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
- Fuzzy model
- analytic hierarchy process
- apparel industry supply chain
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.
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
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
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 |
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.).
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.
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).
The fuzzy rules deduce knowledge about the state of the system according to the linguistic qualifications provided in the fuzzification stage.
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.
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].
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.
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).
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
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
C1 | 1 | W_{1}/W_{2} | W_{1}/W_{3} | …. | W_{1}/W_{n} |
C2 | W_{2}/W_{1} | 1 | W_{2}/W_{3} | …. | W_{2}/W_{n} |
C3 | W_{3}/W_{1} | W_{3}/W_{2} | 1 | …. | W_{3}/W_{n} |
.. | … | …. | … | 1 | … |
Cn | W_{n}/W_{1} | W_{n}/W_{2} | W_{n}/W_{3} | W_{n}/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).
Normalization Matrix
C1 | X_{11} | X_{12} | X_{13} | … | X_{1n} |
C2 | X_{11} | X_{22} | X_{23} | … | X_{2n} |
C3 | X_{31} | X_{32} | X_{33} | … | X_{3n} |
.. | … | … | … | … | … |
Cn | X_{n1} | X_{n2} | X_{n3} | … | X_{nn} |
Step 4: Calculate the row averages “Vs” of the normalized pairwise matrix, a weights vector is obtained:
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
A1 | 1 | W_{1}/W_{2} | W_{1}/W_{3} | …. | W_{1}/W_{n} |
A2 | W_{2}/W_{1} | 1 | W_{2}/W_{3} | …. | W_{2}/W_{n} |
A3 | W_{3}/W_{1} | W_{3}/W_{2} | 1 | …. | W_{3}/W_{n} |
.. | … | …. | … | 1 | … |
An | W_{n}/W_{1} | W_{n}/W_{2} | W_{n}/W_{3} | W_{n}/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
A1 | Y_{11} | Y_{12} | Y_{13} | … | Y_{1n} |
A2 | Y_{11} | Y_{22} | Y_{23} | … | Y_{2n} |
A3 | Y_{31} | Y_{32} | Y_{33} | … | Y_{3n} |
.. | … | … | … | … | … |
An | Y_{n1} | Y_{n2} | Y_{n3} | … | Y_{nn} |
Step 4: Calculate the row averages “Ts” of the normalized pairwise matrix, a weights vector is obtained
To validate the results of the AHP, the consistency ratio (CR) is calculated using the following equation:
In which the consistency index (CI) is, in turn, measured through the following equation:
With:
maximum eigenvalue of the matrix
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 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
RI |
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.
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
A1 | Ts_{11} | Ts_{12} | Ts_{13} | … | Ts_{1n} | |
A2 | Ts_{21} | Ts_{22} | Ts_{23} | … | Ts_{2n} | |
A3 | Ts_{31} | Ts_{32} | Ts_{33} | … | Ts_{3n} | |
.. | … | … | … | … | … | |
An | Ts_{n1} | Ts_{n2} | Ts_{n3} | … | Ts_{nn} |
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.
In this numerical example, we applied the fuzzy logic and the AHP model to choose the best subcontractors for a production order.
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
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
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
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 |
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
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).
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).
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.
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
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
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
Sub 4 | |
Sub 2 | |
Sub 3 | |
Sub 1 |
Step 1: Define the criteria for subcontractor selection for a production order with the following parameters (Table 16).
Production order parameters
Delivery delay (days) | 14 |
Accepted quality level (%) | 4 |
Price / piece (euro) | 0,7 |
Step 2: The AHP process is determined in Figure 8.
Step 3: The criteria matrix of decisions based on Saaty's scale is given as follows (Table 17).
Pairwise comparison matrix of criterion
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
From this figure, subcontractor number 4 represents the best choice to treat the production order.
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
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.
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.
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.
Consistency ratio
CI | 0,07 |
RI | 0,90 |
CR | 0,04 |
Pairwise comparison matrix for each alternative for each criteria
A1 | 1 | W_{1}/W_{2} | W_{1}/W_{3} | …. | W_{1}/W_{n} |
A2 | W_{2}/W_{1} | 1 | W_{2}/W_{3} | …. | W_{2}/W_{n} |
A3 | W_{3}/W_{1} | W_{3}/W_{2} | 1 | …. | W_{3}/W_{n} |
.. | … | …. | … | 1 | … |
An | W_{n}/W_{1} | W_{n}/W_{2} | W_{n}/W_{3} | W_{n}/W_{..} | 1 |
Subcontractors parameters
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
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
A1 | Y_{11} | Y_{12} | Y_{13} | … | Y_{1n} |
A2 | Y_{11} | Y_{22} | Y_{23} | … | Y_{2n} |
A3 | Y_{31} | Y_{32} | Y_{33} | … | Y_{3n} |
.. | … | … | … | … | … |
An | Y_{n1} | Y_{n2} | Y_{n3} | … | Y_{nn} |
Classification of output variables
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
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
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
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
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 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
RI |
Saaty's 1–9 scale for pair-wise comparisons
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
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
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
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
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
Delivery delay (days) | 14 |
Accepted quality level (%) | 4 |
Price / piece (euro) | 0,7 |
Pairwise comparison matrix for each subcontractor for the criterion: quality
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
Sub 4 | |
Sub 2 | |
Sub 3 | |
Sub 1 |
Pairwise comparison matrix for each subcontractor for the criterion: capacity
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 |
Apparel Industry in the EU–China Exports and Circular Economy Automatic Identification Of Wrist Position In A Virtual Environment For Garment Design Pressure Evaluation Of Seamless Yoga Leggings Designed With Partition Structure Experimental and Modelling Studies on Thermal Insulation and Sound Absorption Properties of Cross-Laid Nonwoven Fabrics Tensile Properties Analysis Of 3D Flat-Knitted Inlay Fabric Reinforced Composites Using Acoustic Emission Optimization of Sodium Lignosulfonate Treatment on Nylon Fabric Using Box–Behnken Response Surface Design for UV Protection A Study on the Woven Construction of Fabric Dyed With Natural Indigo Dye and Finishing for Applying to Product Design for Home Textile Products A Calculation Method for the Deformation Behavior of Warp-Knitted Fabric Nondestructive Test Technology Research for Yarn Linear Density Unevenness Numerical Simulation and Analysis of Airflow in the Condensing Zone of Compact Spinning with Lattice Apron Blend Electrospinning of Poly(Ɛ-Caprolactone) and Poly(Ethylene Glycol-400) Nanofibers Loaded with Ibuprofen as a Potential Drug Delivery System for Wound Dressings Application of Plasticized Cellulose Triacetate Membranes for Recovery and Separation of Cerium(III) and Lanthanum(III) Analysing Service Quality and its Relation to Customer Satisfaction and Loyalty in Sportswear Retail Market A Review on the Performance and Comfort of Stab Protection Armor A Fabric-Based Integrated Sensor Glove System Recognizing Hand Gesture Developing Real Avatars for the Apparel Industry and Analysing Fabric Draping in the Virtual Domain Simulations of Heat Transfer through Multilayer Protective Clothing Exposed to Flame Determination of Sewing Thread Consumption for 602, 605, and 607 Cover Stitches Using Geometrical and Multi-Linear Regression Models Evaluation of Functional Insoles for Protective Footwear Under Simulated Use Conditions Designing a Three-Dimensional Woven Fabric Structure as an Element of a Baby Stroller Computer-Assisted Modeling and Design of Compression Garments with Graded Unit Compression Application of Physical Vapor Deposition in Textile Industry Modeling Lean and Six Sigma Integration using Deep Learning: Applied to a Clothing Company Comparative Analysis of Structure and Properties of Stereoscopic Cocoon and Flat Cocoon Effect of Water pH on Domestic Machine Washing Performance of Delicate Textiles Effect of Different Yarn Combinations on Auxetic Properties of Plied Yarns Analysis of Heat Transfer through a Protective Clothing Package Smart Textile for Building and Living Investigation of Twist Waves Distribution along Structurally Nonuniform Yarn 3D Body Scan as Anthropometric Tool for Individualized Prosthetic Socks Preliminary Experimental Investigation of Cut-Resistant Materials: A Biomimetic Perspective Durable Wash-Resistant Antimicrobial Treatment of Knitted Fabrics Modeling Supply Chain Sustainability-Related Risks and Vulnerability: Insights from the Textile Sector of Pakistan Numerical Simulation of Fiber Motion in the Condensing Zone of Lateral Compact Spinning with Pneumatic Groove Study on the Thermal and Impact Resistance Properties of Micro PA66/PU Synergistically Reinforced Multi-Layered Biaxial Weft Knitted Fabric Composites Improvement of Physical Properties of Viscose Using Nano GeO_{2} as Doping Material Fea-Based Structural Heat Transfer Characteristic of 3-D Orthogonal Woven Composite Subjected to the Non-Uniform Heat Load Bending Failure Behavior of the Glass Fiber Reinforced Composite I-Beams Formed by a Novel Bending Pultrusion Processing Technique Comfort-Related Properies of Cotton Seersucker Fabrics Economical and Social Dimensions of Unionization in Turkish Textile and Clothing Sector Conductive Heat Transfer Prediction of Plain Socks in Wet State A Novel Foam Coating Approach to Produce Abrasive Structures on Textiles Textronic Solutions Used for Premature Babies: A Review Effect of Lycra Weight Percent and Loop Length on Thermo-physiological Properties of Elastic Single Jersey Knitted Fabric Texture Representation and Application of Colored Spun Fabric Using Uniform Three-Structure Descriptor Analysis of Mechanical Behavior of Different Needle Tip Shapes During Puncture of Carbon Fiber Fabric Approach to Performance Rating of Retroreflective Textile Material Considering Production Technology and Reflector Size Influence of Multilayer Interlocked Fabrics Structure on their Thermal Performance Prediction of Standard Time of the Sewing Process using a Support Vector Machine with Particle Swarm Optimization A Novel Theoretical Modeling for Predicting the Sound Absorption of Woven Fabrics Using Modification of Sound Wave Equation and Genetic Algorithm Ag Coated Pa-Based Electro-Conductive Knitted Fabrics for Heat Generation in Compression Supports Design Method of Circular Weft-Knitted Jacquard Fabric Based on Jacquard Module Image Analysis as a Method of the Assessment of Yarn for Making Flat Textile Fabrics Investigation of Heat Transfer in Seersucker Woven Fabrics using Thermographic Method Research into the Textile-Based Signal Lines Made Using Ultrasonic Welding Technology Transformable Warning Clothing for Children with Active Light Sources Regenerated Cellulose/Graphene Composite Fibers with Electroconductive Properties High-Performance Workwear for Coal Miners in Northern China: Design and Performance Evaluation Comfort-Related Properties of Double-Layered Woven Car Seat Fabrics Experimental Investigation of the Wettability of Protective Glove Materials: A Biomimetic Perspective An Integrated Lean Six Sigma Approach to Modeling and Simulation: A Case Study from Clothing SME Mechanical Properties of Composites Reinforced with Technical Embroidery Made of Flax Fibers Consumer Adoption of Fast-Fashion, Differences of Perceptions, and the Role of Motivations Across the Adoption Groups A New Consumer Profile Definition Method Based on Fuzzy Technology and Fuzzy AHP Optimal Design of a Novel Magnetic Twisting Device Based on NSGA-II Algorithm Microscopic Analysis of Activated Sludge in Industrial Textile Wastewater Treatment Plant Evaluation of Physical and Mechanical Properties of Cotton Warps Under a Cyclic Load of Stretch-Abrasion Theoretical and Experimental Evaluation of Thermal Resistance for Compression Bandages Effects of Flocks Doping on the Dynamic Mechanical Properties of Shear Thickening Gel Estimation of Seams in Paraglider Wing Sensitivity of Aerodynamic Characteristics of Paraglider Wing to Properties of Covering Material Numerical Investigation of Heat Transfer in Garment Air Gap Determination of State Variables in Textile Composite with Membrane During Complex Heat and Moisture Transport Design and Performance Evaluation of Protective Clothing for Emergency Rescue Biological Properties of Knitted Fabrics Used in Post-Burn Scar Rehabilitation Fabrication and Characterization of Fibrous Polycaprolactone Blended with Natural Green Tea Extracts Using Dual Solvent Systems