the presence of conflicting
factors such as quality, cost, assessing and selecting the
proper suppliers is a very complex problem. Therefore,
numerous solo and integrated models have been presented
in this area.
One of the most attractive techniques for suppliers’ per-
formance evaluation is artificial intelligence (AI)-based
techniques [3,4]. Increasingly, academics are exploring
neural-based techniques such as artificial neural network
(ANN) [5] and adaptive neuro fuzzy inference system
(ANFIS) [6] asthe reliable approachesfor supplierevaluation
and selection. AI models as computer-aided techniques can
predict suppliers’ performance based on the historical data set.
One of the integrated neural-based methods which
recently received much attention is combination of ana-
lytical hierarchy process (AHP) and ANN for assessing
suppliers’ performance [5,7]. Although this model is
robust and accurate in performance evaluation, it has some
limitations. Although AHP is useful in decision making, it
cannot handle vagueness. In addition, ANN is a powerful
tool in pattern recognition, but it is unable to propose an
explicit mathematical model. In order to overcome the
aforementioned problems, this paper is aimed at integrating
fuzzy AHP and fuzzy preference programming (FPP) with
multi-expression programming (MEP).
The main contributions of this model are:
•A new genetic-based model is introduced in the field of
supplier selection.
•A genetic decision model on the basis of the relation-
ship of a set of input and output is developed in a
unique manner to forecast the performance.
•A new pairwise comparison model for weight calculations
and performance values is performed for a MEP model.
•Historical data set is used in assessment and modeling.
&Ezutah Udoncy Olugu
olugu@um.edu.my
Alireza Fallahpour
fallahpour.a@gmail.com
Siti Nurmaya Musa
nurmaya@um.edu.my
1
Department of Mechanical Engineering, Faculty of
Engineering, University of Malaya, Kuala Lumpur, Malaysia
123
Neural Comput & Applic
DOI 10.1007/s00521-015-2078-6
The rest of the model is presented as follows: Sect. 2
provides literature review related to supplier selection.
Section 3provides information about the techniques and
the proposed model. Case study is presented in Sect. 4.
Model performance evaluation is given in Sect. 5. Finally,
conclusion is presented in Sect. 6.
2 Literature
Since a proper supplier has crucial influence on the per-
formance of SCM, various models have been proposed in
this area. The literature reports that it can be categorized
into seven main parts such as multi-attribute decision
making (MADM) like TOPSIS, AHP, ANP, ; mathematical
modeling including linear programing, integer programing,
nonlinear modeling; data envelopment analysis (DEA);
fuzzy set theory (FST); artificial intelligence (AI) such as
ANFIS, ANN, SVM; statistical/probabilistic approaches;
hybrid techniques.
Each category possesses its own advantages and disad-
vantages. MADM is easy to use, but the results are almost
based on decision makers’ opinion. For example, different
weights could be given to the different criteria by the
experts. Mathematical programming technique is an accu-
rate model, but it is unable to take into account qualitative
criteria. In the mathematical models, finding the accurate
model for decision makers is so difficult. DEA method
does not use any assumption in efficiency evaluation, but it
is very sensitive to homogeneity. Most of the other cate-
gories do not consider the interactions among the various
factors and also cannot effectively consider risk and
uncertainty in estimating the supplier’s performance [3].
Among the aforementioned techniques, predictive AI
models have been received much attention from the aca-
demics and practitioners. One of the benefits of AI methods
in contrast with other approaches is that they do not need
assumption in the decision-making process. Moreover, AI
methods provide predictive models based on the historical
data set. This feature is very useful for decision making [5].
Generally, the literature reports that AI techniques can
handle better with complexity and imprecision than pre-
vious approaches [8].
With respect to the literature, there are three main pre-
dictive AI-based models for supplier evaluation and
selection including: pure AI-based model (such as ANN-
based models, ANFIS-based model, SVM-based models,
and FIS-based models); DEA–AI models (such as DEA–
SVM, DEA–ANN) and AHP–AI (AHP–ANN, AHP–
ANFIS) models.
Kuo et al. [9] proposed an intelligent supplier decision
support system which is able to consider both the quanti-
tative and qualitative criteria. The model enables decision
makers to deal with quantitative data such as profit and
productivity. Guneri et al. [6] proposed a predictive
ANFIS-based model in supplier selection in a textile
industry. A 1–10 numeric scale was applied to rate the
criteria. After collecting the data set, three most effective
criteria on the performance were selected and a predictive
ANFIS-based model was proposed to estimate the suppli-
ers’ performance. Golmohammadi [7] proposed a neural-
based structure for decision making and selecting the best
suppliers. After defining the evaluative criteria, using AHP
pairwise comparison the data set was collected. Then, the
collected AHP-based data set was divided into two parts
for training the ANN model and testing its prediction
ability. In order to improve the model, mathematical
models were defined for measuring each criterion. After-
wards, the same operation was done with the new collected
data set. Ozkan and Inal [10] improved the model proposed
by Golmohammadi [5] and presented an ANFIS-based
model for supplier selection. They highlighted that their
model is more accurate than the proposed neural network
model. Fallahpour et al. [11] combined DEA with ANFIS
to evaluate suppliers’ performance. They concluded that
the proposed integrated model is more accurate model
compared to other models. This paper is aimed at extend-
ing Golmohammadi’s model by combining AHP with
MEP.
3 Methodology
In this part, an overview about AHP and MEP is given.
Then, the proposed model is explained.
3.1 Analytical hierarchy process (AHP)
Saati proposed AHP as a useful and flexible decision-
making model which can be used for both qualitative and
quantitative attributes. As the attributes are determined and
the weights are computed by pairwise comparison matrix,
similar procedure can be applied to calculate the weight of
the alternatives. The pairwise comparison matrix of alter-
natives is structured based on attribute. The result is a new
reciprocal square matrix for each criterion, with its corre-
sponding eigenvector. The procedure is repeated for all
attributes, and the number of each alternative and criterion
is obtained. Afterwards, the score of each alternative is
multiplied by the weight of the corresponding attribute. At
the end, all the numbers for an alternative are summed up
to find the overall score, and the final calculation results
show the importance of each alternative [12,13]. The
alternatives are then ranked according to their calculated
values. Generally, problems associated with AHP are split
into three parts [14]:
Neural Comput & Applic
123
1. Structuring the problem; evaluation of local priorities;
determination of global priorities. The main feature of
AHP is pairwise comparisons which enable decision
makers to obtain the best decision. Practically, AHP
includes the following steps:
2. Forming the defined attributes hierarchically.
3. Generating judgment matrix using pairwise
comparison.
4. Computing a priority vector to weight the components
of the matrix.
5. Determining global priorities by gathering all local
priorities with the application of a simple weighted
sum.
6. At the end, the eigenvalue is performed to evaluate the
strength of the consistency ratio of the comparative
matrix and identify whether to accept the information.
In order to measure the rate of the criteria and suppliers’
performance, 1–9 scale (Saaty scale) is used (see Table 1).
The mathematical process starts by normalizing and
obtaining the relative weights for each matrix. The relative
weights are given by the right eigenvector (W) corre-
sponding to the largest eigenvalue (k
max
), as:
AW¼kmaxWð1Þ
3.2 Multi-expression programming (MEP)
Oltean and Dumitrescu [15] presented MEP as an extension
of genetic programming (GP). MEP performs linear chro-
mosomes for solution encoding [16]. MEP is able to
encode multiple computer programs of a problem in a
single chromosome [16]. After checking the fitness of the
programs, the best one is selected to propose the chromo-
some. MEP is not as complex as other GP such as gene
expression programming (GEP). MEP begins by generating
a random population of individuals. MEP applies the fol-
lowing stages to create the best solution:
1. Choosing two parents using a binary tournament
procedure and recombining them with a fixed cross-
over probability;
2. Gaining two offspring by the recombination of two
parents;
3. Mutating the offspring and replacing the worst indi-
vidual in the current population with the best of them.
Number of the MEP genes per chromosome is constant
and determines the length of the chromosome. A terminal
(an element in the terminal set T) or a function symbol (an
element in the function set F) is encoded by each gene. A
gene that encodes a formulation consists of pointers toward
the function arguments. Function parameters always have
indices of lower values than the position of that function
itself in the chromosome. The first symbol in a chromo-
some must be a terminal symbol as stated by the proposed
representation scheme [17].
3.3 Methodology
This paper is aimed at proposing hybrid AHP–MEP model
to cope with the earlier-mentioned problems associated
with the previous intelligent-based model. To this end, the
following steps should be carried out (see Fig. 1):
Step 1 Collecting the importance of each criterion for
suppliers (alternatives) by pairwise comparison
(using AHP),
Step 2 Collecting the suppliers’ performance (scores) by
pairwise comparison (using AHP),
Step 3 Dividing the gathered data set into twofold for
training (pattern recognition) and testing
(prediction evaluation),
Table 1 Range for attributes measuring
Very poor (VP) 1 BWB2
Poor (P) 2 BWB3
Poor medium (PM) 3 BWB4
Medium (M) 4 BWB6
Medium good (MG) 6 BWB7
Good (G) 7 BWB8
Very good (VG) 8 BWB9
Fig. 1 Methodology of the model
Neural Comput & Applic
123
Step 4 Assessing the model using statistical test and
other AI-based models.
In order to evaluate the accuracy of the model, mean
square error (MSE) and mean absolute error (MAE) are
used in training and testing stages.
MSE ¼Pn
i¼1hiOi
ðÞ
2
nð2Þ
MAE ¼1
nX
n
1
ðhioiÞ
ð3Þ
where h
i
and O
i
are, respectively, the real and predicted
performance scores for the ith performance, hiand oiare,
respectively, the average of the real and predicted perfor-
mance scores, and nis the number of suppliers.
4 Case study
To show the feasibility and application of the proposed
model, a real-life supplier selection problem from a textile
company of Iran is considered (the company name is not
disclosed for privacy reasons) which produces open-end
(OE) yarn. Its staff strength is 500. It works with 33 sup-
pliers to fill its daily order. Therefore, there is a great need
to evaluate the suppliers’ performance.
4.1 Determining the supplier selection criteria
The first echelon in evaluating the suppliers’ performance
includes determining and defining the evaluation attributes.
In this study, based on the literature and experts’ opinion,
five criteria were selected and applied to the textile factory.
The five criteria are quality, delivery, technology, cost, and
flexibility. Table 2shows the definition of each criterion.
4.2 Rating each attribute and suppliers’
performance score
As said earlier, AHP-based pairwise comparison is used to
gather the data set. Three experts have been selected to rate
the determined criteria and the suppliers’ performance. The
experts have PhD degree in long-fiber spinning, weft
knitting, and non-woven knitting. Each of them has more
than 10 years of experience in the textile industry. For this
research, they were asked to rate the selected criteria and
the suppliers’ performance based on the 1–9 Saaty scale
(Table 1). Next, pairwise comparison is performed for
obtaining suppliers’ performance scores. Table 3illustrates
the collected data set.
4.3 Training MEP (mathematical model)
and testing
The gathered data set was divided into twofolds for training
and testing (50 % for training and 50 % for testing). In the
training, MEP was run to find a computer program that
connects the criteria to the performance. The best model
was chosen considering the lowest statistical errors (shown
in Sect. 5).
4.3.1 Parameters of the predictive MEP-based algorithm,
the mathematical equation of the suppliers’
performance evaluation and statistical measures
in both the training and testing process
Since there is no exact rule to find the optimum parameters
in MEP (AI-based) techniques [21], for finding the best
structure of MEP several runs were conducted. Table 4
provides the best parameters of MEP predictive algorithm.
To find the optimized MEP-based model, there are some
important parameters which should be structured very well.
Table 2 Selection criteria for
evaluating the suppliers’
performance
Criteria Definition
Quality The excellence ability of supplied materials to meet or exceed purchasers’ expectations. In
order to evaluate this criterion, quality certification and standards are very important
[18]. This attribute has positive impact on the suppliers’ efficiency, and with increasing
QM, the suppliers’ efficiency increases
Delivery (D) This looks at the on-time delivery. As this criterion increases, supplier’s performance is
better
Technology This mainly focuses on the range of material supplied and modernity of the machinery.
This factor has a direct relationship with efficiency
Cost (C) This covers the final cost of the goods and transportation [19]. A supplier is termed as ‘‘the
more efficient supplier’’ whose total cost is lower than other competing suppliers
Flexibility (F) Rate of response to change [20]. With increasing this attribute, the supplier’s performance
increases
Neural Comput & Applic
123
P¼sin xTþxQ18:5ðÞþcos cos Ln xPxQ
xT
þ1:26
3
þsin sin cos e
xF
xQ
hi
þ0:075
ð0:93xDxPxTxQþ0:075Þ
The remaining 50 % of the data set is used for evalu-
ating the predictive ability of the model. In the training, the
MSE, MAE, and Rare 0.002, 0.013, and 0.963, respec-
tively. In the testing stage, MSE, MAE, and R are 0.007,
0.043, and 0.912, respectively. Figure 2shows the accu-
racy of the model for both training and testing.
5 Performance evaluation
To assess the performance of the model, Smith [22] defined
the following circumstances:
•If a model gives |R|[0.8, a strong correlation exists
between the predicted and real values.
•If a model gives 0.2 \|R|\0.8, a correlation exists
between the predicted and real values.
•If a model gives |R|\0.2, a weak correlation exists
between the predicted and real values.
In all conditions, the error values (e.g., MSE) should be
at the minimum [23]. The derived results show that the
MEP models provide very precise predictions for both the
training and testing data sets.
6 Conclusion
Suppliers’ performance evaluation as a common MCDM
problem has received much attention from academics and
practitioners. In today’s competitive world, companies
have concentrated on customer satisfaction and decreasing
price with long-term contracts with reliable suppliers.
Consequently, a robust and applicable method is needed to
ease monitoring suppliers’ performance for managers.
Over the recent decade, combining AHP with ANN has
gaining popularity. Although ANN is very powerful in
model prediction, its major drawback is the black box
system. Therefore, in this paper, a new evolutionary tech-
nique, namely MEP, was introduced to solve the earlier-
mentioned problem.
Generally, it could be concluded that the proposed
model (AHP–MEP) is very powerful and precise in sup-
pliers’ performance evaluation. The main limitation of the
proposed model is that while increasing the number of
criteria and alternative (supplier) the burden of computa-
tional complexity is increased.
Table 3 First data set
Inputs Output
Q D T P F Performance
3 6 3.5 4 1.5 0.05
3.5 3.5 6 6 1.5 0.05*
345470.07
7 6 4.5 6 3 0.10*
6.5 6.5 6.5 6.5 5.5 0.11
5 4 5.5 4 5 0.11*
5 6 6 5.5 2.5 0.12
3.5 5 6 6.5 3.5 0.13*
5.5 4.5 6 4.5 7 0.15
5 6.5 3.5 3.5 8 0.16*
5.5 6.5 5.5 7 5.5 0.19
5 7 5.5 7 5.5 0.19*
467590.19
2 6.5 2 8 4 0.22*
5.5 7.5 5.5 3.5 7.5 0.23
5 7 9 4.5 5 0.23*
4 4 7 6.5 6 0.25
6 6.5 8 4.5 5 0.27*
4 5.5 7 8 4 0.28
5 6.5 8 5 6 0.30*
7 8 7 4.5 2.5 0.34
6.5 7.5 6.0 6.5 3 0.36*
679780.42
787630.44*
8.5 8 7.5 2.5 7.5 0.46
7 6.5 7 5 8 0.47*
676560.48
7.5 6 7 5.5 8 0.49*
7.5 7.5 9 3 4.5 0.59
898450.59*
8.5 7 6.5 4 7 0.61
898540.61*
8 8 8.5 6 4 0.64
* These are the testing data set
Table 4 Optimal parameters of MEP
Parameters Setting
Population size 500–2000
Chromosome length 90 genes
Number of generations 500
Number of tournament 4
Crossover probability 0.5, 0.9
Crossover type Uniform
Mutation probability 0.01
Terminal set Problem input
Neural Comput & Applic
123
Acknowledgments This work is sponsored by Malaysian Ministry
of Higher Education High Impact Research (HIR-MOHE) Project
(UM.C/HIR/MOHE/ENG/01) and the University of Malaya Research
Grant Project (RP018C-13AET).
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Fig. 2 Actual versus predicted suppliers’ performance scores using the GEP model atraining data, btesting
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