Multi-criteria Decision Making Using Hybrid methods for Supplier Selection in the Clothing Industry

This study aims to present hybrid multi-criteria decision-making methods, including the analytic hierarchy process (AHP), the technique for the order of preference by similarity to the ideal solution (TOPSIS), the weighted sum method (WSM), and the weighted product method (WPM) for selecting the best supplier in the apparel industry and fill the gap in the literature. This study consists of several steps. In the first, the literature was reviewed in order to determine the criteria set for evaluating and selecting the best supplier in the manufacturing sector. A questionnaire was then designed, and an investigation was conducted with 10 purchasing experts to evaluate the suppliers. Next, the weights of criteria and the decision matrix were established using the AHP method. In another step, hybrid MCDM models (AHP-TOPSIS, AHP-WSM, and AHP-WPM) were used to select the best supplier. Finally, in the last step, the hybrid models were compared. The methodology of our research is summarized in Figure 1.

Fig. 1

As for the MCDM methods used in this paper, they are explained in the following section.

The AHP developed by Saaty is one of the MCDM methods frequently used. It is a structured technique for organising, analysing, and solving complex decisions [29]. The AHP process begins by defining problems, criteria, and alternatives and then establishing a pair-wise comparison between criteria and alternatives. The process ends by determining the rank of alternatives. The TOPSIS method is a multi-criteria decision method proposed by Ching-Lai Hwang and Yoon [30,31,32], based on the positive ideal solution and negative ideal solution. AHP-TOPSIS is a combination of the AHP and TOPSIS methods. The use of AHP is to calculate the weight of the criteria and, as in the TOPSIS method, rank alternatives. The following steps can be described for using AHP-TOPSIS:

Step 1. Construct the decision matrix: as mentioned in Table 1.

Step 2. Construct the normalised decision matrix: as shown in Equation 1: (1) Rij=Xij∑k=1nXkj2 {{\rm{R}}_{{\rm{ij}}}} = {{{X_{ij}}} \over {\sqrt {\sum\nolimits_{k = 1}^n {X_{kj}^2} } }}

Step 3. Calculate the weight of the criteria: using the AHP method

• –

  Construct a pair-wise comparison matrix (n*n) for criteria concerning objectives as shown in Table 3. The criteria’ weights should be calculated using a pair-wise comparison between criteria by applying Saaty’s l–9 scale [33]. Saaty’s scale is mentioned in Table 2.

• –

  Normalise the resulting matrix as mentioned in Table 4.

• –

  Calculate the row averages “W” of the normalised pair-wise matrix; a weights vector is obtained: W=[W1W2W3..Wj]=[∑j=1nX1Jn∑j=1nX2Jn∑j=1nX3Jn..∑j=1nXnJn] {\rm{W}}{{ = }}\left[ {\matrix{ {{{\rm{W}}_{\rm{1}}}} \cr {{{\rm{W}}_{{2}}}} \cr {{{\rm{W}}_{{3}}}} \cr {..} \cr {{{\rm{W}}_{\rm{j}}}} \cr } } \right] = \left[ {\matrix{ {{{\sum\nolimits_{{j}{{ = 1}}}^{n} {{X}{{1}}{J}} } \over {n}}} \cr {{{\sum\nolimits_{{j}{{ = 1}}}^{n} {{X}{{2}}{J}} } \over {n}}} \cr {{{\sum\nolimits_{{j}{{ = 1}}}^{n} {{X}{{3}}{J}} } \over {n}}} \cr {..} \cr {{{\sum\nolimits_{{j}{{ = 1}}}^{n} {{XnJ}} } \over {n}}} \cr } } \right]

Step 4. Calculate the weighted normalised decision matrix.

Calculate the weighted normalised value. V_ij is presented in Equation 2: (2) Vij=Rij*Wj for i=1, …, n; j = 1, …, m. {\rm{Vij = Rij*Wj}}\,{\rm{for}}\,{\rm{i = 1,}}\, \ldots {\rm{,}}\,{\rm{n;}}\,{\rm{j}}\,{\rm{ = }}\,{\rm{1,}}\, \ldots {\rm{,}}\,{\rm{m}}{\rm{.}}

Step 5. Determine the positive ideal and negative ideal solutions

Positive ideal solution A⁺ has the form presented in Equation 3: (3) A+=(V1+, V2+, …., Vn+)=((max Vij /j ∈I),(min Vij / j ∈ J)) \matrix{ {{{\rm{A}}^ + } = \left( {{\rm{V}}{1^ + },\,{\rm{V}}{2^ + },\, \ldots .,\,{\rm{V}}{{\rm{n}}^ + }} \right) = } \cr {\left( {\left( {\max \,{\rm{Vij}}\,/{\rm{j}}\, \in {\rm{I}}} \right),\left( {\min \,{\rm{Vij / j}}\, \in \,{\rm{J}}} \right)} \right)} \cr } Negative ideal solution A⁻ has the form presented in Equation 4: (4) A−=(V1−, V2−, ….., Vn−)=((min Vij /j ∈I),(max Vij / j ∈ J)) \matrix{ {{{\rm{A}}^ - } = \left( {{\rm{V}}{1^ - },\,{\rm{V}}{2^ - },\, \ldots .\,.,\,{\rm{V}}{{\rm{n}}^ - }} \right) = } \cr {\left( {\left( {\min \,{\rm{Vij}}\,/{\rm{j}}\, \in {\rm{I}}} \right),\left( {\max \,{\rm{Vij / j}}\, \in \,{\rm{J}}} \right)} \right)} \cr } I is associated with benefit criteria and J with the worst criteria, i=1, …, m; j=1, …, n

Step 6. Calculate the separation measures from the positive ideal solution and negative ideal solution.

In the TOPSIS method, the separation coefficient of each alternative from the positive ideal solution S_i⁺ is given by the following Equation (5): (5) Si+=∑j=1m(Vij−Vj+)^2 {{\rm{S}}_{\rm{i}}}^ + = \sqrt {\sum\nolimits_{{\rm{j = 1}}}^{\rm{m}} {\left( {{{\rm{V}}_{{\rm{ij}}}} - {V_{\rm{j}}}^ + } \right) ^\land 2} } The separation coefficient of each alternative from the negative ideal solution S_i⁻ is given by the following Equation 6: (6) Si−=∑j=1m(Vij−Vj−)^2 {{\rm{S}}_{\rm{i}}}^ - = \sqrt {\sum\nolimits_{{\rm{j = 1}}}^{\rm{m}} {\left( {{{\rm{V}}_{{\rm{ij}}}} - {V_{\rm{j}}}^ - } \right)^\land2} }

Step 7. Calculate the relative closeness coefficient to the positive ideal solution Ri: as shown in Equation 7: (7) Ri=Si−Si−+Si+; i=1,2,3,..,n {\rm{Ri = }}{{{\rm{Si}} - } \over {{\rm{Si}} - + {\rm{Si}} + }};\,{\rm{i}} = 1,2,3,..,{\rm{n}}

Step 8. Rank the alternatives.

Rank the alternatives according to R_i; i=1,2,3,..,n

The Weighted Sum Method (WSM) is a multi-criterion decision-making method [34]. There will be multiple alternatives, and we have to determine the most suitable one based on several criteria. The AHP-WSM method is a combination of the AHP method and WSM method. The use of the AHP method is to calculate the weight of the criteria and that of the WSM method to rank alternatives.

The Weighted Product Method (WPM) is a multi-criterion decision-making method. There will be multiple alternatives, and one has to determine the most suitable based on several criteria. WPM is very similar to WSM. The main difference consists in using multiplication instead of the sum in the last step of computing the model outputs. The AHP-WPM method is an integrated approach allowing to calculate as a first step the criteria weights on the basis of the AHP method, and then the WSM method will be used to rank alternatives.

This work was carried out in a company specialised in manufacturing denim products, employing 400 persons, with an annual production of 900,000 pieces, and operating as an ordering party for various subcontractors as well as a manufacturer of several items (pants, jackets, skirts) in small and medium orders for different international brands, requiring high-quality, right and short-time delivery. There are several types of purchases in this company, such as textile accessories, fabric, and other items. As for the fabric purchase, the customers ordering impose their suitable suppliers on the company. Consequently, in this work, we dealt essentially with textile purchasing accessories; in fact, it represents the most important part in terms of variety and cost. Besides, this company has an important database for these items, but there is no objective method for supplier selection; the purchasing operations have been based only on the supply chain manager’s experience. In this case study, to apply the models proposed, we have sorted and retained successful purchasing actions and considered them as a database in the current supplier’s selection study. As a result, the sorted database is composed of 40 various textile accessories, 40 purchase orders, and 120 suppliers.

To define the main criteria for the supplier selection decision, an investigation was conducted with 10 experts having a professional career in textile purchasing ranging from 6 to 18 years. The list of criteria used for the investigation was determined on the basis of the literature review and mentioned in Table 8 [35,36,37,38,39].

The steps of the investigation were as follows:

• –

  Order the criteria according to their importance

• –

  Determine the weights of the first four criteria using the AHP method.

• –

  Determine the four most important criteria for the10 experts according to the ABC diagram.

The results of the investigation are mentioned in Table 9 and Figure 2.

Fig. 2

After determining the criteria mentioned in the literature, the choice and weights of each expert’s criteria are obtained, shown in Table 9.

After the investigation, an ABC chart was plotted to determine the final criteria choice and classify the most important ones, presented in Figure 2.

From the ABC chart, the most important criteria (Zone A) are cost, quality, compliance to quantity, and compliance to deadlines.

In this section, we applied AHP-TOPSIS, AHP-WSM, and AHP-WPM models to choose the best suppliers from three suppliers (S1, S2, and S3) for purchasing textile supplies and accessories. The problem’s overall objective in this example is the purchase of a button with reference 001.

To evaluate the performance of the AHP-TOPSIS, AHP-WSM, and AHP-WPM models in predicting the best choice of supplier, a dataset composed of 40 samples was used. Then, these data were tested in a real case. It should be noted that these purchase orders, which are given to well-defined suppliers, were selected from those which had already been conducted successfully in the supplier selection and purchase process. The purchase orders chosen were of good quality, reasonable price, convenient delivery time, and the desired quantity. Table 23 presents the rank of the suppliers adopted by the company in the list of suppliers determined by the AHP-TOPSIS, AHP-WSM, and AHP-WPM models.

On the basis of these results, a statistical study was carried out on the two methods, in which we took the results of the 1st rank for each method, and variance analysis was conducted to determine if the differences between group means are statistically significant or not. The results are mentioned in Table 24 and Table 25.

In Table 24, we calculated the correlation coefficient to determine the dependence between AHP-TOPSIS /AHP-WSM, AHP-TOPSIS/AHP-WPM, and AHP-WSM/AHP-WPM supplier rankings. As a result, a non-significant correlation between the various MCDM couples was observed, where the correlation coefficient values Rxy do not exceed 0,47.

From table 25, the p-value is less than the significance level, thus we rejected the null hypothesis and concluded that not all of the population means are equal. We can conclude that the differences between group means are statistically significant.

Besides this, from Table 23 we determined the ratio of coincidence of supplier rankings between the AHP-TOPSIS, AHP-WSM, and AHP-WPM models and the supply manager’s choice for all the successful purchase operations in the database. The results obtained are displayed in Figure 3.

Fig. 3

According to Figure 3, it is clearly shown that the three integrated models have led to satisfactory results. Indeed, the percentage of coincidence of supplier rankings between the AHP-TOPSIS, AHP-WPM, and AHP-WSM models and the choice of supply chain manager are equal to 93%, 82%, and 78%, respectively. In our case study, the results obtained highlight the greatest performance of the AHP-TOPSIS model in selecting the best supplier, the model results do not fit the choice of the company only in 7% of the cases tested in comparison with the others. It can be considered as an excellent outcome in the industrial framework. This model is expected to be adopted in the supply chain department to avoid subjective selection methodology.

In this step, further developments were carried out to allow model implementation into a smart MCDM application so that supplier evaluation and selection decisions will be made rapidly and efficiently using a digital process.

For the development of this application, visual basic .NET version 2015 was used as a programming language and Microsoft access version 2016 as a database.

Figure 4 presents a screenshot of the MCDM application developed. Which was exploited by the supply chain manager to optimise the supplier selection decisions in garment company.

Fig. 4

This digital decision-aided application was performed in the clothing industry using the same database of section 4.1 and compared to the choice of company. The results obtained are displayed in Figure 5.

Fig. 5

According to Figure 5, the percentage of coincidence of supplier rankings between our application outcomes and the choice of supply chain manager was equal to 93%. This ratio is considered very satisfactory. In a further study, the database will be more and more extended to include all the real cases in the company and to enhance the decision-aided application performance.