logistics

Article
Supplier Selection Risk: A New Computer-Based
Decision-Making System with Fuzzy Extended AHP
Marcus V. C. Fagundes 1,2, * , Bernd Hellingrath 3 and Francisco G. M. Freires 1

1 Graduate Program in Industrial Engineering, Federal University of Bahia, Salvador, BA 40210-630, Brazil;
francisco.gaudencio@ufba.br
2 Department of Applied Social Sciences, State University of Southwest Bahia,
Vitória da Conquista, BA 45031-900, Brazil
3 Department of Information Systems, Münster School of Business and Economics, University of Münster,
48149 Münster, Germany; bernd.hellingrath@wi.uni-muenster.de
* Correspondence: marcus@uesb.edu.br; Tel.: +55-77-99156-1916

Abstract: Supplier risks have attracted significant attention in the supply chain risk management
literature. In this article, we propose a new computational system based on the ‘Fuzzy Extended
Analytic Hierarchy Process (FEAHP)’ method for supplier selection while considering the relevant
risks. We sought to evaluate the opportunities and limitations of using the FEAHP method in supplier
selection and analyzed the support of the system developed through the real case of a Brazilian
oil and natural gas company. The computational approach based on FEAHP automates supplier
selection by determining a hierarchy of criteria, sub-criteria, and alternatives. First, the criteria
and sub-criteria specific to the selection problem were identified by the experts taking the relevant
literature as a starting point. Next, the experts performed a pair-wise comparison of the predefined





 requirements using a linguistic scale. This evaluation was then quantified by calculating the priority
weights of criteria, sub-criteria, and alternatives. The best decision alternative is the one with the
Citation: Fagundes, M.V.C.;
Hellingrath, B.; Freires, F.G.M.
highest final score. Sensitivity analysis was performed to verify the results of the proposed model.
Supplier Selection Risk: A New The FEAHP computer approach automated the supplier selection process in a rational, flexible, and
Computer-Based Decision-Making agile way, as perceived by the focal company. From this, we hypothesized that using this system can
System with Fuzzy Extended AHP. provide helpful insights in choosing the best suppliers in an environment of risk and uncertainty,
Logistics 2021, 5, 13. https:// thereby maximizing supply chain performance.
doi.org/10.3390/logistics5010013
Keywords: supplier selection risk; multi-criteria programming; decision-making system; AHP;
Academic Editor: Željko Stević Fuzzy logic

Received: 29 January 2021

Accepted: 26 February 2021
Published: 3 March 2021
1. Introduction

Publisher’s Note: MDPI stays neutral

Currently, the supplier selection process is a vital aspect of the supply chain, as it
with regard to jurisdictional claims in
encompasses several risks inherent to businesses. Supplier performance can influence the
published maps and institutional affil-
competitiveness of the overall supply chain. Selecting the right suppliers for a supply chain
iations. brings benefits such as reduced procurement costs, contributes to product innovation, and
helps achieve effective production processes. In addition, the growing market competition
forces supply chains to establish more successful and sustainable relationships with their
suppliers. However, as the structure of a supply chain becomes broader, more complex,
and more globalized, companies become more dependent on their suppliers and also
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
vulnerable to risks and disruptions [1].
This article is an open access article
Certain ruptures can hinder the flow of products, resources, and capital, causing criti-
distributed under the terms and
cal reactions from customers and markets. As a dramatic example of this, we experienced
conditions of the Creative Commons the coronavirus pandemic (COVID-19), which severely affected the companies’ operations
Attribution (CC BY) license (https:// worldwide, highlighting the need for effective supply risk management plans. Therefore, a
creativecommons.org/licenses/by/ suitable methodology for the selection of suppliers is an increasingly important need for
4.0/). the supply chain’s resilience and robustness.

Logistics 2021, 5, 13. https://doi.org/10.3390/logistics5010013 https://www.mdpi.com/journal/logistics

Logistics 2021, 5, 13 2 of 17

A part of the previous literature on supply chain risk establishes that supplier selection
can be treated as a multi-criteria decision-making problem. The different supplier selection
criteria may vary depending on a company’s needs, preferences, technology strategy, and
risks [2]. Modeling a decision problem may involve one single or multiple decision-makers,
affecting one or more criteria throughout the process, such as price, quality, delivery,
service, etc. Each decision-maker has personal judgment values on these selection criteria,
so the value of these decision variables is subjectively influenced [3]. Hence, the supplier
selection process involves imprecision, uncertainty, subjectivity, and ambiguity.
Decision-making models that involve more than one criterion are called multi-criteria
decision-models. In these models, decision alternatives are evaluated according to the
number of criteria (and sub-criteria) defined, requiring the use of an appropriate method for
preference classification [4]. For this, the Analytic Hierarchy Process (AHP) has been widely
used because it can deal with real multi-criteria decision-making problems [5]. Despite its
popularity and conceptual simplicity, this method is often criticized for the inability to deal
with the uncertainty and inaccuracy inherent in mapping the perception of the decision-
maker [6]. In the traditional formulation of AHP, human judgments are represented as exact
or crisp numbers. However, in many practical cases, such as the supplier selection problem,
the human preference model is uncertain, vague, and subjective, and it is not feasible for
the decision-maker to express his preferences through exact numerical values. In these
cases, it is best for the decision-maker to use ‘interval evaluations’ or ‘fuzzy evaluations’.
Fuzzy set theory resembles human reasoning, mathematically representing the use
of approximate and uncertain information in decisions [7]. The need of today’s world to
find real solutions to problems with inherent inaccuracy has made fuzzy logic important
in the economic, social, industrial, and political spheres [8]. In order to deal with the
uncertainties of the decision problem and eliminate the disadvantages of AHP, the Fuzzy
AHP integrated approach is preferred in supplier selection research [6] because it is more
effective in representing the priority judgments of decision-makers.
Thus, in this article, we propose a new computational system based on the ‘Fuzzy
Extended Analytic Hierarchy Process (FEAHP)’ method, introduced by Chang [9], for
supplier selection considering risks. Specifically, we seek to: (i) evaluate the opportunities
and limitations of using the FEAHP method in the selection of supplier considering risks;
and (ii) analyze the support of the developed system through the real case of a Brazilian oil
and natural gas company. There are three contributions provided by this article. First, we
discussed the use of an integrated multi-criteria decision-making approach for solving an
important problem in today’s supply chains, second, we proposed a new computational
system that supports supplier selection in a rational, flexible, and agile way, and third,
we applied the computational tool developed in a real case of supplier selection while
considering risks of a large oil company, which allowed important empirical analyses for
the area of supply chain, logistics, and operations management.
Besides this introduction, this paper has five more sections. In the next section,
we present the literature review. In Section 3, we discuss the research methodology. In
Section 4, we present the application of the FEAHP-based computing system in a Brazilian
oil and natural gas company. We discuss the research empirical results in Section 5. Finally,
in Section 6 we present the conclusion, limitations, and future work.

2. Literature Review
In the first two decades of this century, several events have highlighted the inter-
dependencies between supply chain companies and their vulnerabilities to disruptive
triggers with dramatic consequences [10,11]. According to [12], the risk of supply chain
disruptions has increased in recent years due to the progress of globalization, increased
outsourcing, and an intensified focus on efficiency and lean management. Despite the
increased risks of the supply chain, few companies take effective measures to manage
them [13]. This gap makes supply chain risk management (SCRM) an attractive area of
research and professional practice. According to [14], SCRM results from coordination or
Logistics 2021, 5, 13 3 of 17

collaboration between supply chain partners to ensure profitability and continuity, encom-
passing two dimensions: operational risks and violation; mitigation of risks. According
to [15], SCRM involves all risks of the flow of finance, information, materials, and prod-
ucts, from suppliers to delivery of the product to the end user. From a process-oriented
perspective, many scholars define the SCRM as a structure that involves the identification,
evaluation, mitigation, and control of possible interruptions in the supply chain and its
negative impacts [16–22].
According to [18], the supplier risks attracted significant attention in the studies on
SCRM, with emphasis on supplier selection problems. Supplier selection is a critical issue
because poor decisions can cause various supply-related difficulties, such as delays in
deliveries and high defect rates [23]. In addition, as supply chains become global, external
factors, in addition to internal factors, increasingly influence supplier risks [14]. The risks
of supplier selection can be grouped into recurring risks if risk events are frequent but
short, and risks of interruption if risk events are rare but long [24,25].
To identify and classify the supplier selection risks proposed in the literature, we
reviewed several journal papers published between 2000 and 2020. First, the research terms
were defined. The keywords used in the search process were ‘supplier’ or ‘vendor’ or
‘provider’ and ‘risk’ or ‘risk type’ or ‘risk factor’. Secondly, several academic databases
were used to identify journal articles, including Emerald, Google Scholar, IEEExplore,
ScienceDirect, Scopus, Springer, Taylor and Francis, and Web of Science. Only peer-
reviewed articles written in English and published in international journals were selected.
We did not restrict the list of journals to ensure the capture of all relevant studies.
Third, the reference lists of articles were also evaluated to ensure that there were
no other relevant articles omitted from the research. Finally, the content of each article
was completely revised to ensure that it fits the context of supplier selection considering
risks. This analysis resulted in 26 journal articles. To classify these articles, we developed a
conceptual structure that integrates several risks of supplier selection, as shown in Table 1.
By synthesizing several points of view of the literature, we grouped the risks of supplier
selection into 11 types. Each established ‘risk type’ has associated ‘risk factors’, i.e., several
events and situations that lead to a specific ‘risk type’ [18].

Table 1. Articles on supplier selection risk.

Risk Type Risk Factor Reference

1. Quality Poor quality [26–29]
Delay in delivery [26–29]
2. Delivery
Low delivery speed [30]
Uncertain capacity [31,32]
Supplier failure [33–35]
Poor performance [30]
Unwillingness to cooperate and lack of supplier
[30,36]
3. Performance involvement
Supply restriction, restriction between
[37]
buyer-supplier and bad supplier profile
Interruption of supply [28,38–40]
Poor supplier service [41,42]
Low supplier reliability [1]
Low manufacturing capacity, high defect rate,
lack of warranty and after-sales service and lack [29]
of plans to deal with interruptions
4. Location Dispersed geographical location [2]
5. Flexibility Lack of/or low supplier flexibility [29,43]
6. Price High supplier price [29,30]
Logistics 2021, 5, 13 4 of 17

Table 1. Cont.

Risk Type Risk Factor Reference

7. Technology Technological risks [29,30,44]
Financial risks [30]
8. Financial Supplier financial stress [45]
Bad financial condition [29]
Economic risks [44,46]
9. Economic
Economic sustainability risk [47]
Environmental risk [44,47]
10. Environmental
Environmental project defect, high emission of
greenhouse gases, pollution, environmental [48]
non-compliance and natural wear
11. Social Social risks [44,49]
sustainability Social sustainability risk [47]

As shown in Table 1, the risk types related to performance, delivery, quality, and
sustainability attracted important attention in the literature, being considered as the main
criteria in the selection of suppliers. The most significant risk factors were poor quality,
delay in delivery, interruption of supply, supplier failure, and technological risks, which
can be defined as the most relevant sub-criteria in supplier selection according to the
above-mentioned literature review.
After determining the criteria (risk types) and sub-criteria (risk factors), decision-
makers should choose an appropriate and systematic method to evaluate and select al-
ternative suppliers. Many studies have reviewed the literature on supplier selection
models [50–53]. Multi-criteria decision-making models (MCDM), mathematical program-
ming (MP), and artificial intelligence (AI) techniques are some of the most popular ap-
proaches [50,53,54]. MCDM provides a methodological framework for decision support
systems; MP is used to optimize or evaluate supplier selection; AI identifies approximate
solutions to complex optimization problems [54]. MCDM approaches are the most popular
and within MCDM the Analytical Hierarchy Process (AHP) is most often applied [53].
AHP is widely used because it is effective in evaluating qualitative and quantitative
decision criteria [6]. It can be used alone or combined with other methods. The interaction
and interdependent relationships between evaluation criteria are critical and should be
considered in order to properly select a supplier. The hierarchy of decision criteria is
the subject of an AHP pair-wise comparison, which converts human preferences among
the available alternatives into ‘equal, not very strong, strong, very strong, and extremely
strong’ [5]. Although the crisp scale of AHP has the advantages of simplicity and ease
of use, it is unable to consider the uncertainty associated with subjective and individual
evaluation of the decision-maker. Therefore, to deal with the uncertainties of the decision
problem and eliminate the disadvantages of AHP, Fuzzy AHP is the preferred method
in supplier selection studies [6]. The main motivation behind incorporating the Fuzzy
set theory into the original AHP is based on the argument that human judgments and
preferences cannot be accurately represented by crisp numbers due to the uncertainty
inherent in human perception [55]. The Fuzzy set theory implements data classes with
unclear limits, that is, fuzzy limits [56].
There are several approaches in the studies on supplier selection that used the AHP
and Fuzzy methods in an individual or integrated way [57–61]. However, the literature
on the use of AHP and Fuzzy methods in the problem of supplier selection that considers
risks is more limited. In the work of [2], the integrated approach Fuzzy AHP is adopted
to evaluate the relevant decision criteria, including risk factors, in the development of a
global supplier selection system. In [32], Fuzzy, AHP, and TOPSIS (Technique for order
preference by similarity to the ideal solution) methods are used in the selection of suppliers
based on supply chain ecosystem, performance, and risk criteria. In [37], the integrated
Logistics 2021, 5, 13 5 of 17

method Fuzzy AHP is applied to the concept of benefits, opportunities, costs, and risks
to evaluate various aspects of suppliers. In [49], the combined Fuzzy-AHP-Input/Output
model approach is used to evaluate the social risks of supplier selection in the German
automotive industry. Finally, in [62] an integrated Fuzzy-AHP-VIKOR approach is used to
select sustainable global suppliers.
Based on the literature review presented in this section, we identified some important
observations on the problem of supplier selection considering risks: a. the risk types
(decision criteria) and risk factors (decision sub-criteria) prominent in the literature refer
mainly to aspects of supplier operational efficiency; b. the integrated Fuzzy AHP approach
helps to develop the capabilities of traditional AHP and Fuzzy methods, overcoming some
of their individual weaknesses; c. there is limited literature on the use of Fuzzy AHP
integrated into supplier risk evaluation, as well as on the feasibility of its implementation
in a practical and real manufacturing environment; and d. there is an insufficient discussion
on the development of a computational tool for supporting the evaluation and selection of
suppliers considering risks. Thus, to the best of our knowledge, this paper is an original
effort at evaluating suppliers in the context of the risks inherent in a real supply chain
through a computational solution that integrates the powerful AHP and Fuzzy techniques.

3. Methodology
The computational system for supplier selection considering risks proposed in this
paper is based on the ‘Fuzzy Extended Analytic Hierarchy Process’ (FEAHP) method by
Chang [9]. Although the first integrated Fuzzy AHP algorithm was introduced by [63],
other authors presented different approaches to deal with this method, such as [64–66].
However, the extent analysis approach presented by [9] has become more successful, as
it has a faster algorithm, requires less computational effort, and has more flexibility of
practical implementation compared to the algorithms proposed by [63–66].
Chang’s method uses triangular fuzzy numbers (TFN) for the pair-wise comparison
in AHP and consists of three essential parts [9]. In the first, the AHP approach is used to
structure the problem into hierarchy. In the second, the fuzzy extent analysis is performed,
from which normalized judgment matrices are obtained. Finally, the defuzzification and/or
classification of the weights is conducted through the principle of comparing fuzzy numbers
based on the degree of possibility.
Let X = { x1, x2 x3, ..., xn } be an object set, and U = {u1, u2, u3, ..., um } be a goal
set. According to the method of Chang’s extent analysis, each object is taken and extent
analysis for each goal, gi , is performed, respectively. Therefore, m extent analysis values
m with
for each object can be obtained, with the following signs: M1gi , M2gi , M3gi , . . . , Mgi
j
i = 1, 2, 3, . . . , n, where all Mgi are TFN, i.e., j = 1, 2, 3, . . . , m. The steps of Chang’s
extent analysis can be given as in the following [9]:
Step 1. The fuzzy synthetic extent with respect to i th object is defined as:
h i −1
m n m
∑ j=1 Mgi ⊗ ∑i=1 ∑ j=1 Mgi
j j
Si = . (1)

j
To obtain ∑m j=1 M gi , the operation of fuzzy addition of the values of the m extent
analysis for a particular matrix is performed such that:
 
m m m m
∑ j=1 Mgi = ∑ j=1 l j , ∑ j=1 m j , ∑ j=1 u j .
j
(2)

j −1
h i
j
Also to get ∑in=1 ∑mj =1 M gi , the fuzzy addition operator of the values Mgi is per-
formed such that:
 
n m n n n
∑i=1 ∑ j=1 gi ∑i=1 i ∑i=1 i ∑i=1 i .
j
M = l , m , u (3)
Logistics 2021, 5, 13 6 of 17

Then, the inverse of the calculated vector is obtained as:

j −1
 
h
n m
i 1 1 1
∑i=1 ∑ j=1 Mgi = ∑n ui , ∑n mi , ∑n li . (4)
i =1 i =1 i =1

Step 2. The degree of possibility of M2 = (l2 , m2 , u2 ) ≥ M1 = (l1 , m1 , u1 ) can be

defined as:


V ( M2 ≥ M1 ) = supy≥ x min µ M1 ( x ), µ M2 (y) = hgt( M1 ∩ M2 ) = µM2 (d). (5)

The result of Equation (5) corresponds to the point of highest intersection between M1
and M2 . This intersection is represented by the “point d” of Figure 1. However, to solve
Equation (5), the calculations established in Equation (6) are necessary:


 1 i f m2 ≥ m1
V ( M2 ≥ M1 ) = 0 i f l1 ≥ u 2 . (6)
( l1 − u 2 )
, otherwise


(m −u )−(m −l )
2 2 1 1

Figure 1. Intersection between M1 and M2 .

Step 3: The degree of possibility for a convex fuzzy number to be greater than k convex
fuzzy numbers Mi (i = 1, 2, . . . , k) can be defined by Equation (7):

V ( M ≥ M1 , M2 , . . . , Mk ) = V [( M ≥ M1 ) and ( M ≥ M2 ) and . . . and ( M ≥ Mk )] =

(7)
minV ( M ≥ Mi ).

Equation (8) is:

d0 ( Ai ) = minV (Si ≥ Sk ). (8)
For k = 1, 2, . . . , n, k 6= i, weight vector is given by:
T
W 0 = (d0 ( A1 ), d0 ( A2 ), . . . , d0 ( An )) (9)

where Ai (i = 1, 2, . . . , n) are n elements.

Step 4: after normalization, the normalized weight vectors are (where W is a non-
fuzzy number):
W = (d( A1 ), d( A2 ), . . . , d( An )) T . (10)
To automate the calculation of Chang’s FEAHP method [9], we developed a computa-
tional system, in Matlab language, in the software MATLAB 2020a, The MathWorks, Inc.
Logistics 2021, 5, 13 7 of 17

This system is structured in three interactive and interdependent modules. Modules 1 and
2 represent codes called ‘functions’ and module 3 corresponds to the ‘main program’. In
the execution of the developed programming, modules 1 and 2 are activated by module 3,
according to the system architecture shown in Figure 2.

Figure 2. Architecture computational system proposed.

Module 1 converts the pair-wise evaluation/judgement matrices of the decision-

maker(s) and applies the TFN concept. The results of module 1 are arranged hierarchically
in module 2. Module 3 provides the system’s communication interface with the end user
and is able to model the fuzzy extended analytical hierarchy of any multi-criteria decision
problem, regardless of the number of variables. The interaction between the three modules
of the system provides as the main output the most appropriate multi-criteria decision,
i.e., the best supplier among the available supplier alternatives. If the system output
meets the general decision goal, the result is approved by the decision-maker(s); otherwise,
the structure of the decision problem and its data can be rectified and, consequently,
reprocessed (system feedback).

4. Application of the FEAHP-Based Computing System in a Real Case of Supplier

Selection Risk
Brazil’s largest independent onshore oil and natural gas exploration and production
company is specialized in operating mature and/or economically marginal fields through
innovative hydrocarbon recovery methodologies and efficient operating costs. The com-
pany’s long-term goal is to be the safest, most efficient, and most profitable independent
onshore oil operator in Brazil. To this end, it has established in its new strategic directives
a global supplier development plan, in which the problem of supplier selection should
become of vital importance. However, the current supplier determination process in this
company is often carried out intuitively and with weak operating procedures in terms of
standardization. The company’s managers recognize that this current supplier selection
practice consumes a lot of effort and time from the purchasing team, as several risks have
Logistics 2021, 5, 13 8 of 17

to be considered when determining the priority supplier. Therefore, the desired global
supplier development strategy of this company depends directly on the decision to select
the best suppliers considering multiple criteria.
It is within this context that we applied the FEAHP-based computing system to select
the best supplier for a critical component of the aforementioned company: industrial
steel pipes and fittings for gas and oil pipelines. For this, we had the participation of
a specialized team of five members from the purchasing and supply management area
of the focal company, with an average experience of more than nine years. This team
consists of a Purchasing Executive, a Purchasing Planner, a Purchasing Supervisor, and
two Material Controllers.
The participation of this expert team took place through a series of brainstorming
sessions and interviews. First, the consent of all experts was obtained in order to identify the
main criteria and sub-criteria relevant in supplier selection considering risks. Subsequently,
the consent of all experts was obtained to comparatively evaluate the predefined criteria,
sub-criteria, and supplier alternatives.
Taking the typical risk types and risk factors for most companies as a starting point,
as presented in Table 1, the experts identified by consensus the following criteria (Cx ) and
sub-criteria (Subc x ) as the most important in the company’s supplier selection process:
C1 delivery (Subc1 —delay in delivery; Subc2 —low delivery speed), C2 performance (Subc3 —
supplier failure; Subc4 —interruption of supply; Subc5 —low supplier reliability), C3 price
(Subc6 —high supplier price; Subc7 —increase in supplier costs), and C4 financial (Subc8 —
bad financial condition of the supplier; Subc9 —single supply that causes the buyer’s
financial loss). Almost all of these criteria and sub-criteria identified by the company
have already been considered in previous research of the area, with the exception of the
sub-criteria Subc7 and Subc9 . Therefore, the specific risk factors represented by Subc7 and
Subc9 can be considered as unique to the Brazilian oil and gas company studied.
From these criteria and sub-criteria for supplier selection, the hierarchy of the decision
problem was structured, as shown in Figure 3. The alternative suppliers were identified as
A1 , A2 , and A3 . Thus, in the hierarchical structuring of the selection problem, we defined
the general goal at the first level, the criteria in the second level, the sub-criteria in the
third level, and the alternatives suppliers in the fourth level. After the development of
the problem hierarchy, the different priority weights of each criterion, sub-criterion, and
alternative supplier were calculated using the FEAHP method. The comparison of the
importance of the criteria, sub-criteria, and alternative suppliers in relation to others was
carried out with the help of the questionnaire applied to the focal company’s purchasing
experts. The questionnaires made it easier to answer pair-wise comparison questions. The
preference of one measure over another was decided consensually by the experience of the
company’s experts. First, these experts compared the criteria with respect to the general
goal, then, they compared the sub-criteria with respect to the main criteria. At the end,
they compared the supplier in relation to each sub-criterion.

Table 2. Linguistic variables with corresponding triangular fuzzy values.

Triangular Fuzzy Value Triangular Fuzzy Value

Linguistic Variables
Corresponding Corresponding Reverse
Equal (1, 1, 1) (1, 1, 1)
Not very strong (2, 3, 4) (1/4, 1/3, 1/2)
Strong (4, 5, 6) (1/6, 1/5, 1/4)
Very strong (6, 7, 8) (1/8, 1/7, 1/6)
Extremely strong (9, 9, 9) (1/9, 1/9, 1/9)
Logistics 2021, 5, 13 9 of 17

Figure 3. Real problem hierarchy of supplier selection risk. The linguistic variables were used to
make the pair-wise comparisons. These linguistic variables were then converted to triangular fuzzy
numbers (TFN), as shown in Table 2. That is, for each numerical value of the pair-wise comparison
matrices, three values were associated that correspond to the ‘lower’, ‘middle’ and ‘upper’ values.

To define the different priority weights of each criterion, sub-criterion, and alternative
supplier, a first fuzzy evaluation matrix was constructed by pair-wise judging the criteria
in relation to the general goal, as shown in Table 3.

Table 3. Fuzzy evaluation of the criteria in relation to the general goal.

Gg C1 C2 C3 C4 Wo
C1 (1, 1, 1) (1, 1, 1) (6, 7, 8) (4, 5, 6) 0
C2 (1, 1, 1) (1, 1, 1) (9, 9, 9) (9, 9, 9) 1
C3 (1/8, 1/7, 1/6) (1/9, 1/9, 1/9) (1, 1, 1) (1, 1, 1) 0
C4 (1/6, 1/5, 1/4) (1/9, 1/9, 1/9) (1, 1, 1) (1, 1, 1) 0
Logistics 2021, 5, 13 10 of 17

The values of the fuzzy synthetic extension in relation to each of the criteria were cal-
culated using Equation (1) and the fuzzy algebraic operations defined in Equations (2)–(4),
according to S1 , S2 , S3 , and S4 :
 
1 1 1
S1 = (12, 14, 16) ⊗ , , = (0.2952, 0.363, 0.438)
40.638 38.565 36.513
 
1 1 1
S2 = (20, 20, 20) ⊗ , , = (0.4921, 0.5186, 0.5477)
40.638 38.565 36.513
 
1 1 1
S3 = (2.236, 2.253, 2.277) ⊗ , , = (0.055, 0.0584, 0.0623)
40.638 38.565 36.513
 
1 1 1
S4 = (2.277, 2.311, 2.361) ⊗ , , = (0.056, 0.0599, 0.0646).
40.638 38.565 36.513
The degree of possibility Si over S j (i 6= j) was determined using Equation (6):

V (S1 ≥ S2 ) = 0, V (S1 ≥ S3 ) = 1, V (S1 ≥ S4 ) = 1, V (S2 ≥ S1 ) = 1,V (S2 ≥ S3 ) =

1, V (S2 ≥ S4 ) = 1, V (S3 ≥ S1 ) = 0, V (S3 ≥ S2 ) = 0, V (S3 ≥ S4 ) = 0.8103, V (S4 ≥ S1 ) =
0, V (S4 ≥ S2 ) = 0, V (S4 ≥ S3 ) = 1.

Using Equation (8), the minimum degree of possibility was established as:

d0 (S1 ou C1 ) = V (S1 ≥ S2 , S3 , S4 ) = min(0, 1, 1) = 0

d0 (S2 ou C2 ) = V (S2 ≥ S1 , S3 , S4 ) = min(1, 1, 1) = 1

d0 (S3 ou C3 ) = V (S3 ≥ S1 , S2 , S4 ) = min(0, 0, 0.8103) = 0
d0 (S4 ou C4 ) = V (S4 ≥ S1 , S2 , S3 ) = min(0, 0, 1) = 0.
Therefore, with Equation (9) the weight vector was given as W 0 = (0, 1, 0, 0).
After the normalization process, the weight vector in relation to the decision criteria
S1 (C1 ), S2 (C2 ), S3 (C3 ), and S4 (C4 ) was represented in Equation (10) as Wo = (0, 1, 0, 0) T .
Subsequently, the different sub-criteria were compared separately according to each
of the criteria, following the same procedure described above. As an example, the fuzzy
evaluation matrix of the sub-criteria (Subc1 , Subc2 , Subc3 ) with respect to the criterion C1
and the respective weight vectors are shown in Table 4. The fuzzy evaluation procedure
of the other sub-criteria (Subc4 , . . . , Subc9 ) in relation to the criteria C2 , C3, and C4 was
the same.

Table 4. Fuzzy evaluation of the sub-criteria in relation to the criterion C1 .

C1 Subc1 Subc2 Subc3 Wc1

Subc1 (1, 1, 1) (6, 7, 8) (4, 5, 6) 0.799
Subc2 (1/8, 1/7, 1/6) (1, 1, 1) (9, 9, 9) 0.2
Subc3 (1/6, 1/5, 1/4) (1/9, 1/9, 1/9) (1, 1, 1) 0

Similarly, we determined the fuzzy evaluation matrices of the decision alternatives

and their weight vectors in relation to the corresponding sub-criteria. As an example, we
present in Table 5 the fuzzy evaluation matrix of the alternatives ( A1 , A2 , A3 ) in relation
to Subc1 and their weight vectors. The fuzzy evaluation procedure of decision alternatives
( A1 , A2 , A3 ) in relation to the other sub-criteria (Subc2 , . . . , Subc9 ) was also the same.
Logistics 2021, 5, 13 11 of 17

Table 5. Fuzzy evaluation of the alternatives in relation to the sub-criterion Subc1 .

Subc1 A1 A2 A3 WSubc1
A1 (1, 1, 1) (2, 3, 4) (4, 5, 6) 0.536
A2 (1/4, 1/3, 1/2) (1, 1, 1) (1/8, 1/7, 1/6) 0
A3 (1/6, 1/5, 1/4) (6, 7, 8) (1, 1, 1) 0.463

At this point, based on the values obtained, we performed the summary combination
of the priority weights of the alternatives of suppliers in relation to each of the criteria.
For this, the supplier’s weights were added, which were multiplied by the corresponding
sub-criteria. To exemplify this procedure, we present the results of Table 6. The same
conduct was carried out in the calculation of the weights of the alternatives in relation to
the other sub-criteria (Subc4 , . . . , Subc9 ) of the criteria C2 , C3 , and C4 .

Table 6. Combination of priority weights: sub-criteria of the criterion C1 .

Alternatives Priority
Weights Subc1 0.799 Subc2 0.2 Subc3 0
Weights
Alternatives
A1 0.536 0.135 1 0.4552
A2 0 0.15 0 0.03
A3 0.463 0.713 0 0.5125

Finally, the final priority weights of each supplier were calculated by adding the
supplier’s weights multiplied by the corresponding criteria weights. The alternative that
obtained the highest priority weight was defined as the best supplier for the company
studied. The results of this procedure are shown in Table 7.

Table 7. Summary combination of priority weighting: criteria of the general goal.

Weights of the Alternatives

C1 0 C2 1 C3 0 C4 0
Criteria Priority Weights
Alternatives
A1 0.4552 0.848 1 0.135 0.848
A2 0.03 0.151 0 0.15 0.151
A3 0.5125 0 0 0.713 0

According to the final score shown in Table 7, the best supplier for the focal company
is the A1 which obtained the highest priority weight of the alternatives (0.848), followed
by the alternative supplier A2 (0.151). Figure 4 shows this result in the computer system
interface developed.
Logistics 2021, 5, 13 12 of 17

Figure 4. Final priority weights of suppliers in the computer system interface.

5. Results and Discussions

According to the results of Table 7, the final priority weights of the different criteria
show that the performance (C2 ) of the supplier has had the greatest importance. Because it
is a critical supply for the addressed company, any supplier failure, interruption of supply,
or low reliability of the products/services provided could affect industrial operations
and the value delivered to the end customer. This result of the case experts’ evaluation
corroborates the validation of performance as a key criterion for most companies’ supplier
selection risk problem, as described in the previous literature review. In fact, suppliers are
manufacturer’s external organizations or business partners, and indeed their performance
will decide the future performance of the whole supply chain [2].
A finding that contributes to the understanding of the importance of the performance
(C2 ) criterion is the high priority weight of one of its sub-criteria, the sub-criterion ‘low
reliability of the supplier (Subc5 )’ (which obtained weight equal to 1). The interpretation of
this result is that the component to be supplied to the focal company must strictly meet the
safety and maintainability requirements intrinsic to the oil and natural gas exploration and
production industry. Regarding the other sub-criteria, we found that the sub-criteria ‘high
supplier price (Subc6 )’ and ‘single supply (Subc9 )’ also obtained high priority weights
(weight equal to 1 for each): the first for the risk of increasing the buyer’s production and
operating costs, and the second for the risk of increasing dependence with the supplier,
decreasing the buyer’s bargaining strength. In addition, the fact that the sub-criterion
‘single supply (Subc9 )’ has not been considered in previous literature as a typical risk factor,
thus proving to be unique to the company studied, allowed us to infer that certain sub-
criteria common to most companies may not present typical results for other companies, as
evidenced in the case studied.
Figure 5 shows the sensitivity analysis graph in relation to the general goal, in which it
is possible to evaluate suppliers in relation to each of the four criteria. It is clear to note that
Logistics 2021, 5, 13 13 of 17

supplier A3 has a higher priority weight in relation to the delivery (C1 ) and financial (C4 )
criteria, while supplier A1 has a higher weight in relation to the performance (C2 ) and price
(C3 ) criteria. Therefore, sensitivity analysis confirms A1 as the best alternative supplier for
the focal company.

Figure 5. Sensitivity analysis graph.

Finally, we found that the developed computing system adequately supported all the
calculation steps of the FEAHP method applied in the real process of supplier selection
considering risks. It provided efficient decision problem hierarchy modeling, computed
fuzzy extended analysis without failures and/or errors, and provided final priority weight
rankings of all evaluated criteria, sub-criteria, and alternatives. The adoption of this
computational system allowed automated decision-making support to choose the best
supplier for the focal company in a rational, flexible, and agile way. By applying the FEAHP
computational approach, the company’s experts have qualitatively perceived a one-off
decrease in the effort and time normally required to select a priority supplier. This allowed
us to hypothesize that the continued use of the new system by the studied company can
promote the improvement of the overall supplier risk evaluation, the reduction of lead
time and procurement costs for industrial materials and equipment, and an improved
performance of the whole supply chain.

6. Conclusions, Limitations and Future Work

Supplier risks have attracted significant attention in the supply chain risk management
literature. However, the literature on the problem of supplier selection risks is limited. In
addition, there is insufficient research on the computational model for supplier selection
considering risks and its feasibility of practical implementation in real operating and manu-
facturing environments. Therefore, this study proposes a new computational system based
on the ‘Fuzzy Extended Analytic Hierarchy Process (FEAHP)’ method for the selection of
suppliers considering risks. We seek to evaluate the opportunities and limitations of using
the FEAHP method in the supplier selection considering the risks and analyze the support
of the system developed through the real case of a Brazilian oil and natural gas company.
The computational approach based on FEAHP automates the selection of suppliers
considering risks by determining a hierarchy of criteria, sub-criteria, and alternatives. First,
the criteria and sub-criteria specific to the selection problem were identified by the focal
company’s decision-makers (experts) using relevant literature as a starting point. Next,
the experts performed a pair-wise comparison of the predefined requirements using a
Logistics 2021, 5, 13 14 of 17

linguistically scaled questionnaire. This evaluation was then quantified by calculating the
priority weights of criteria, sub-criteria, and alternatives using the FEAHP method. The
best decision alternative is the one with the highest final score.
We applied the FEAHP computer system to support supplier selection considering
risks of a Brazilian oil and natural gas company. The experts identified four criteria,
nine sub-criteria, and three alternative suppliers as the most important in the company’s
supplier selection process. After the general computation of the final priority weighs,
we found that the supplier’s performance (C2 ) criterion is the most important one. This
finding is aligned with previous literature in the field which also considers performance
as a key criterion regarding supplier selection risks for most companies. The sub-criteria
‘low reliability of the supplier (Subc5 )’, ‘high supplier price (Subc6 )’, and ‘single supply
(Subc9 )’ obtained the highest priority weights. In turn, the sub-criterion ‘single supply
(Subc9 )’ presented unique importance for the company studied, distinguishing itself from
the other sub-criteria typical of most companies. Supplier A1 is the best supplier for the
focal company as it obtained the highest priority weight (0.848), followed by alternative
supplier A2 (0.151). The sensitivity analysis of the general goal shows that the A1 supplier
has the highest priority weight in relation to the criteria performance (C2 ) and price (C3 ),
confirming it as the best alternative for the studied company.
The FEAHP computational approach rationally, flexibly, and agilely automated the
supplier selection process, as qualitatively evidenced by the case study experts. From this,
we hypothesized that using this system can provide helpful insights in choosing the best
suppliers in an environment of risk and uncertainty, maximizing supply chain performance.
This research has some limitations. Since the empirical analysis is based only on a case
study of a Brazilian oil company, there are restrictions in generalizing the results, that
is, the conclusions of the paper cannot be extended to other companies. In addition, the
methodology for evaluating the main criteria, sub-criteria, and alternative suppliers is
based on the experience of the company’s experts, so there may be noise and distortion in
the respondents’ perception of the accuracy of the information provided.
Future research may examine a larger set of business samples, including various
industry types or empirical research in other developing countries. In addition, risk and
uncertainty criteria from various supply chain echelons as well as emerging social and
environmental risk criteria may be added to the proposed model. Finally, further work can
be done to analyze the economic efficiency of the FEAHP computational approach, and to
compare or integrate it with alternative supplier selection methods based on MCDM, MP,
and AI.

Author Contributions: Conceptualization, M.V.C.F., B.H. and F.G.M.F.; methodology, M.V.C.F. and
F.G.M.F.; programming and software development, M.V.C.F.; data collection and analysis, M.V.C.F.;
writing and revision, M.V.C.F., B.H. and F.G.M.F. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: This study did not require ethical review and approval
according to the norms of the Graduate Program in Industrial Engineering at the Federal University
of Bahia, Brazil.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: The data presented in this study are available within the article.
Acknowledgments: We appreciate the valuable contributions of researchers from the Chair for
Information Systems and Supply Chain Management, Department of Information Systems at the
Münster School of Business and Economics, University of Münster, Germany.
Conflicts of Interest: The authors declare no conflict of interest.
Logistics 2021, 5, 13 15 of 17

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