# Looking At The Improvements Of Network Technology Construction Essay

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Due to the recent agile improvement of network technology and economic globalization, purchasing management has come to play a critical role as a key to business success in supply chain management. One of the curial challenges confronted by purchasing managers is the evaluation and selection of suppliers. Existing researches in the field of supplier selection have been applied multiple criteria decision making methods , such as analytic hierarchy process (AHP), analytic network process (ANP), artificial neural network(ANN), data envelopment analysis(DEA), fuzzy set theory, mathematical programming, technique for order preference by similarity to ideal solution(TOPSIS), and their hybrids.

There are at least five journal articles reviewing the literature regarding supplier evaluation and selection models (Weber et al., 1991, Holt, 1998, Degraeve et al., 2000, De Boer et al., 2001, Ho et al., 2010).Since these articles review the literature up to 2008, this paper extends them through a literature review and taxonomy of the 72 international journal articles from 2008 to 2011.

This paper presents a comprehensive review of literature to identify three issues, including evaluation factors, applied methods, and implementations of methods in these articles. The paper is further arranged as follows: section 2 and 3 describe the single and hybrid methods, respectively but all of the criteria and implementations are summarized in Appendix. Section 4 analyses the most prevalently used methods, discusses the most usable evaluating criteria, and find out the limitations of the approaches. Section 5 suggests for future work. Section 6 concludes the papers.

## 2. Research methodology

A comprehensive bibliography of the academic literature on supplier evaluation and selection was obtained through four following online journal databases:

Web of science

Science direct

Emerald

Springer

The literature search was conducted based on the key words "supplier selection", and "vendor selection". First the full text of each article was red to omit the articles that were not related to evaluation methods and evaluation criteria for supplier selection. Also, conference papers, masters and doctoral dissertation, textbooks and unpublished working papers were excluded. Finally 72 journal articles which derived from 20 journals were gathered.

## 3. Single Methods

Twelve out of sixty seven articles (17.9%) applied single methods to evaluate the performance of suppliers and select the best one. Their implementations and evaluation criteria utilized in the methods are presented in Attachment 1.

## 3.1 Mathematical programming

Among the Twelve single methods, four papers (33.3%) suggested different kinds of mathematical programming models for the supplier selection problem.

## 3.1.1 Mixed integer programming

Li and Zabinsky (2009) suggested a two-stage stochastic programming model and a chance-constrained programming model to identify the best suppliers and to assign order quantities in business volume discounts environments. Both models were formulated on a mixed integer program. The uncertainties for demand and supplier capacity were considered with a probability distribution in the models (Li and Zabinsky, 2009).

Sawik(2010) presented mixed integer programming models for single or multiple objective supplier selection in non-discount or discount environment to determine the optimal allocation of orders for approved suppliers. Risk constraints associated with uncertain quality and reliability of supplies, were considered in this model (Sawik, 2010).

## 3.1.2 Linear programming

Ng (2008) suggested a weighted linear programming model applying transformation technique without using optimization function to select appropriate suppliers (Ng, 2008).

## 3.1.3 Mixed-integer non linear programming

Kheljani et al. (2009) formulated a mixed-integer non linear programming model in the supplier selection process. In the objective function of the model, the total cost of the supply chain included the buyer's cost and suppliers' cost was minimized. Demand rate for the buyers and production rate for the suppliers were considered as constraints (Gheidar Kheljani et al., 2009).

## 3.2 Artificial neural network

Two out of Twelve single methods (16.7%) suggested ANN theory for the supplier selection process.

Luo et al. (2009) developed a quantitative model of classifying suppliers in to one of four various types of the Kraljic's classification matrix (1983). The model was based on radial basis function artificial neural network to reduce the information-processing time and to achieve a robust and speedy solution (Luo et al., 2009).

Aksoy and Ozturk (2011) applied ANN technique to select suppliers and to evaluate the selected suppliers' performance in just-in time production environments. The suppliers were classified through this model (Aksoy and Ã-ztürk, 2011).

## 3.3 Data envelopment analysis

Two out of Twelve single methods (16.7%) suggested DEA approach for the supplier selection process.

Saen (2008) employed super-efficiency analysis in DEA for supplier selection under volume discount offers. On the basis of super efficiency, efficient suppliers were ranked besides inefficient suppliers (Saen, 2008).

Saen (2010) developed DEA model for selecting the best suppliers in the presence of weight restrictions and dual-role factors. In this model decision maker's preferences were allowed and simultaneously dual role factors were considered (Saen, 2010).

## 3.4 Fuzzy set theory

Two out of Twelve single methods (16.7%) suggested fuzzy set theory for the supplier selection process.

Carrera and Mayorga (2008) provided an application of fuzzy set theory to handle uncertainty in the supplier selection process. Fuzzy Inference System approach was applied to convert the multi-objective problem to a single one along four modules (Carrera and Mayorga, 2008).

Wang (2010) proposed a fuzzy linguistic multi-agent model to cope with heterogeneous information and to prevent information loss problems in the supplier evaluation issue. The model was based on 2-tuple fuzzy linguistic information which composed by a linguistic term and a number (Wang, 2010).

## 3.5 Rough set theory

One out of twelve single methods (8.3%) suggested rough set theory for the supplier selection process.

Chang and Hung (2010) adopted rough set theory to identify the best suppliers. Firs attributes were cored and reduced and then decision making rules were created by the supplier selection model (Chang and Hung, 2010).

## 3.6 Vague sets

One out of twelve single methods (8.3%) suggested vague sets for the supplier selection process.

Zhang et al. (2009) implemented vague sets group decisions to handle the problem of supplier selection in uncertain environments. The model not only considered the relative importance of different decision-makers, but also included the accordance and difference in the decision group. To rank the suppliers, the judgments of all the decision-makers were integrated into a decision matrix (Zhang et al., 2009).

## 4 Hybrid and innovative Methods

Fifty five out of sixty seven articles (82.1%) applied hybrid methods to evaluate the performance of suppliers and select the best one.

## 4.1 Hybrid fuzzy Methods

Thirty five out of fifty five hybrid methods (63.7%) applied hybrid fuzzy method for the supplier selection process. Their implementations and evaluation criteria utilized in the methods are presented in Attachment 2. The supplier selection problem is often faced by ambiguity and vagueness in practice. Very often decision makers express their preferences in linguistic terms instead of numerical values. In such circumstance fuzzy logic and fuzzy set theory are used to handle these uncertainties.

## 4.1.1 Hybrid fuzzy-mathematical programming

Ten out of Thirty five hybrid fuzzy methods (28.6%) used hybrid fuzzy- mathematical programming method for the supplier selection problem. In this group, hybrid fuzzy- mathematical programming was integrated with other models such as AHP and SWOT in some articles.

Ozgen et al. (2008) used AHP to calculate the weights of the alternative suppliers for selecting the best ones. Then fuzzy theory was implemented to handle the imprecision data and consequently a multi-objective possibilistic linear programming approach was suggested to allocate order quantities to selected suppliers (Ã-zgen, 2008).

Sevkli et al. (2008) integrated fuzzy linear programming model with AHP to address fuzziness issue and to take in to account resource constraints in the supplier selection problem. The weights of the various criteria were calculated using AHP, were considered as the weights of the fuzzy multi-objective linear programming model (Sevkli et al., 2008).

Amid et al. (2009) developed a fuzzy multi objective model to handle simultaneously the imprecision of data and determine the order quantities based on price breaks for each supplier. In this model, The weighted additive model was applied to cope with the unequal importance of fuzzy goals and fuzzy constraints (Amid et al., 2009).

Chen (2009) suggested a decision support model for supplier selection and order allocation problems in the rebuy purchasing situation. An interactive procedure based on past problem solving experiences was applied through a fuzzy-based mathematical programming approach to incorporate multiple uncertain criteria under the demand constraint of multiple items with varied importance to the purchasing firm (Chen, 2009).

Guneri et al. (2009) proposed fuzzy linear programming model to solve multiple sourcing supplier selection problems. Linguistic variables in form of trapezoidal fuzzy numbers were used to assess the importance weight of each criterion and the ratings of suppliers with respect to each criterion. The distances between alternative suppliers and fuzzy positive and negative ideal solutions were calculated to obtain closeness coefficients for using as coefficients of each supplier in linear programming model (Guneri et al., 2009).

Wang and Yang (2009) applied a Multi-Objective Linear Programming model for allocating order quantities to each supplier in quantity discount environments. In this model, AHP was applied to calculate the weights of the objective functions for each criterion. Then the multi-objective model was reformulated in to a fuzzy compromise programming approach to have a more reasonable compromise solution (Wang and Yang, 2009).

Amid et al. (2010) developed a weighted max-min fuzzy multi-objective model to complete the Amid et al.'s work in 2009 for supplier selection and order allocation problems. The current model considered imprecision of data and varying importance of quantitative/qualitative criteria. AHP was used to determine the weights of criteria in the model (Amid et al., 2010) .

Amin et al. (2010) suggested a strategically model for supplier selection which included two stages. In the first stage, fuzzy logic was integrated with quantified SWOT algorithm (Strengths, Weaknesses, Opportunities and Threats). In the second stage, the output of SWOT algorithm was implemented as an input in a fuzzy linear programming model to determine the order quantity (Amin et al., 2010) .

Diaz-Madronero et al. (2010) applied fuzzy multi objective linear model for vendor selection problem. A non-linear membership function called S-curve was utilized in this model. To find a preferred compromise solution for the model, an interactive solution methodology was suggested (Díaz-Madroñero et al., 2010).

Yucel and Guneri (2010) proposed a weighted additive fuzzy programming approach for supplier selection and order allocation problems. Linguistic variables were used to assess weights of the factors as trapezoidal fuzzy numbers. The weights were obtained by applying a procedure to calculate fuzzy positive ideal rating and fuzzy negative ideal rating for appling in a fuzzy multi-objective linear model (Yucel and Guneri, 2010).

## 4.1.2 Hybrid fuzzy- AHP

Nine out of Thirty five fuzzy hybrid methods (25.7%) used hybrid fuzzy -AHP method for the supplier selection problem. In this group, hybrid fuzzy- AHP was integrated with other models such as interpretive structural modeling (ISM), goal programming, TOPSIS, structural equation modeling (SEM), and DEA.

Yang et al. (2008) employed ISM approach to clarify the relationships among the sub-criteria in the vendor selection problem. The fuzzy AHP method was used to compute the relative weights for each criterion. Also, the non-additive fuzzy integral was applied to obtain the fuzzy synthetic performance of each criterion. Finally, the best vendor was determined according to the overall aggregating score of each vendor using the fuzzy weights with fuzzy synthetic utilities (Yang et al., 2008).

Lee (2009) applied a fuzzy AHP model with the consideration of opportunities and risk besides benefits and costs for buyers to select the best suppliers(Lee, 2009).

Lee et al. (2009) operated fuzzy AHP to analyze the importance weights of multiple factors in the supplier selection problem. These weights were used as the coefficient of goals in the goal programming model (Lee et al., 2009).

Wang et al. (2009) developed fuzzy hierarchical TOPSIS method to simplify the complicated metric distance method which had been applied by Chen et al. (2005) and to rectify Chen's fuzzy TOPSIS idea (2000) in the supplier selection problem. In the modified model, fuzzy AHP was used to calculate the fuzzy weight of each criterion. Also, the weights were inserted to TOPSIS method for ranking suppliers (Wang et al., 2009).

Chamodrakas et al. (2010) suggested an approach to modify Mikhailov's fuzzy preference programming method (2000) according to Liberatore's rating scale AHP method (1987) for the supplier selection problem in an electronic marketplace environment. A Simon's satisfying model was used for supplier pre-qualification and the modified rating-scale AHP version fuzzy preference programming method was applied for final supplier evaluation (Chamodrakas et al., 2010).

Ku et al. (2010) utilized fuzzy goal programming considering the manufacturer's supply chain strategies for the supplier selection problem. Fuzzy AHP was applied to calculate the relative weights of criteria and then the weight numbers were used as goals' coefficients in objective function of fuzzy goal programming to determine the optimal order allocation (Ku et al., 2010).

Jolai et al. (2010) employed fuzzy AHP to calculate the importance weights of criteria and a modified fuzzy TOPSIS approach to gain the scores of alternative suppliers in multi product environment. Also, the goal programming method was applied to construct a multi-objective mixed integer linear programming model to determine the quantity of order allocation to each selected supplier in each period (Jolai et al., 2010).

Punniyamoorthy et al. (2011) employed SEM approach to obtain the relative weights of the quantitative and qualitative criteria in the supplier selection problem. Fuzzy AHP was used to gain the relative weights of suppliers to achieve supplier selection score (Punniyamoorthy et al., 2010).

Zeydan et al. (2011) applied fuzzy AHP model to find criteria weights and also fuzzy TOPSIS model to rank the suppliers. In this model, qualitative variables were transformed into a quantitative variable for using in DEA approach as an output to determine the efficient and inefficient suppliers (Zeydan et al., 2011).

## 4.1.3 Hybrid fuzzy-TOPSIS

Five out of Thirty five fuzzy hybrid methods (14.3%) used hybrid fuzzy -TOSIS method for the supplier selection problem. In this group, some methods such as mathematical programming, SWOT, DEA, and Decision-Making Trial and Evaluation Laboratory (DEMATEL) were integrated with hybrid fuzzy-TOPSIS in some articles.

Boran et al. (2009) applied intuitionistic fuzzy set to determine the importance of each criterion and the score of each supplier with respect to each criterion in the supplier selection problem. Also intuitionistic fuzzy averaging operator was used for aggregation of expert opinions. The intuitionistic fuzzy numbers were passed to TOPSIS model for ranking suppliers (Boran et al., 2009).

Awasthi et al. (2010) applied fuzzy TOPSIS method to generate an overall performance score for each supplier in supply chain. The sensitivity analysis was performed to present the impact of criteria weights on decision making process (Awasthi et al., 2010).

Chen (2010) suggested a strategically method based on SWOT analysis to identify the criteria of the supplier selection process. First, potential suppliers through DEA approach were screened to efficient and inefficient groups. Then membership functions for the fuzzy weights of criteria were calculated and the efficient suppliers were ranked through TOPSIS model (Chen, 2010).

Dalalah et al. (2011) employed DEMATEL to determine the cause and effect relationship between criteria in the supplier selection problem. The DEMATEL model was modified to handle fuzzy rating and linguistic evaluations. Also, the overall importance weights of all criteria were shifted to modified TOPSIS model to find the best supplier (Dalalah et al., 2011).

Soner Kara (2011) applied fuzzy TOPSIS method to rank suppliers in unknown environment. Furthermore a group of ranked suppliers were shifted in to a two-stage stochastic programming model to determine order quantities under demand uncertainty. (Soner Kara, 2011)

## 4.1.4 Hybrid fuzzy- ANP

Four out of Thirty five fuzzy hybrid methods (11.4%) used hybrid fuzzy- ANP method for the supplier selection problem. In this group, hybrid fuzzy- ANP was integrated with another model such as TOPSIS. Also various kinds of fuzzy models were used in some articles.

Lin (2009) integrated the Fuzzy preference programming method with ANP to measure the weights of the suppliers. Then, the weights were used as coefficients in the objective function of the multi-objective linear programming model to obtain optimal allocation of orders (Lin, 2009).

Onut et al. (2009) applied fuzzy ANP to calculate criteria weights in the supplier selection problem. Then these weights were shifted to the fuzzy TOPSIS methodology to rank the suppliers (Ã-nüt et al., 2009).

Buyukozkan and Cifci (2010) utilized fuzzy ANP model in sustainable supplier selection problems. In this model, missing values were estimated through the preferences of evaluators applying incomplete preference relations and fuzzy linguistic terms were used to analyze criteria (Buyukozkan and Çifçi, 2010).

Vindoh et al. (2010) implemented fuzzy ANP approach to find the most appropriate supplier on the basis of weighted index. Also a sensitivity analysis was performed on varying the relative importance of different criteria (Vinodh et al., 2010).

## 4.1.5 Hybrid fuzzy- neural network

Three out of Thirty five hybrid fuzzy methods (8.6%) used hybrid fuzzy- neural network method for the supplier selection problem. Not only various models of neural network were applied in two articles of this group but also one of them integrated hybrid fuzzy- neural network method with genetic algorithm.

Sadeghi Moghadam et al. (2008) applied fuzzy neural network to control the inventory and select the optimal supplier. The results of the model were passed to a mixed integer programming and because of the complexity and non-linear nature of the model, a genetic algorithm was used to solve it .(Sadeghi Moghadam et al., 2008).

Aydin Keskin et al. (2010) presented Fuzzy Adaptive Resonance Theory Neural Networks for supplier evaluation and selection. In this model, the most appropriate supplier(s) were selected and clustered (Aydin Keskin et al., 2010).

Kuo et al. (2010) suggested a particle swarm optimization based fuzzy neural network for the supplier selection problem. The model derived the fuzzy relationship for qualitative factors. Then quantitative data and fuzzy knowledge decision were integrated to get the best decision (Kuo, 2010).

## 4.1.6 Hybrid fuzzy-other

Four out of Thirty five fuzzy hybrid methods (11.4%) used hybrid fuzzy-other method for the supplier selection problem.

Chou and Chang (2008) proposed fuzzy set theory in to simple multi-attribute rating technique (SMART) to select the appropriate supplier. A fuzzy SMART was implemented to cope with the ratings of both qualitative and quantitative criteria for evaluating of suppliers. Also, a sensitivity analysis was carried out to present the effect of variance in the risk coefficients in ranking order of suppliers (Chou and Chang, 2008).

Amin and Razmi (2009) operated quality function deployment (QFD) to determine the best suppliers based on qualitative criteria. Also, a weighted linear programming model was adopted to consider quantitative metrics as a quantitative model. Finally these two models were composed and selected the best suppliers (Amin and Razmi, 2009).

Azadeh and Alem (2010) suggested a model included DEA for deterministic data, Fuzzy DEA for fuzzy data and Chance Constraint DEA for probabilistic data under certainty, uncertainty and probabilistic conditions. The Mont Carlo simulation was applied to solve the three models (Azadeh and Alem, 2010)

Sanayei et al. (2010) developed multi-criteria optimization and compromise solution approach (the Serbian name is VIKOR) for ranking suppliers. A hierarchy MCDM model based on fuzzy sets theory and VIKOR method was introduced to determine the closeness to the ideal solution. Also, the differences between this method and TOPSIS model were referred in the article (Sanayei et al., 2010).

## .

## 4.2 Hybrid mathematical programming Method

Thirteen out of fifty five hybrid methods (23.6%) applied hybrid mathematical programming Method for the supplier selection problem. Their implementations and evaluation criteria utilized in the methods are presented in Attachment 3.

## 4.2.1 Hybrid mathematical programming-AHP

Four out of Thirteen Hybrid mathematical programming Methods (30.8%) used Hybrid mathematical programming-AHP method for the supplier selection problem.

Ting and Cho (2008) applied AHP to choose a set of candidate suppliers. Subsequently, a multi objective linear programming model was constructed to determine the optimum order quantities allocation to the candidate suppliers (Ting and Cho, 2008).

Ebrahim et al. (2009) introduced the multi objective linear integer programming model for supplier selection and order lot sizing in consideration of various kinds of discount in single item purchasing problem. AHP was utilized to obtain a total weight for each supplier. Because of the complexity of the model a scatter search algorithm and a branch and bound algorithm were applied to solve the model and the results of two algorithms were compared (Ebrahim et al., 2009).

Kokangul and Susuz (2009) applied AHP to make a trade offs between criteria and to determine the score of suppliers in the supplier selection problem. The obtained scores were considered as coefficients of an objective function in a multi-objective non-linear integer programming model to allocate order quantities under quantity discounts (Kokangul and Susuz, 2009).

Liao and Kao (2010) employed Taguchi loss function to estimate the total loss of evaluation criteria in the supplier selection problem. The AHP was applied to assign the relative weight of each criterion. Furthermore a multi-choice goal programming model was costructed to let decision makers to have multi-aspiration levels for decision criteria in selecting the best supplier (Liao and Kao, 2010)

## 4.2.2 Hybrid mathematical programming-ANP

Four out of Thirteen Hybrid mathematical programming Methods (30.8%) used Hybrid mathematical programming-ANP method for the supplier selection problem. In this group, TOPSIS approach was integrated with Hybrid mathematical programming-ANP in one of the articles.

Aktar Demirtas and Ustun (2009) integrated ANP and multi objective mixed integer linear programming models to select the appropriate suppliers and determine the order quantities in multi-period lot sizing condition. Furthermore Achimedean goal programming model was applied to solve the model (Aktar Demirtas and Ustun, 2009).

Wu et al. (2009) integrated analytic network process (ANP) and multi-objective mixed integer programming to select appropriate supplier in consideration of bundling strategy. The weighted scores of suppliers were derived from ANP model and these scores were used as coefficients of an objective function in mathematical model to assign order quantities to each supplier (Wu et al., 2009).

Similar to other scholars, Kirytopoulos et al. (2010) applied ANP to rate the suppliers and then exploited a multi objective mathematical programming method to assign order quantities. The suppliers were clustered besides ranking in the model (Kirytopoulos et al., 2010).

Lin et al. (2011) combined ANP and TOPSIS models to obtain the weights of suppliers in the ERP environment. The final weight of each supplier was considered as a coefficient of objective function in linear programming model to assign optimal order quantity to each supplier(Lin et al., 2011).

## 4.2.3 Hybrid mathematical programming -GA

Two out of Thirteen Hybrid mathematical programming Methods (15.4%) used Hybrid mathematical programming -GA method for the supplier selection problem.

Che and Wang (2008) developed an optimal mathematical model for multiple products in the supplier selection problem due to common and non-common parts. The model was constructed to allocate suitable order quantities to selected suppliers under the limitation of production capacity. A GA approach was applied to find acceptable results for the model (Che and Wang, 2008).

Basnet and Weintraub (2009) constructed a mixed integer programming model for the supplier selection problem. A GA approach was applied to determine the efficient supplier for large-sized problems in the model (Basnet and Weintraub, 2009).

## 4.2.4 Hybrid mathematical programming-Other

Three out of Thirteen Hybrid mathematical programming Methods (23%) used Hybrid mathematical programming-Other method for the supplier selection problem.

Sanayei et al. (2008) applied multi-attribute utility theory to rate the suppliers while considering uncertainty. The obtained rates were then utilized as coefficients for the objective function of the linear programming model to identify the optimal quantities of order allocation (Sanayei et al., 2008).

Osman and Demirli (2010) developed a bilinear goal programming model to handle the supplier selection problem. A modified Benders decomposition method was applied to decompose the model in to a binary supplier selection model and a mixed integer distribution planning model(Osman and Demirli, 2010).

Zhang and Zhang (2010) structured a mixed integer programming model for the supplier selection problem. A branch and bound algorithm was applied to solve the model and to obtain the exact optimal solution (Zhang and Zhang, 2010).

## 4.3 Other Methods

Seven out of fifty five articles (12.7%) applied other methods for the supplier selection problem. These methods could not be classified in any groups. Their implementations and evaluation criteria utilized in the methods are presented in Attachment 4.

Ha and Krishnan (2008) applied AHP to assign weight to the qualitative criteria in single sourcing and multiple sourcing of supplier selection process. Then, the remained quantitative criteria along with the scores for each supplier obtained by AHP were shifted to DEA and ANN to calculate the performance efficiency of each supplier. Both results were compiled into one efficiency index using a simple averaging method. Also a cluster analysis was performed for suppliers (Ha and Krishnan, 2008).

Ming-Lang et al. (2009) integrated ANP and Choquet integral to deal with the interdependency of criteria, the nonlinear relationship among criteria, and the environmental uncertainties in the supplier selection problem. The ANP was used simultaneously to consider the relationships of feedback and dependence of criteria. Choquet integral was applied to eliminate the interactivity of expert subjective judgment problems (Ming-Lang et al., 2009).

Wu (2009) suggested a classification model and a regression model for the supplier selection problem. First DEA was utilized to classify suppliers into efficient and inefficient clusters. Then firm performance-related data was used to train decision tree or neural networks model and to apply the trained models to new suppliers (Wu, 2009).

Bhattacharya et al (2010) proposed QFD approach within the AHP framework for the supplier selection problem. The proposed model considered both subjective as well as objective factors to rank suppliers (Bhattacharya et al., 2010).

Kuo et al. (2010) operated ANN model to predict the performance values of suppliers and ANP model to calculate the weight of each criterion in the supplier selection problem. Also DEA was implemented to obtain a final evaluation of suppliers (Kuo et al., 2010).

Lin et al (2010) applied ISM approach to present the interrelation amongst the criteria in the supplier selection problem. Then ANP was employed to determine the weightings of each criteria (Lin et al., 2010).

Ordoobadi (2010) exploited Taguchi loss function to rank the suppliers with consideration of benefit and risk categories in the supplier selection issue. AHP method was utilized to calculate the relative importance of each category. While the composite loss score for each supplier was obtained by calculating the average of the weighted loss scores of two categories. Finally the supplier with the lowest composite loss score was chosen (Ordoobadi, 2010).

## 5. Comments

## 5.1 The most practical method

Due to previous section, the hybrid methods (82.1%) were obviously more practical than single methods (17.9%). Because every single method has some drawbacks and the integration of methods is implemented to overcome the drawbacks. According to Appendix, the most practical single method is mathematical programming. Other practical single methods were DEA, fuzzy set theory, ANN, rough set theory, and vague set theory sequentially.

Supplier selection is a multi criteria decision making and this problem can be modeled as a multi-objective programming technique. Usually one or more criteria were considered as objective functions, and other criteria were considered as constraints. Besides evaluation and selection criteria, companies are exposed to various constraints in the supplier selection problem which can be formulated as mathematical programming models. Moreover, in multiple sourcing environments mathematical programming methods are famous because not only to select the appropriate suppliers but also determine the amount of order allocation to selected supplier simultaneously. That is why; mathematical programming is the most practical single method. However, mathematical programming method has some drawbacks as follows. Mathematical Programming models often neglect to consider scaling and subjective weighting issues and have no possibility for the decision makers to apply his or her preference. The weight determination is a challenging task for implementing these models. Moreover, mathematical programming models have no ability to cope with the qualitative criteria.

As shown in section 4, there are different hybrid methods for supplier selection. It was noticed that the hybrid fuzzy methods are more practical. The supplier selection problem is often faced by ambiguity and vagueness in practice. Very often decision makers express their preferences in linguistic terms instead of numerical values. In such circumstance fuzzy logic and fuzzy set theory are used to handle these uncertainties. Fuzzy concept has been integrated with other techniques, including AHP, ANN, ANP, DEA, mathematical programming, SMART, TOPSIS, and VIKOR. Comparatively, the hybrid fuzzy-mathematical programming models are more prevalent. The reasons of wide applicability of mathematical programming models were mentioned before. On the other hand, because of the weightless characteristic of mathematical programming models, all of the studies in fuzzy- mathematical programming group suggested a kind of solution methods to overcome this drawback. AHP is the most functional solution methods in this group. AHP is a common approach for calculating the relative importance weightings of criteria and sub-criteria owing to its simplicity and flexibility. Based on the above analysis, it is obvious that mathematical programming models are the most prevalent single methods also integrated fuzzy mathematical programming and AHP method is the most practical hybrid methods.

## 5.2 The most usable Criteria

Many criteria were suggested in the supplier selection problem and they were gathered in Appendix () completely. The most usable criterion is quality, followed by cost/price, delivery, service, organization and management, financial situation, flexibility, production facilities and capacities, technological level, relationship, social and environmental criteria, research and development, communication, reputation, strategic programming, risk, information technology, productivity, and innovation.

The quality criterion was applied in 60 articles (89.5%). Different quality related attributes have been found in the articles, such as "quality management system audit", "quality system assessment", "defect and scrap ratio", "low defect rate", total quality management", "number of bills receive from suppliers without errors"," return rate", "test and inspection management", "corrective and preventive actions management"," reliability of product performance", "key quality characteristics", "net rejections", "test capability", "yield rate", "quality system certifications", "internal audit", quality abnormal rate"," length of guarantee period", "capability to prevent repeated error", "return product velocity", " quality system outcome", and "lean process planning".

The cost/price criterion was implemented in 55 articles (82.1%). Its related attributes include "price and terms", "unit price and payment", "fixed cost", "setup cost", "production variable cost", "transaction and inventory cost", "total cost of shipment", "R&D cost", "investment cost", "purchase cost", "holding cost", "cost of product", "cost of relationship", "total logistics management costs", "environmental costs", "warrant costs", "measurement and assessment cost", "transportation costs", "ordering costs", "cost reduction capability", "testing price", and "reduction of capital investment".

The third most usable criterion is delivery in 53 articles (79.1%). Its related attributes include "fill rate", "perfect order fulfillment", "number of on time shipment", "order delays", "lead time to order", "damage free order", "on time orders", geographical location", "lead time", "accuracy of delivered contents", net late deliveries", product response time", "dispatch problems", "distance", and "wrong quantity/items".

## 6. Conclusion, Suggestions, research limitations

This literature review on the multiple criteria decision making methods for supplier evaluation and selection from 2008 to February 2011 provides valuable insights and a complete classification on this issue. The number of articles on the supplier selection problem is on the rise as shown in Fig. 1. The numerous proposed single and hybrid methods to deal with supplier selection problem were discussed. The most practical single method is Mathematical Programming, whereas the most practical hybrid method is fuzzy AHP-Mathematical Programming. Second, the most usable criterion to evaluate suppliers is quality, followed by cost/price, delivery, and so on.

To pave to future researches, the sustainable development issue can be considered in the supplier selection problem. Based on our findings, a few articles have worked on sustainable supplier selection problem and this topic is at initial stage of investigation. Environmental/ecological, social and ethical criteria should have been executed for sustainable supplier selection. On the other hand, after analyzing the implementations of applied methods in this review article, we found that the researchers have focused on manufacturing industries. It is worthwhile and essential to apply the methods for supplier selection in service industries and sectors.

This paper might have some limitations. First, only English publications were considered and may be some outstanding studies exist in non-English languages. Second, the review paper was only based on a sample of 67 articles were limited to 4 online databases.

Fig.1 Distribution of articles by year of publication (web of science)