1. bookVolume 21 (2021): Issue 4 (December 2021)
Journal Details
License
Format
Journal
First Published
19 Oct 2012
Publication timeframe
4 times per year
Languages
English
access type Open Access

Development of Subcontractor Selection Models Using Fuzzy and AHP Methods in the Apparel Industry Supply Chain

Published Online: 27 Nov 2020
Page range: 413 - 427
Journal Details
License
Format
Journal
First Published
19 Oct 2012
Publication timeframe
4 times per year
Languages
English
Abstract

The subcontractor selection decision is inherently a multicriterion problem. It is a decision of strategic importance for companies. The nature of this decision is usually complex and unstructured. Management science techniques might be helpful tools for solving these kinds of decision-making problems. In this research, the fuzzy logic method and the analytic hierarchy process were applied for the selection of suitable subcontractors in an apparel supply chain.

In general, many factors, such as quality level, price offer, and delivery delay, were considered to determine the most suitable and reliable subcontractors that fit the company's strategy. This survey is carried out using the database of an apparel company manufacturing denim products.

Keywords

Introduction

Nowadays subcontractors’ categorization, selection, and performance evaluation are decisions of strategic importance for companies. Global competition, mass customization, high customer expectations, and harsh economic conditions are forcing companies to rely on external subcontractors to contribute a larger portion of parts, materials, and assemblies to finished products and to manage a growing number of processes and functions that were once controlled internally. The literature suggests that many studies are interested in this topic, one of them focused on supplier selection and evaluation using the multiple criteria decision-making model (MCDM) according to the concept TOPSIS based on the closeness coefficient, and as a result, this model gave the ranking of supplier and evaluation status of all suppliers [1]. Other research studies have used the fuzzy supplier selection algorithm, based on the ranking of the supplier, and found that the used model is an easy and realistic approach for supplier selection. It gives a concrete result by recording the purchasing experts’ experiences and processes these with fuzzy logic arithmetic [2]. Maurizio et al. have used a fuzzy approach to determine the rank of the supplier, their attempts based on the fuzzy suitability index to determine the final ranking, and they approved that the fuzzy approach is able to deal with linguistic variables [3]. Felix et al. have developed their research according to the model fuzzy analytic hierarchy process (AHP), they combined the fuzzy method with the AHP method to clarify the fuzzy. As a result, the used model is proved to be simple, less time taking, and having a less computational expense. They found that the use of fuzzy AHP does not involve cumbersome mathematical operation and it is easy to handle the multiattribute decision-making problems like global supplier selection. They found that the combined fuzzy-AHP has the ability to capture the vagueness of human thinking style and effectively solve multiattribute decision-making problems [4]. In addition, Sharon et al. have described a decision model that incorporates a decision maker's subjective assessments and applies fuzzy arithmetic operators to manipulate and quantify these assessments. This model treated the subjectivity in linguistic terms [5]. Some other research studies have used an integrated approach of fuzzy multiattribute utility theory and multiobjective programming for rating and selecting the best suppliers and allocating the optimum order quantities; however, this study integrates fuzzy AHP, fuzzy TOPSIS, and fuzzy MOLP to solve the problem of supplier selection and order allocation. At first, they have used the fuzzy AHP to calculate the relative weights of supplier selection criteria; then, they have used the fuzzy TOPSIS for ranking of suppliers according to the selected criteria. Finally, the weights of the criteria and ranks of suppliers were incorporated into the MOLP model to determine the optimal order quantity from each supplier [6]. In the construction field, many research studies have used fuzzy logic for the selection and evaluation of subcontractors [7,8,9]. Kumar et al. have used a fuzzy goal programming approach for solving the vendor selection problem with multiple objectives, in which some of the parameters are fuzzy and they showed that this approach has the capability to handle realistic situations in a fuzzy environment and provides a better decision tool for the vendor selection decision in a supply chain [10]. Many researchers have used the fuzzy logic to predict the hydrophobic nature of knitted fabrics [11] and others have used the fuzzy logic for modeling the residual bagging behaviors of denim fabric [12]. Weber and Current have developed their research according to the model multiobjective programming [13]. In the work of Soukoup, he used the payoff matrix model that allows defining several scenarios of the future behavior of suppliers [14]. Ellram used a vendor profile analysis model to choose the best supplier [15]. Roodhooft and Konings have used a method based on the total cost to classify the supplier in descending order [16]. Hinkle et al. have used a cluster analysis model, which allows to group the suppliers according to the scores obtained [17]. In the field of supply chain management and, in particular, in the selection and evaluation of textile subcontractors, the majority of articles in the literature are concerned with the selection of the supplier. Given the importance of outsourcing in the textile sector, we have focused on this theme and tried to model the selection of subcontractors in a clothing supply chain for specific orders by using two methods, namely, the AHP and the fuzzy logic.

Experimental section
Materials and methods
Data set used

This work was carried out in a company specialized in manufacturing Denim products employing 350 persons with an annual production of 800,000 pieces. This company operates as an ordering party for several subcontractors and as a manufacturer of several items (pants, jackets, skirts, etc.) in small and medium orders for different international brands requiring high-quality level, good price, and short-time delivery.

In this study, a database composed of nine subcontractors of the company was used, and each subcontractor is characterized by four parameters, namely, daily production, late delivery, second choice ratio, and subcontractor price. The variation range of the dataset is indicated in Table 1.

Subcontractors’ parameters

Daily production (pieces/day) Late delivery (days) Second choice ratio (%) Price / piece (euro)
Sub 1 650 7 0,66 0,7
Sub 2 700 6 0,8 1
Sub 3 600 4 0,4 0,6
Sub 4 600 0 0,3 0,5
Sub 5 700 8 0,7 1
Sub 6 500 4 0,71 0,5
Sub 7 700 2 0,51 0,7
Sub 8 650 5 0,5 1,2
Sub 9 800 10 0,9 0,9

As a sample, 30 production orders were used, and each production order is characterized by quantity, delivery delay, accepted defects ratio, and price per piece (Table 2).

Production order parameters

Number of production order Quantity (pieces) Delivery delay (days) Accepted Defects ratio (%) Price /piece (euro)
1 1200 14 4 0,7
2 1415 14 2 0,4
3 1001 14 4 0,7
4 610 8 1 0,6
5 240 8 1 1
6 313 8 6 0,5
7 178 23 6 0,5
8 518 10 3 0,9
9 805 17 2 0,6
10 2329 17 3 1
11 3003 14 2 0,6
12 5000 10 2 0,9
13 2560 17 1,5 1,1
14 800 14 1 1
15 300 7 4 0,5
16 2329 17 2 0,7
17 6780 11 5 0,45
18 452 8 1 0,7
19 4000 18 2 1
20 586 14 3 1
21 3000 15 1 0,8
22 3350 12 2 0,5
23 3200 11 1 0,5
24 587 13 1 0,9
25 782 1 1 0,5
26 520 15 4 0,6
27 250 0 2 0,5
28 221 10 1 0,9
29 224 3 2 0,7
30 238 4 3 0,7
Fuzzy logic modeling

The fuzzy logic is an extension of crisp logic, which was first proposed by Lotfi Zadeh [18]. In crisp logic, like binary logic, variables are true or false, 1 or 0. In fuzzy logic, a fuzzy set contains elements with only partial membership ranging from 0 to 1 to define the uncertainty of classes that do not have clearly defined boundaries. For each input and output variable of a fuzzy inference system, the fuzzy sets are created by dividing the universe of discourse into several subregions, named in linguistic terms (high, medium, low, etc.).

Fuzzy logic steps:
Step 1: Define the linguistic variables and terms

Linguistic variables are the input or output variables of the system whose values are words or sentences from a natural language instead of numerical values.

Step 2: Develop membership functions

Membership functions are used in the fuzzification and defuzzification steps of a fuzzy logic system to map the nonfuzzy input values to fuzzy linguistic terms and vice versa. A membership function is used to quantify a linguistic term. There are different forms of membership functions such as triangular, trapezoidal, piecewise linear, Gaussian, or singleton [19] (Figure 19).

Figure 1

Different shapes of membership function graphs

Step 3: Fuzzy inference

The fuzzy rules deduce knowledge about the state of the system according to the linguistic qualifications provided in the fuzzification stage.

Step 4: Defuzzification

Fuzzy rule-based systems evaluate linguistic if-then rules using fuzzification, inference, and composition procedures. They produce fuzzy results that usually have to be converted into crisp output by defuzzification.

Analytic hierarchy process

The process of hierarchical analysis is a structured technique for organizing and analyzing complex decisions, based on mathematics and psychology. It was developed by Thomas L. Saaty in 1970 [20]. It is used worldwide for a wide variety of decision-making processes whether government decisions, business, industry, health, shipbuilding, or education [21].

AHP process

The principal steps of the AHP algorithm are as follows:

Structure a decision problem and criteria selection.

Develop a pairwise comparison matrix for each criterion.

Develop a pairwise comparison matrix for each alternative for each criterion.

Calculate the coefficient consistency.

Obtain an overall relative score for each alternative.

Structuring a decision problem and the selection of criteria

The first step in AHP is to develop a graphical representation of the problem in terms of the overall goal, the criteria, and the decision alternatives (Figure 2).

Figure 2

Analytic hierarchy process

Developing a pairwise comparison matrix for each criterion

Step 1: Construct a pairwise comparison matrix (n*n) for criteria with respect to objective. The weights of the criteria should be calculated by using a pairwise comparison between criteria by applying Saaty's scales ranging from l to 9 (Table 3, 4).

Saaty's 1–9 scale for pair-wise comparisons

Numerical rate Verbal judgment of preference
1 Equal importance
3 Weak importance of one over another
5 Essential or strong importance
7 Demonstrated importance
9 Absolute importance
2, 4, 6, 8 Intermediate values between the two adjacent judgment

Pairwise comparison matrix of criterion

Criteria C1 C2 C3 …. Cn
C1 1 W1/W2 W1/W3 …. W1/Wn
C2 W2/W1 1 W2/W3 …. W2/Wn
C3 W3/W1 W3/W2 1 …. W3/Wn
.. …. 1
Cn Wn/W1 Wn/W2 Wn/W3 Wn/W.. 1

Step 2: Normalize the resulting matrix: Sum the values in each column of the pairwise matrix.

Step 3: Divide each element in the matrix by its column total to generate a normalized pairwise matrix (Table 5).

VS=[Vs1Vs2....Vsn]=[j=1nX1jnj=1nX2jn....j=1nXnjn] {\rm{VS}} = \left[ {\matrix{ {Vs1} \cr {Vs2} \cr {....} \cr {Vsn} \cr } } \right] = \left[ {\matrix{ {{{\sum _{j = 1}^n{\rm{X}}1{\rm{j}}} \over n}} \cr {{{\sum _{j = 1}^n{\rm{X}}2{\rm{j}}} \over n}} \cr {....} \cr {{{\sum _{j = 1}^n{\rm{Xnj}}} \over n}} \cr } } \right]

Normalization Matrix

Criteria C1 C2 C3 …. Cn
C1 X11 X12 X13 X1n
C2 X11 X22 X23 X2n
C3 X31 X32 X33 X3n
..
Cn Xn1 Xn2 Xn3 Xnn

Step 4: Calculate the row averages “Vs” of the normalized pairwise matrix, a weights vector is obtained:

Developing a pairwise comparison matrix for each alternative for each criterion

Step 1: Construct a pairwise comparison matrix (n*n) for criteria with respect to objective. The weights of the alternatives should be calculated by using a pairwise comparison between alternatives for each criterion by applying Saaty's scales ranging from l to 9. The alternative in the row is being compared to the alternative in the column.

The next table shows the comparison matrix for each alternative for each criterion: for criteria C1 (Table 6).

Pairwise comparison matrix for each alternative for each criteria

Alternative A1 A2 A3 …. An
A1 1 W1/W2 W1/W3 …. W1/Wn
A2 W2/W1 1 W2/W3 …. W2/Wn
A3 W3/W1 W3/W2 1 …. W3/Wn
.. …. 1
An Wn/W1 Wn/W2 Wn/W3 Wn/W.. 1

Step 2: Normalizing the resulting matrix: Sum the values in each column of the pairwise matrix.

Step 3: Divide each element in the matrix by its column total to generate a normalized pairwise matrix (Table 7).

Normalization Matrix

Alternative A1 A2 A3 …. An
A1 Y11 Y12 Y13 Y1n
A2 Y11 Y22 Y23 Y2n
A3 Y31 Y32 Y33 Y3n
..
An Yn1 Yn2 Yn3 Ynn

Step 4: Calculate the row averages “Ts” of the normalized pairwise matrix, a weights vector is obtained Ts=[Ts1Ts2....Tsn]=[j=1nY1jnj=1nY2jn....j=1nYnjn] {\rm{Ts}} = \left[ {\matrix{ {Ts1} \cr {Ts2} \cr {....} \cr {Tsn} \cr } } \right] = \left[ {\matrix{ {{{\sum _{j = 1}^n{\rm{Y}}1{\rm{j}}} \over n}} \cr {{{\sum _{j = 1}^n{\rm{Y}}2{\rm{j}}} \over n}} \cr {....} \cr {{{\sum _{j = 1}^n{\rm{Ynj}}} \over n}} \cr } } \right]

Calculate the coefficient consistency

To validate the results of the AHP, the consistency ratio (CR) is calculated using the following equation: CR=CIRI: {\rm{CR}} = {{{{CI}}} \over {{{RI}}}}:

In which the consistency index (CI) is, in turn, measured through the following equation: CI=λmaxnn1: {\rm{CI}} = {{\lambda \max - {\rm{n}}} \over {{\rm{n}} - 1}}:

With: ^max:

maximum eigenvalue of the matrix

n:

order of the matrix.

The value of RI is related to the dimension of the matrix and will be extracted from the table (Table 8).

Random Consistency Index (RI)

N 1 2 3 4 5 6 7 8 9 10
RI 0 0.0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49

The CR has shown that a CR of 0.10 or less is acceptable to continue the AHP analysis. If the CR is greater than 0.10, it is necessary to revise the judgments to locate the cause of the inconsistency and correct it.

Obtaining an overall relative score for each alternative:

Step 1: A matrix of solutions was created. For each alternative, the average value of each criterion for each alternative was taken (Table 9).

Matrix of solution

Criteria
alternatives C1 C2 C3 …. Cn
A1 Ts11 Ts12 Ts13 Ts1n
A2 Ts21 Ts22 Ts23 Ts2n
A3 Ts31 Ts32 Ts33 Ts3n
..
An Tsn1 Tsn2 Tsn3 Tsnn

Tsij: It represents the average vector for each alternative for each criterion.

Step 2: Determines the final ratings of the subcontractors: multiply the matrix of the solution and the average vector.

(Ts11Ts12Ts13Ts1nTs21Ts22Ts23Ts2nTs31Ts32Ts33Ts3nTsn1Tsn2Tsn3Tsnn)*(Vs1Vs2....Vsn)=(Ts11*Ts1+Ts12*Ts2++Ts1n*VsnTs21*Ts1+Ts22*Ts2++Ts2n*VsnTsn1*Ts1+Tsn2*Ts2++Tsnn*Vsn) \left( {\matrix{ {{\rm{T}}{{\rm{s}}_{11}}} & {{\rm{T}}{{\rm{s}}_{12}}} & {{\rm{T}}{{\rm{s}}_{13}}} & \cdots & {{\rm{T}}{{\rm{s}}_{1{\rm{n}}}}} \cr {{\rm{T}}{{\rm{s}}_{21}}} & {{\rm{T}}{{\rm{s}}_{22}}} & {{\rm{T}}{{\rm{s}}_{23}}} & \cdots & {{\rm{T}}{{\rm{s}}_{2{\rm{n}}}}} \cr {{\rm{T}}{{\rm{s}}_{31}}} & {{\rm{T}}{{\rm{s}}_{32}}} & {{\rm{T}}{{\rm{s}}_{33}}} & \cdots & {{\rm{T}}{{\rm{s}}_{3{\rm{n}}}}} \cr \cdots & \cdots & \cdots & \cdots & \cdots \cr {{\rm{T}}{{\rm{s}}_{{\rm{n1}}}}} & {{\rm{T}}{{\rm{s}}_{{\rm{n2}}}}} & {{\rm{T}}{{\rm{s}}_{{\rm{n3}}}}} & \cdots & {{\rm{T}}{{\rm{s}}_{{\rm{nn}}}}} \cr } } \right)*\left( {\matrix{ {{\rm{V}}{{\rm{s}}_1}} \cr {{\rm{V}}{{\rm{s}}_2}} \cr {....} \cr {{\rm{V}}{{\rm{s}}_{\rm{n}}}} \cr } } \right) = \left( {\matrix{ {{\rm{T}}{{\rm{s}}_{11}}*{\rm{T}}{{\rm{s}}_1} + {\rm{T}}{{\rm{s}}_{12}}*{\rm{T}}{{\rm{s}}_2} + \ldots \ldots + {\rm{T}}{{\rm{s}}_{1{\rm{n}}}}*{\rm{V}}{{\rm{s}}_{\rm{n}}}} \cr {{\rm{T}}{{\rm{s}}_{21}}*{\rm{T}}{{\rm{s}}_1} + {\rm{T}}{{\rm{s}}_{22}}*{\rm{T}}{{\rm{s}}_2} + \ldots \ldots + {\rm{T}}{{\rm{s}}_{2{\rm{n}}}}*{\rm{V}}{{\rm{s}}_{\rm{n}}}} \cr { \ldots \ldots } \cr {{\rm{T}}{{\rm{s}}_{{\rm{n}}1}}*{\rm{T}}{{\rm{s}}_1} + {\rm{T}}{{\rm{s}}_{{\rm{n}}2}}*{\rm{T}}{{\rm{s}}_2} + \ldots \ldots + {\rm{T}}{{\rm{s}}_{{\rm{nn}}}}*{\rm{V}}{{\rm{s}}_{\rm{n}}}} \cr } } \right)
Numerical example

In this numerical example, we applied the fuzzy logic and the AHP model to choose the best subcontractors for a production order.

Application of fuzzy logic method
Step 1: Definition of inputs and outputs

The commands are taken as input and the subcontractors are taken as output into our system.

The variables of an order (input):

Quantity of the order

Delivery delay

Accepted defects ratio

Production order price per piece

The variables of a subcontractor (Output):

Daily production capacity

Late delivery

Second choice ratio

Subcontractor price per piece

Fuzzy sets for each input and output:

Three classes are chosen for each input and output variables, which are as follows:

Low

Medium

High

Step 2: Develop membership functions

Before creating the membership function, the classes of each input and output variable were determined in collaboration with an expert in industrial planning as already indicated in the tables (Table 10, 11, Figure 3, 4).

Classification of input variables

Classification
Low Medium High
quantity of production order (pieces) 0 – 450 450 – 2000 2000–10000
Delivery delay (days) 0–12 12 – 26 26–28
Accepted quality level (%) 0–2,5 2,5–4,5 4,5–6
Production order price / piece (Euro) 0–0,6 0,6–1,1 1,1–2

Classification of output variables

Classification
Low Medium High
Daily production (pieces) 0 – 400 400 – 650 650–1000
Late delivery (days) 0–2 2–6 6–10
Second choice ratio (%) 0–0,3 0,3–0,65 0,65–2
subcontractor price / piece (euro) 0–0,6 0,6–1,1 1,1–2

Figure 3

The membership function for the input variables

Figure 4

The membership function for the output variables

Step 3: Fuzzy inference:

In this step, we have entered the fuzzy rules that connect the subsets of inputs and outputs. This step is to determine the relationships between the input set and the outputs. Table 12 shows the relationships between inputs and outputs (H: high; M: medium; L: low) (Table 12).

List of Rules

Accepted defects ratio (%) Quantity of production order (pieces) Delivery delay (days) Production order price / piece (euro) Second choice ratio (%) Daily production (pieces/day) Late delivery (days) Subcontractor price / piece (euro)
H L L L L H L L
H L M M L H M M
L M L M H M L M
M L H L M M L L
H L M H L L L M
M M M L M M L L
L L L L H L L L
H H H H L H L H
L L L L H H L L
H - - - L L L L
M - - - M M L M

The operators used in this case are the “Mamdani”-type operators. So, the inference engine will be like this (Figure 5).

Figure 5

Table of inference rules under Matlab

Step 4: Defuzzification

In this step, the center of gravity method was used for defuzzification. Figure 6 shows the rules window under Matlab where we can choose our inputs for the system to predict results (Figure 6).

Figure 6

The defuzzification steps under Matlab.

Step 5: Model validation

To evaluate the fuzzy system, a dataset composed of 10 samples was used. Each input data is characterized by the order number, quantity, delivery delay, accepted defects ratio, and price per piece. Then, these data were tested in a real case. It should be noted that these orders, which are already assigned to well-chosen subcontractors, are selected from those which have been successfully performed. The selected subcontractors are called desired results, as shown in Figure 7. Afterward, these data were tested in our fuzzy logic system. The obtained results are mentioned in the same figure as the calculated results. Since each subcontractor is defined, the fuzzy model will calculate and deduct four outputs (daily production, the late delivery, the second choice ratio, and subcontractor price). To test the reliability of our system, the correlation between the desired and the calculated values for the three output parameters is established as plotted in Figure 7.

Figure 7

The correlation between the desired and the calculated values: (a) the daily production, (b) the late delivery, (c) second choice defects ratio and subcontractor price per piece

According to Figure 7, it is shown that we have obtained good correlation results. The correlation coefficients are 0.807, 0.702, 0.823, and 0.871 for, respectively, the daily production, the late delivery, the second choice defects ratio, and the subcontractor price. Our model was tested for a production order with the values of the following parameters summarized in Table 13.

Production order parameters

Quantity (pieces) 1001
Delivery delay (days) 14
Accepted quality level (%) 4
Price / piece (euro) 0,7

The parameters of the subcontractors are used in Table 14.

Subcontractors parameters

Daily production (pieces/day) Late delievery (days) Second choice ratio (%) Price / piece (euro)
Sub 1 650 7 0,66 0,7
Sub 2 700 6 0,8 1
Sub 3 600 4 0,4 0,6
Sub 4 640 0 0,3 0,5

The result was indicated in Table 15.

Subcontractors rank

Subcontractors Subcontractors rank for the production order
Sub 4 1
Sub 2 2
Sub 3 3
Sub 1 4
Application of AHP method

Step 1: Define the criteria for subcontractor selection for a production order with the following parameters (Table 16).

Production order parameters

Quantity (pieces) 1001
Delivery delay (days) 14
Accepted quality level (%) 4
Price / piece (euro) 0,7

Step 2: The AHP process is determined in Figure 8.

Figure 8

AHP process of production order

Step 3: The criteria matrix of decisions based on Saaty's scale is given as follows (Table 17).

Pairwise comparison matrix of criterion

Criteria Quality Capacity Delivery delay Price/piece
Quality 1 1/5 1/7 3
Capacity 5 1 7 7
Delivery delay 7 1/7 1 3
Price / piece 1/3 1/7 1/3 1

Step 4: Normalize the resulting matrix (Table 18).

Normalization matrix

Criteria Quality Capacity Delivery delay Price / piece Vs
Quality 0,08 0,13 0,02 0,21 0,11
Capacity 0,38 0,67 0,83 0,50 0,59
Delivery delay 0,53 0,10 0,12 0,21 0,24
Price / piece 0,03 0,10 0,04 0,07 0,06

Step 5: Develop a pairwise comparison matrix for each subcontractor for the criterion: quality (Table 19).

Pairwise comparison matrix for each subcontractor for the criterion: quality

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 1/3 1/5 1/7
Sub 2 3 1 1/3 ½
Sub 3 5 3 1 ½
Sub 4 7 2 2 1

Step 6: Normalize the resulting matrix (Table 20).

Normalization matrix

alternatives Sub 1 Sub 2 Sub 3 Sub 4 Ts
Sub 1 0,06 0,02 0,06 0,07 0,05
Sub 2 0,19 0,16 0,09 0,23 0,17
Sub 3 0,31 0,47 0,28 0,23 0,33
Sub 4 0,44 0,32 0,57 0,47 0,45

Step 7: To validate the results, the CR was calculated as follows (Table 21).

Consistency ratio

4,14
CI 0,05
RI 0,90
CR 0,05

The coefficient consistency is equal to 0.05, so the results are considered good.

Step 8: Develop a pairwise comparison matrix for each subcontractor for the criterion: capacity (Table 22).

Pairwise comparison matrix for each subcontractor for the criterion: capacity

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 1/3 1/5 1/9
Sub 2 3 1 1/2 1/3
Sub 3 5 2 1 1/7
Sub 4 9 3 7 1

Step 9: Normalize the resulting matrix (Table 23).

Normalization matrix

alternatives Sub 1 Sub 2 Sub 3 Sub 4 Ts
Sub 1 0,06 0,05 0,02 0,07 0,05
Sub 2 0,17 0,16 0,06 0,21 0,15
Sub 3 0,28 0,32 0,11 0,09 0,20
Sub 4 0,50 0,47 0,80 0,63 0,60

Step 10: To validate the results, the CR was calculated as follows (Table 24).

Consistency ratio

4,34
CI 0,11
RI 0,90
CR 0,10

Acceptable results are obtained since the coefficient consistency is equal to 0.1.

Step 11: Develop a pairwise comparison matrix for each subcontractor for the criterion: delivery delay (Table 25).

Pairwise comparison matrix for each subcontractor for the criterion: delivery delay

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 1/3 1/5 1/7
Sub 2 3 1 1/2 1/3
Sub 3 5 2 1 1/5
Sub 4 7 3 5 1

Step 12: Normalize the resulting matrix (Table 26).

Normalization matrix

alternatives Sub 1 Sub 2 Sub 3 Sub 4 Ts
Sub 1 0,06 0,05 0,03 0,09 0,06
Sub 2 0,19 0,16 0,07 0,20 0,15
Sub 3 0,31 0,32 0,15 0,12 0,22
Sub 4 0,44 0,47 0,75 0,60 0,56

Step 13: To validate the results, the CR was calculated as follows (Table 27).

Consistency ratio

4,21
CI 0,07
RI 0,90
CR 0,08

Acceptable results are obtained since the coefficient consistency is equal to 0.08 less than 0.1.

Step 14: Develop a pairwise comparison matrix for each subcontractor for the criterion: price/piece (Table 28).

Pairwise comparison matrix for each subcontractor for the criterion: Price/piece

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 3 4 1/5
Sub 2 1/3 1 2 1/7
Sub 3 1/4 1/2 1 1/8
Sub 4 5 7 8 1

Step 15: Normalize the resulting matrix (Table 29).

Normalization matrix

alternatives Sub 1 Sub 2 Sub 3 Sub 4 Ts
Sub 1 0,15 0,26 0,27 0,14 0,20
Sub 2 0,05 0,09 0,13 0,10 0,09
Sub 3 0,04 0,04 0,07 0,09 0,06
Sub 4 0,76 0,61 0,53 0,68 0,65

Step 16: To validate the results, the CR was calculated as follows (Table 30).

Consistency ratio

4,12
CI 0,07
RI 0,90
CR 0,04

Acceptable results are obtained since the coefficient consistency is equal to 0.04 less than 0.1.

Step 17: Obtain an overall relative score for each alternative by creating a matrix of solutions. For each subcontractor, the average value of each criterion for each subcontractor was taken (Table 31).

Matrix of solution

Criteria
alternatives Quality Capacity Delivery delay Price / piece
Sub 1 0,05 0,05 0,06 0,02
Sub 2 0,17 0,15 0,15 0,09
Sub 3 0,33 0,2 0,22 0,06
Sub 4 0,45 0,6 0,56 0,65

Step 15: The final ratings of the suppliers were determined by multiplying the matrix of the solution and the average vector (Vs) (Figure 9).

Figure 9

The ranking of subcontractors

From this figure, subcontractor number 4 represents the best choice to treat the production order.

Results and discussion

To evaluate the performance of the method AHP and fuzzy logic in predicting the best choice of the subcontractor, a dataset composed of 30 samples was used. Each input data is characterized by the order number, quantity, delivery delay, accepted defects ratio, and production order price per piece. Then, these data were tested in a real case. It should be noted that these orders, which are given to well-defined subcontractors, are selected from those which have been successful in the choice that was made.

Table 32 presents the rank of the solution adopted by the company in the list of solutions determined by both the AHP method and the fuzzy logic.

Test evaluation

Number of production order Quantity (pieces) Delivery delay (days) Accepted Defects ratio (%) Price / piece (euro) The selected Subcontractors by company The selected Subcontractors by AHP The rank of subcontractors The selected Subcontractors by Fuzzy logic The rank of subcontractors
1 1200 14 4 0,7 Sub 1 Sub 1 1 Sub 2 2
2 1415 14 2 0,4 Sub 1 Sub 1 1 Sub 8 3
3 1001 14 4 0,7 Sub 4 Sub 4 1 Sub 4 1
4 610 8 1 0,6 Sub 5 Sub 3 2 Sub 5 1
5 240 8 1 1 Sub 5 Sub 4 3 Sub 5 1
6 313 8 6 0,5 Sub 6 Sub 6 1 Sub 5 4
7 178 23 6 0,5 Sub 6 Sub 6 1 Sub 7 2
8 518 10 3 0,9 Sub 9 Sub 7 2 Sub 9 1
9 805 17 2 0,6 Sub 2 Sub 3 2 Sub 3 2
10 2329 17 3 1 Sub 2 Sub 2 1 Sub 2 1
11 3003 14 2 0,6 Sub 3 Sub 3 1 Sub 3 1
12 5000 10 2 0,9 Sub 9 Sub 9 1 Sub 9 1
13 2560 17 1,5 1,1 Sub 8 Sub 8 1 Sub 8 1
14 800 14 1 1 Sub 5 Sub 5 1 Sub 5 1
15 300 7 4 0,5 Sub 6 Sub 6 1 Sub 6 1
16 2329 17 2 0,7 Sub 7 Sub 7 1 Sub 7 1
17 6780 11 5 0,45 Sub 4 Sub 4 1 Sub 4 1
18 452 8 1 0,7 Sub 1 Sub 1 1 Sub 1 1
19 4000 18 2 1 Sub 2 Sub 2 1 Sub 2 1
20 586 14 3 1 Sub 5 Sub 5 1 Sub 2 2
21 3000 15 1 0,8 Sub 1 Sub 1 1 Sub 5 3
22 3350 12 2 0,5 Sub 4 Sub 4 1 Sub 4 1
23 3200 11 1 0,5 Sub 4 Sub 4 1 Sub 4 1
24 587 13 1 0,9 Sub 9 Sub 9 1 Sub 9 1
25 782 1 1 0,5 Sub 4 Sub 4 1 Sub 4 1
26 520 15 4 0,6 Sub 3 Sub 3 1 Sub 3 1
27 250 0 2 0,5 Sub 4 Sub 4 1 Sub 4 1
28 221 10 1 0,9 Sub 9 Sub 9 1 Sub 9 1
29 224 3 2 0,7 Sub 7 Sub 7 1 Sub 7 1
30 238 4 3 0,7 Sub 7 Sub 7 1 Sub 7 1

From Figure 10, we can conclude that the found results are very acceptable. The percentage of a coincidence for the AHP method with the choice of the company is equal to 87%, as for the fuzzy logic method, this percentage is about 77%. Based on these results, we can conclude that both methods are efficient, but, in our case, the AHP method was more efficient than the fuzzy logic method. Figures 11 and 12 give more details.

Figure 10

Percentage of coincidence for the AHP method and the fuzzy logic with the choice of the company

Figure 11

Distribution of the results for the AHP method

Figure 12

Percentage of coincidence for the fuzzy logic with the choice of the company

From Figure 11, the solutions found in the first rank, second rank, and third rank represent 87%, 10%, and 3%, respectively.

From Figure 12, the solutions found in the first rank, second rank, third rank, and fourth rank represent 77%, 13%, 6.66%, and 3.33%, respectively.

Conclusions

In this work, we have used two methods for the selection of subcontractors in a Denim manufacturing company. Indeed, the first one was the fuzzy logic and represents a tool to understand practically the similarity, the preferences, and the uncertainty in the inference systems. The second one is the AHP, and it is very important to make a decision or to evaluate several options in situations where no possibility is perfect.

In our case study, it has been proved that the AHP method is more efficient than the fuzzy logic method for the selection of the best subcontractors. Indeed, this interpretation is based on the coincidence percentage between the obtained solutions using the developed models and those corresponding to the best choice made by the managers in the company. Therefore, it can be concluded that the AHP model and the fuzzy logic method are feasible for predicting and selecting subcontractors in the supply chain of our Denim clothing company.

Figure 1

Different shapes of membership function graphs
Different shapes of membership function graphs

Figure 2

Analytic hierarchy process
Analytic hierarchy process

Figure 3

The membership function for the input variables
The membership function for the input variables

Figure 4

The membership function for the output variables
The membership function for the output variables

Figure 5

Table of inference rules under Matlab
Table of inference rules under Matlab

Figure 6

The defuzzification steps under Matlab.
The defuzzification steps under Matlab.

Figure 7

The correlation between the desired and the calculated values: (a) the daily production, (b) the late delivery, (c) second choice defects ratio and subcontractor price per piece
The correlation between the desired and the calculated values: (a) the daily production, (b) the late delivery, (c) second choice defects ratio and subcontractor price per piece

Figure 8

AHP process of production order
AHP process of production order

Figure 9

The ranking of subcontractors
The ranking of subcontractors

Figure 10

Percentage of coincidence for the AHP method and the fuzzy logic with the choice of the company
Percentage of coincidence for the AHP method and the fuzzy logic with the choice of the company

Figure 11

Distribution of the results for the AHP method
Distribution of the results for the AHP method

Figure 12

Percentage of coincidence for the fuzzy logic with the choice of the company
Percentage of coincidence for the fuzzy logic with the choice of the company

Consistency ratio

4,12
CI 0,07
RI 0,90
CR 0,04

Pairwise comparison matrix for each alternative for each criteria

Alternative A1 A2 A3 …. An
A1 1 W1/W2 W1/W3 …. W1/Wn
A2 W2/W1 1 W2/W3 …. W2/Wn
A3 W3/W1 W3/W2 1 …. W3/Wn
.. …. 1
An Wn/W1 Wn/W2 Wn/W3 Wn/W.. 1

Subcontractors parameters

Daily production (pieces/day) Late delievery (days) Second choice ratio (%) Price / piece (euro)
Sub 1 650 7 0,66 0,7
Sub 2 700 6 0,8 1
Sub 3 600 4 0,4 0,6
Sub 4 640 0 0,3 0,5

Matrix of solution

Criteria
alternatives Quality Capacity Delivery delay Price / piece
Sub 1 0,05 0,05 0,06 0,02
Sub 2 0,17 0,15 0,15 0,09
Sub 3 0,33 0,2 0,22 0,06
Sub 4 0,45 0,6 0,56 0,65

Normalization Matrix

Alternative A1 A2 A3 …. An
A1 Y11 Y12 Y13 Y1n
A2 Y11 Y22 Y23 Y2n
A3 Y31 Y32 Y33 Y3n
..
An Yn1 Yn2 Yn3 Ynn

Classification of output variables

Classification
Low Medium High
Daily production (pieces) 0 – 400 400 – 650 650–1000
Late delivery (days) 0–2 2–6 6–10
Second choice ratio (%) 0–0,3 0,3–0,65 0,65–2
subcontractor price / piece (euro) 0–0,6 0,6–1,1 1,1–2

Pairwise comparison matrix of criterion

Criteria Quality Capacity Delivery delay Price/piece
Quality 1 1/5 1/7 3
Capacity 5 1 7 7
Delivery delay 7 1/7 1 3
Price / piece 1/3 1/7 1/3 1

Pairwise comparison matrix for each subcontractor for the criterion: delivery delay

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 1/3 1/5 1/7
Sub 2 3 1 1/2 1/3
Sub 3 5 2 1 1/5
Sub 4 7 3 5 1

Subcontractors’ parameters

Daily production (pieces/day) Late delivery (days) Second choice ratio (%) Price / piece (euro)
Sub 1 650 7 0,66 0,7
Sub 2 700 6 0,8 1
Sub 3 600 4 0,4 0,6
Sub 4 600 0 0,3 0,5
Sub 5 700 8 0,7 1
Sub 6 500 4 0,71 0,5
Sub 7 700 2 0,51 0,7
Sub 8 650 5 0,5 1,2
Sub 9 800 10 0,9 0,9

Normalization matrix

alternatives Sub 1 Sub 2 Sub 3 Sub 4 Ts
Sub 1 0,15 0,26 0,27 0,14 0,20
Sub 2 0,05 0,09 0,13 0,10 0,09
Sub 3 0,04 0,04 0,07 0,09 0,06
Sub 4 0,76 0,61 0,53 0,68 0,65

Random Consistency Index (RI)

N 1 2 3 4 5 6 7 8 9 10
RI 0 0.0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49

Saaty's 1–9 scale for pair-wise comparisons

Numerical rate Verbal judgment of preference
1 Equal importance
3 Weak importance of one over another
5 Essential or strong importance
7 Demonstrated importance
9 Absolute importance
2, 4, 6, 8 Intermediate values between the two adjacent judgment

Classification of input variables

Classification
Low Medium High
quantity of production order (pieces) 0 – 450 450 – 2000 2000–10000
Delivery delay (days) 0–12 12 – 26 26–28
Accepted quality level (%) 0–2,5 2,5–4,5 4,5–6
Production order price / piece (Euro) 0–0,6 0,6–1,1 1,1–2

Test evaluation

Number of production order Quantity (pieces) Delivery delay (days) Accepted Defects ratio (%) Price / piece (euro) The selected Subcontractors by company The selected Subcontractors by AHP The rank of subcontractors The selected Subcontractors by Fuzzy logic The rank of subcontractors
1 1200 14 4 0,7 Sub 1 Sub 1 1 Sub 2 2
2 1415 14 2 0,4 Sub 1 Sub 1 1 Sub 8 3
3 1001 14 4 0,7 Sub 4 Sub 4 1 Sub 4 1
4 610 8 1 0,6 Sub 5 Sub 3 2 Sub 5 1
5 240 8 1 1 Sub 5 Sub 4 3 Sub 5 1
6 313 8 6 0,5 Sub 6 Sub 6 1 Sub 5 4
7 178 23 6 0,5 Sub 6 Sub 6 1 Sub 7 2
8 518 10 3 0,9 Sub 9 Sub 7 2 Sub 9 1
9 805 17 2 0,6 Sub 2 Sub 3 2 Sub 3 2
10 2329 17 3 1 Sub 2 Sub 2 1 Sub 2 1
11 3003 14 2 0,6 Sub 3 Sub 3 1 Sub 3 1
12 5000 10 2 0,9 Sub 9 Sub 9 1 Sub 9 1
13 2560 17 1,5 1,1 Sub 8 Sub 8 1 Sub 8 1
14 800 14 1 1 Sub 5 Sub 5 1 Sub 5 1
15 300 7 4 0,5 Sub 6 Sub 6 1 Sub 6 1
16 2329 17 2 0,7 Sub 7 Sub 7 1 Sub 7 1
17 6780 11 5 0,45 Sub 4 Sub 4 1 Sub 4 1
18 452 8 1 0,7 Sub 1 Sub 1 1 Sub 1 1
19 4000 18 2 1 Sub 2 Sub 2 1 Sub 2 1
20 586 14 3 1 Sub 5 Sub 5 1 Sub 2 2
21 3000 15 1 0,8 Sub 1 Sub 1 1 Sub 5 3
22 3350 12 2 0,5 Sub 4 Sub 4 1 Sub 4 1
23 3200 11 1 0,5 Sub 4 Sub 4 1 Sub 4 1
24 587 13 1 0,9 Sub 9 Sub 9 1 Sub 9 1
25 782 1 1 0,5 Sub 4 Sub 4 1 Sub 4 1
26 520 15 4 0,6 Sub 3 Sub 3 1 Sub 3 1
27 250 0 2 0,5 Sub 4 Sub 4 1 Sub 4 1
28 221 10 1 0,9 Sub 9 Sub 9 1 Sub 9 1
29 224 3 2 0,7 Sub 7 Sub 7 1 Sub 7 1
30 238 4 3 0,7 Sub 7 Sub 7 1 Sub 7 1

List of Rules

Accepted defects ratio (%) Quantity of production order (pieces) Delivery delay (days) Production order price / piece (euro) Second choice ratio (%) Daily production (pieces/day) Late delivery (days) Subcontractor price / piece (euro)
H L L L L H L L
H L M M L H M M
L M L M H M L M
M L H L M M L L
H L M H L L L M
M M M L M M L L
L L L L H L L L
H H H H L H L H
L L L L H H L L
H - - - L L L L
M - - - M M L M

Pairwise comparison matrix for each subcontractor for the criterion: Price/piece

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 3 4 1/5
Sub 2 1/3 1 2 1/7
Sub 3 1/4 1/2 1 1/8
Sub 4 5 7 8 1

Production order parameters

Quantity (pieces) 1001
Delivery delay (days) 14
Accepted quality level (%) 4
Price / piece (euro) 0,7

Pairwise comparison matrix for each subcontractor for the criterion: quality

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 1/3 1/5 1/7
Sub 2 3 1 1/3 ½
Sub 3 5 3 1 ½
Sub 4 7 2 2 1

Subcontractors rank

Subcontractors Subcontractors rank for the production order
Sub 4 1
Sub 2 2
Sub 3 3
Sub 1 4

Pairwise comparison matrix for each subcontractor for the criterion: capacity

alternatives Sub 1 Sub 2 Sub 3 Sub 4
Sub 1 1 1/3 1/5 1/9
Sub 2 3 1 1/2 1/3
Sub 3 5 2 1 1/7
Sub 4 9 3 7 1

Chen-Tung, C., Lin, C.-T., Huang, S.-F. (2006). A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal Production Economics, 102, 289–301. Chen-TungC. LinC.-T. HuangS.-F. 2006 A fuzzy approach for supplier evaluation and selection in supply chain management International Journal Production Economics 102 289 301 10.1016/j.ijpe.2005.03.009 Search in Google Scholar

Bayrak, M. Y., Çelebi, N., Taşkin, H. (2007). A fuzzy approach method for supplier selection. Production Planning & Control, 18, 54–63. BayrakM. Y. ÇelebiN. TaşkinH. 2007 A fuzzy approach method for supplier selection Production Planning & Control 18 54 63 10.1080/09537280600940713 Search in Google Scholar

Maurizio, B., Alberto, P. (2010). From traditional purchasing to supplier management: A fuzzy logic based approach to supplier selection. International Journal of Logistics Research and Applications: A Leading Journal of Supply Chain Management, 5(3), 235–255. MaurizioB. AlbertoP. 2010 From traditional purchasing to supplier management: A fuzzy logic based approach to supplier selection International Journal of Logistics Research and Applications: A Leading Journal of Supply Chain Management 5 3 235 255 Search in Google Scholar

Felix, T. S., Kumar, N., Tiwari, M. K., Lau, H. C. W., Choy, K. L. (2008). Global supplier selection: a fuzzy-AHP approach. International Journal of Production Research, 46(14), 3825–3857. FelixT. S. KumarN. TiwariM. K. LauH. C. W. ChoyK. L. 2008 Global supplier selection: a fuzzy-AHP approach International Journal of Production Research 46 14 3825 3857 10.1080/00207540600787200 Search in Google Scholar

Sharon, M. O. (2009). Development of a supplier selection model using fuzzy logic. Supply Chain Management: An International Journal, 14/4, 314–327. SharonM. O. 2009 Development of a supplier selection model using fuzzy logic Supply Chain Management: An International Journal 14/4 314 327 Search in Google Scholar

Devika, K. A. (2013). Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain. Journal of Cleaner Production, 47, 355–367. DevikaK. A. 2013 Integrated fuzzy multi criteria decision making method and multiobjective programming approach for supplier selection and order allocation in a green supply chain Journal of Cleaner Production 47 355 367 10.1016/j.jclepro.2013.02.010 Search in Google Scholar

Michał, K. The selection of construction sub contractors using the fuzzy sets theory, Warsaw University of Technology, Faculty of Civil Engineering, Institute of Building Engineering, The Division of Production Engineering and Construction Management, Al. ArmiiLudowej 16, 00-637 Warsaw, Poland. MichałK. The selection of construction sub contractors using the fuzzy sets theory Warsaw University of Technology, Faculty of Civil Engineering, Institute of Building Engineering, The Division of Production Engineering and Construction Management Al. ArmiiLudowej 16, 00-637 Warsaw, Poland Search in Google Scholar

Min-Yuan, C. (2011). Evaluating subcontractor performance using evolutionary fuzzy hybrid neural network. International Journal of Project Management, 29(3), 349–356. Min-YuanC. 2011 Evaluating subcontractor performance using evolutionary fuzzy hybrid neural network International Journal of Project Management 29 3 349 356 10.1016/j.ijproman.2010.03.005 Search in Google Scholar

Okoroh, M. I., Torrance, V. (1999). A model for subcontractor selection in refurbishment projects. Construction Management and Economics, 17, 315–327. OkorohM. I. TorranceV. 1999 A model for subcontractor selection in refurbishment projects Construction Management and Economics 17 315 327 10.1080/014461999371529 Search in Google Scholar

Kumar, M., Vrat, P., Shankar, R. (2004). A fuzzy goal programming approach for vendor selection problem in a supply chain. Computers & Industrial Engineering, 46(1), 69–85. KumarM. VratP. ShankarR. 2004 A fuzzy goal programming approach for vendor selection problem in a supply chain Computers & Industrial Engineering 46 1 69 85 10.1016/j.cie.2003.09.010 Search in Google Scholar

Kabbari, M., et al. (2015). Predicting the hydrophobic nature of knitted fabric using fuzzy logic modeling. International Journal of Applied Research on Textile, 3, 58–68. KabbariM. 2015 Predicting the hydrophobic nature of knitted fabric using fuzzy logic modeling International Journal of Applied Research on Textile 3 58 68 Search in Google Scholar

Mouna, G. et al. (2017). Ann and fuzzy techniques for modeling bagging behaviors of denim fabrics as function of frictional properties. International Journal of Applied Research on Textile, 2, 36–55. MounaG. 2017 Ann and fuzzy techniques for modeling bagging behaviors of denim fabrics as function of frictional properties International Journal of Applied Research on Textile 2 36 55 Search in Google Scholar

Charles, A. W., John, R. (1993). A multiobjective approach to vendor selection. European Journal of Operational Research, 68(2), 173–184. CharlesA. W. JohnR. 1993 A multiobjective approach to vendor selection European Journal of Operational Research 68 2 173 184 10.1016/0377-2217(93)90301-3 Search in Google Scholar

William, R. S. (1987). Supplier selection strategies. Journal of Purchasing and Materials Management, 23(2), 7–12. WilliamR. S. 1987 Supplier selection strategies Journal of Purchasing and Materials Management 23 2 7 12 Search in Google Scholar

Lisa, M. (1990). The supplier selection decision in strategic partenrship. Journal of Purchasing and Materials Management, 26(4), 8–14. LisaM. 1990 The supplier selection decision in strategic partenrship Journal of Purchasing and Materials Management 26 4 8 14 Search in Google Scholar

Roodhooft, J., Konings, J. (1997). Vendor selection and evaluation: An activity based costing approach. European Journal of Operational Research, 96, 97–102. RoodhooftJ. KoningsJ. 1997 Vendor selection and evaluation: An activity based costing approach European Journal of Operational Research 96 97 102 10.1016/0377-2217(95)00383-5 Search in Google Scholar

Hinkle, C. L., Robinson, P. J., Green, P. E. (1969). Vendor evaluation using cluster analysis. Journal of Purchasing, 5(3), 49–58. HinkleC. L. RobinsonP. J. GreenP. E. 1969 Vendor evaluation using cluster analysis Journal of Purchasing 5 3 49 58 10.1111/j.1745-493X.1969.tb00602.x Search in Google Scholar

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. ZadehL. A. 1965 Fuzzy sets Information and Control 8 3 338 353 10.21236/AD0608981 Search in Google Scholar

Lotfi, B. (1999). Contribution to the control of the asynchronous machine, use of fuzzy logic, neural networks and genetic algorithms. Doctoral thesis, Université de Henri Poincaré, Nancy-I. LotfiB. 1999 Contribution to the control of the asynchronous machine, use of fuzzy logic, neural networks and genetic algorithms Doctoral thesis, Université de Henri Poincaré Nancy-I Search in Google Scholar

Thomas L. S., Kirti, P. (2008). Group decision making: Drawing out and reconciling differences. Pittsburgh, Pennsylvania: RWS Publications. ThomasL. S. KirtiP. 2008 Group decision making: Drawing out and reconciling differences Pittsburgh, Pennsylvania RWS Publications Search in Google Scholar

Saracoglu, B. O. (2013). Selecting industrial investment locations in master plans of countries. European Journal of Industrial Engineering, 4, 416–441. SaracogluB. O. 2013 Selecting industrial investment locations in master plans of countries European Journal of Industrial Engineering 4 416 441 10.1504/EJIE.2013.055016 Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo