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Symmetry 2018, 10(6), 221; https://doi.org/10.3390/sym10060221

Article
A Hybrid Fuzzy Analytic Network Process (FANP) and Data Envelopment Analysis (DEA) Approach for Supplier Evaluation and Selection in the Rice Supply Chain
1
Department of Industrial Engineering and Management, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan
2
Department of Industrial Engineering and Management, Fortune Institute of Technology, Kaohsiung 83160, Taiwan
3
Department of Industrial Systems Engineering, CanTho University of Technology, CanTho 900000, Vietnam
*
Authors to whom correspondence should be addressed.
Received: 18 May 2018 / Accepted: 12 June 2018 / Published: 14 June 2018

Abstract

:
In the market economy, competition is typically due to the difficulty in selecting the most suitable supplier, one that is capable to help a business to develop a profit to the highest value threshold and capable to meet sustainable development features. In addition, this research discusses a wide range of consequences from choosing an effective supplier, including reducing production cost, improving product quality, delivering the product on time, and responding flexibly to customer requirements. Therefore, the activities noted above are able to increase an enterprise’s competitiveness. It can be seen that selecting a supplier is complex in that decision-makers must have an understanding of the qualitative and quantitative features for assessing the symmetrical impact of the criteria to reach the most accurate result. In this research, the multi-criteria group decision-making (MCGDM) approach was proposed to solve supplier selection problems. The authors collected data from 25 potential suppliers, and the four main criteria within contain 15 sub-criteria to define the most effective supplier, which has viewed factors, including financial efficiency guarantee, quality of materials, ability to deliver on time, and the conditioned response to the environment to improve the efficiency of the industry supply chain. Initially, fuzzy analytic network process (ANP) is used to evaluate and rank these criteria, which are able to be utilized to clarify important criteria that directly affect the profitability of the business. Subsequently, data envelopment analysis (DEA) models, including the Charnes Cooper Rhodes model (CCR model), Banker Charnes Cooper model (BCC model), and slacks-based measure model (SBM model), were proposed to rank suppliers. The result of the model has proposed 7/25 suppliers, which have a condition response to the enterprises’ supply requirements.
Keywords:
fuzzy analytic network process (FANP); data envelopment analysis (DEA); supplier selection; multi-criteria group decision-making (MCGDM)

1. Introduction

The task of selecting suppliers becomes more important in today’s competitive and global environment when it is impractical or virtually impossible to create high-quality, low-cost, successful products without a vendor. For businesses today, vendor selection is one of the most important and indispensable components of the supply chain function of Florez–Lopez [1]. The enterprises’ expected goal of selecting a vendor is necessary to reduce the risk in buying, making an optimum decision, and establishing a sustainable alliance between buyers and suppliers [2]. Basically, choosing suppliers is a decision-making process because a business expects to obtain a supplier [3]. Additionally, it requires a powerful analytical approach, via utilizing decision-support tools, which is capable of addressing multiple criteria [4]. Incidentally, the supplier’s price includes many qualitative and qualitative conflicts.
The author represents two techniques, i.e., DEA and the FANP, which are used to design a method for evaluating suppliers. In order to obtain the accurate result as the chosen supplier based on the frontier point of the DEA model from input and output decision-makers (DMUs) [5]. The drawback of DEA, related to this study, is the requirement of data for various inputs and outputs to be in a quantitative format. This DEA limitation is addressed by analyzing the qualitative factors/attributes associated with the supplier using FANP. FANP is a more general form of the decentralized process, which includes the feedback and interdependencies of decision attributes and alternatives. This additional feature provides a more accurate and robust approach when modeling a complex decision-making environment [6].
The decision-making process is designed to provide a holistic approach in which the relevant factors and criteria are integrated into the FANP’s decentralized network. Different relationships are combined in these structures and then both judgment and logic are used to estimate the relative effect from which the overall response is derived [7]. The FANP model used here provides a unique quantitative value for vendor-specific qualitative factors and is based on buyers’ preferences and perceptions. This quantitative value from FANP for each supplier is used as a qualitative benefit in the DEA model to obtain the ranking or performance of different suppliers.
This research proposed hybrid FANP and DEA approaches for supplier selection in the rice supply chain, which also considers green issues under uncertain environment conditions. The aim of this research is to provide a useful guideline for supplier selection based on qualitative and quantitative factors (including the main criteria, such as financial, delivery services, qualitative factors, and environmental management systems) to improve the efficiency of supplier selection in the rice supply chain and other industries.
In the remainder of this paper, this research provides the platform data to further support the need of the development of a decision approach. Then, the synthetic supplier evaluation approach was applied to a case study of a company, which could be used for the explanation of the findings. Finally, this paper ends with a summary, and conclusions are made.

2. Literature Review

2.1. Supplier Selection Methods

Aissaoui et al. [8] presented a literature review that covers the entire purchasing process, considered both parts and services outsourcing activities, and covers Internet-based procurement environments, such as electronic marketplace auctions. Govindan et al. [9] presented a literature review for multi-criteria decision-making approaches for green supplier evaluation and selection. Chai et al. [10] provided a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection.
Wu and Blackhurst [11] proposed a methodology termed augmented DEA, which has enhanced discriminatory power over basic DEA models to rank suppliers. Amirteimoori and Khoshandam [12] developed a DEA model for evaluating the performance of suppliers and manufacturers in supply chain operations. Lin et al. [13] provided a MCDM model by combining the Delphi method and the ANP method for evaluating and selecting suppliers for the sustainable operation and development of enterprises in the aerospace industry. Galankashi et al. [14] proposed an integrated balanced scorecard (BSC) and fuzzy analytic hierarchical process (FAHP) model to select suppliers in the automotive industry. Kilincci and Onal [15] used a fuzzy AHP approach for supplier selection in a washing machine company.
Tyagi et al. [16] proposed fuzzy AHP and AHP methods to prioritize the alternatives of the supply chain performance system. Karsak and Dursun [17] proposed a fuzzy MCDM model including the quality function deployment (QFD), fusion of fuzzy information, and 2-tuple linguistic representation for supplier evaluation and selection. Chen et al. [18] proposed a hybrid AHP and TOPSIS for evaluating and ranking the potential suppliers. Guo et al. [19] used fuzzy MCDM approaches for green supplier selection in apparel manufacturing. Wu et al. [20] constructed a multiple criteria decision-making model for the selection of fishmeal suppliers. Hu et al. [21] proposed a hybrid fuzzy DEA/AHP methodology for ranking units in a fuzzy environment. He and Zhang [22] used a hybrid evaluation model based on factor analysis (FA), data envelopment analysis (DEA), with analytic hierarchy process (AHP) for a supplier selection from the perspective of a low-carbon supply chain.
Parkouhi et al. [23] used the fuzzy analytic network process and VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) techniques for supplier selection. Wan et al. [24] proposed a hybrid DEA and Grey Model (1,1) approach for partner selection in the supply chain of Vietnam’s textile and apparel industry. Wu et al. [25] used the fuzzy Delphi method, ANP, and TOPSIS for supplier selection. Rezaeisaray et al. [26] proposed a hybrid DEMATLE, FANP, and DEA model for outsourcing supplier selection in pipe and fittings manufacturing. Rouyendegh and Erol [27] applied the DEA-fuzzy ANP for department ranking at Iran Amirkabir University. Fuzzy set theory formalized by Zadeh [28] is an effective tool, which has been widely used in the supplier selection decision process because it provides a suitable language to transform imprecise criteria to precise criteria.
Junior et al. [29] presented a comparison between fuzzy AHP and fuzzy TOPSIS methods to supplier selection. The linear programming of data envelopment analysis (DEA), which is proposed by Charnes et al. [30], and is able to produce the result of measured efficiency without having specific weights for inputs and outputs or specify the form of the production function, is a nonparametric technique used to measure the relative efficiency of peer decision-making units with multiple inputs and outputs [31,32]. In the supplier’s evaluation and selection process, many researchers calculated the supplier’s performance by using the ratio of weighted outputs to weighted inputs [32]. Thus, the integrated FANP and DEA method is used to determine supplier selection criteria and select supplier in this paper.
Talluri et al. [33] provided vendor evaluation models by presenting a chance-constrained data envelopment analysis (CCDEA) approach in the presence of multiple performance measures that are uncertain. Saen [34] applied a DEA model for ranking suppliers in the presence of nondiscretionary factors. Saen [35] also proposed a new AR-IDEA model for supplier selection. Saen and Zohrehbandian [36] proposed a DEA approach for supplier selection. Saen [37] proposed an innovative method, which is based on imprecise data envelopment analysis (IDEA) to select the best suppliers in the presence of both cardinal and ordinal data. Lo Storto [38] proposed a double DEA framework to support decision making in the choice of advanced manufacturing technologies. Adler et al. [39] reviewed of ranking method in the data envelopment analysis context. Lo Storto [40] presented a peeling DEA-game cross efficiency procedure to classify suppliers.
Kuo et al. [41] developed a supplier selection system through integrating fuzzy AHP and fuzzy DEA on an auto lighting System Company in Taiwan. Kuo and Lin [42] used ANP and DEA for supplier selection.
Taibi and Atmani [43] proposed a MCDM model combining fuzzy AHP with GIS and decision rules for industrial site selection. Molinera et al. [44] used fuzzy ontologies and multi-granular linguistic modelling methods for solving MCGDM problems under environments with a high number of alternatives. Adrian et al. [45] proposed a conceptual model development of big data analytics implementation assessment effect on decision making.
Staníčková and Melecký used DEA models to evaluate the performances of Visegrad Four (V4) countries and regions [46]. Schaar and Sherry have been shown to contribute to the overall performance efficiency of the air transportation network by used three DEA models (CCR, BCC and SBM) [47].

2.2. Criteria and Sub-Criteria for Supplier Selection

The initial criteria for the supplier set are developed based on a literature study.
Financial: The firm should require its suppliers to have a sound financial position. Financial strength can be a good indicator of the supplier’s long-term stability. A solid financial position also helps ensure that performance standards can be maintained and that products and services will continue to be available [48].
Delivery and service: A firm can use service performance criteria to evaluate the benefits provided by supplier services. When considering services, a firm needs to clearly define its expectations since there are few uniform, established service standards to draw upon. Since any purchase involves some degree of service, such as order processing, delivery, and support, a firm should always include some service criteria in its evaluation. If the supplier provides a solution combining products and services, the firm should be sure to adequately represent its service needs in the selection criteria [48]. The suppliers have to follow the predefined delivery schedule for achieving on-time delivery. All the manufacturers want to work with the supplier who can manage the supply chain system on time and has the ability for following the exact delivery schedule table [49].
Qualitative: Qualitative criteria are developed to measure important aspects of the supplier’s business: business experience and position among competitors, expert labor, technical capabilities and facilities, operational control, and quality [50].
Environmental management system: Due to increasing awareness about environmental degradation manufacturing companies and customers are both becoming alert of environmental protection [51]. This has led stakeholders of companies to ensure safe practices, like pollution control, reuse, recovery, etc. It includes criteria like pollution control: resource consumption of raw materials, use of environmentally friendly technology and materials, design capability for reduced consumption of materials/energy, reuse, and recycling of materials. To reduce the harm to the environment, organizations should also consider factors like permit requirements, compliance requirements, strategic considerations, climatic considerations, and government policy [52,53].
There are four main criteria and some sub-criteria, as shown in Table 1.

3. Material and Methodology

3.1. Research Development

Figure 1 illustrates the selection process, which is sequentially presented in three steps. In the first step, the decision-maker examines the material, interviews the experts, and surveys managers to determine the criteria and sub-criteria affecting to decision making. In the second step data are then processed using the FANP method to rank the criteria. Results from the FANP method are used for the input and output of the DEA model. The DEA model is implemented in the final stage.
Step 1: Determining evaluation criteria and sub-criteria
Determine the key criteria and sub-criteria for a comprehensive assessment of the potential supplier. At this stage, the identification of key criteria and sub-criteria is based on a review of the literature and scientific reports related to the content of the research to determine the necessary criteria for the topic [50]. After identifying the groups of criteria required, the decision-maker should select the potential supplier that matches the set criteria. Here, the criteria are defined as four main criteria and 15 sub-criteria, as shown in Figure 2.
Step 2: Implementing the FANP technique
Incorporating hybrid fuzzy set theory into the ANP model is the most effective tool for addressing complex problems of decision-making, which has a connection with various qualitative criteria [37]. As can be seen from the solution algorithm in this technique, as presented in Figure 3, at first, the decision-making hierarchical structure is determined to assist the selection [71].
Step 3: Implementation of the DEA model
In this study, the FANP and DEA techniques for efficiency measurement have advantages over other fuzzy ANP approaches. In this step, several DEA models, including the Charnes–Cooper–Rhodes model (CCR model), Banker–Charnes–Cooper model (BCC model), Slacks-Based Measure model (SBM model), and Super Slacks-Based Measure model (Super SBM model) are applied to rank suppliers and potential suppliers.

3.2. Methodology

3.2.1. Fuzzy Set Theory

Fuzzy set was proposed by Zadeh to solve problems existing in uncertain environments. Fuzzy sets are functions that show the dependence degree of one fuzzy number on a set number. A tilde (~) is placed above any symbol representing a fuzzy set number. If A ˜ is a TFN, each value of the membership function is between [0, 1] and can be explained, as shown in Equation (1):
μ A ˜ ( x ) = { ( x l ) ( m l )    l x m ( u x ) ( u m )    m x u 0     0 . W
Each degree of membership includes a left- and right-side representation of a TFN, as shown here:
N ˜   =   ( N 1 ( y ) , N r ( y ) )   =   ( 1     ( m     l ) y ,   u   +   ( m     u ) y ) , y [ 0 ,   1 ] .
A TFN is shown in Figure 2.

3.2.2. Fuzzy Analytic Network Process

ANP does not require a strict hierarchical structure, such as AHP. It allows elements to control, and be controlled, by different levels or clusters of attributes. Several control elements are also present at the same level. Interdependence between factors and their level is defined as a systematic approach to feedback or interactions between elements.
During the ANP process, the elements will be compared pairwise using the expert rating scale, from which the weighting matrix is established. The weights are then adjusted by defining the product of the super matrix.
The AHP method provides a structured framework to set priorities for each level of the hierarchy by using pairwise comparisons quantitated with a priority scale of 1–9, as shown. In contrast, the ANP approach allows for more complex relationships between the elements and their ranks. The 1–9 scale for AHP is shown in Table 2.
It is clear that the disadvantage of ANP in dealing with the impression and objectiveness in the pairwise comparison process has been improved in the fuzzy analytic network process. The FANP applies a range of values to incorporate the decision-makers’ uncertainly [38], whereas the ANP model shows a crisp value. The author assigns the fuzzy conversion scale of this formula, which will be used in the Saaty [72] fuzzy prioritization approach, as shown in Table 2, where Oab = ( O ab x , O ab o , O ab v ) is a triangular fuzzy number with the core O ab o , the support [ O ab x , O ab v ], and the triangular fuzzy number, as shown in Figure 3.
The 1–9 fuzzy conversion scale is shown in Table 3:
The reversed degree to Oab expressing the non-preference is also expressed by a triangular fuzzy number: (1/ O a b v , 1/ O a b o ,   1 / O a b x . ). By the way, the weights of criteria from the fuzzy Saaty’s matrix can be divided into four steps [73]:
  • Fuzzy synthetic extension calculation will transformed into TNT, called fuzzy synthetic extensions K a ( k a x , k a o , k a u v ) . using Equations (2)–(4) [74]:
    K a = b = 1 n O a b ( a = 1 n b = 1 n O a b ) 1
    j = 1 n O a b = ( b = 1 n M a b x , j = 1 n O a b o , b = 1 n O a b v )
    O a b 1 = 1 / O a b v , 1 / O a b o , 1 / O a b x
    O N = ( O x   .   N x ,   O 0 .   N 0 ,   O v . N v )
    Assign a = 1, 2, …, n, in which a and b specifically are triangular fuzzy number (Ox, Oo, Ov) and (Nx, N0, Nv).
  • Weights of criteria are addressed by using relations of the fuzzy-valued. In this step, fuzzy synthetic extensions are blurred by using the min fuzzy extension of the valued relation ≤ given by Equation (5), and weights Wi are calculated (for more detail, see [75]):
    Q a = m i n b { k b b k a v ( k a o k a v ) ( k b o k b x ) }
    For a, b = 1, 2, …., n.
  • The standardization of the weights. If we expect to obtain the sum of weights within one matrix equal to 1, final weights wi are solved using Equation (7):
    q i = Q i / a = 1 n Q a
    For a, b = 1, 2, …, n.
  • An assessment of a Saaty’s matrix consistency. In the line with [74], a consistency of the matrix is sufficient if inequality from Equation (8) holds:
    R T =   C T R R = λ ¯ n ( n 1 ) . R R 0.1
    where λ ¯ is a symbol for the arithmetic mean of the maximum real eigenvalues of the matrices ( a a b ξ ) 1 a , b n , ξ { x , o , v } for a, b = 1, 2, ..., n is the size of the Saaty’s matrix, and RR represents a random index whose value depends on [74].

3.3. Data Envelopment Analysis

3.3.1. Charnes-Cooper-Rhodes Model (CCR Model)

Charnes, Cooper, and Rhodes (1978) [30] proposed a basic DEA model, called the CCR model:
max f . g   γ   = f V y 0 g V x 0 S . t . f V y b   g V x b   0 ,   b = 1 ,   2 , , n f 0 g 0
Due to constraints, the optimal value γ * is a maximum of 1.
DMU0 is efficient if γ * = 1 and have at least one optimal f* > 0 and g* > 0. In addition, the fractional program can be presented as follows [76]:
min g . f   γ = g v y 0 S t . g v x 0 1 = 0 f v y j g v x j 0 ,   j = 1 ,   2 , , n g 0 f 0
The Farrell [77] model of Equation (10) with variable γ and a nonnegative vector β = β 1 , β 2 , β 3 , , β n is expressed as [76].
m a x i = 1 m d i + r = 1 s d r + S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q β j 0 ,   j = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
Equation (11) has a feasible solution, γ * = 1 , β 0 * = 1 , β j * = 0 , ( j 0 ) ,   which effects the optimal value γ * not greater than 1. The process will be repeated for each DMUj, j = 1, 2, …, n. DMUs are inefficient when γ * < 1, while DMUs are boundary points if γ * = 1 . We avoid the weakly efficient frontier point by invoking a linear program as follows [76]:
m a x i = 1 m d i + r = 1 d d r + S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q β j 0 ,   j = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
In this case, note that the choices the d i and d r + do not affect the optimal γ * . The performance of DMU0 achieves 100% efficiency if, and only if, both (1) γ * = 1 and (2) d i * = d r + = 0 . The performance of DMU0 is weakly efficient if, and only if, both (1)   γ * = 1 and (2) d i * 0 and d r + 0 for i or r in optimal alternatives. Thus, the preceding development amounts to solving the problem as follows [76]:
m i n θ α ( i = 1 m d i + r = 1 d d r + ) S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q β j 0 ,   j = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
In this case, d i and d r + variables will be used to convert the inequalities into equivalent equations. This is similar to solving Equation (11) in two stages by first minimizing γ and then fixing γ = γ * as in Equation (12). This would reset the objective from max to min, as in Equation (9), to obtain [76]:
max g . f   γ = g V x 0 f V y j S . t g V x 0 g V y j ,   j = 1 ,   2 , , n g ε > 0 f ε > 0
If the α > 0 and the non-Archimedean element is defined, the input models are similar to Equations (10) and (13), as follows [76]:
max g . f   γ = g V x 0 S . t f V y 0 = 1 g V x o f V y j 0 ,   j = 1 ,   2 , , n g ε > 0 f ε > 0
and:
m a x ϕ ε ( i = 1 m d i + r = 1 d d r + ) S . t j = 1 n x i j β j + d i = x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q β j 0 ,   j = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
The input-oriented CCR (CCR-I) has the dual multiplier model, expressed as [76]:
max z = r = 1 q g r y r 0 S . t r = 1 q g r y r j r = 1 q f r y r j 0 i = 1 p f i x i 0 = 1 g r , f i ε > 0
The output-oriented CCR (CCR-O) has the dual multiplier model, expressed as [76]:
min q = i = 1 p f i x i 0 S . t i = 1 p f i x i j r = 1 q g r y r j 0 r = 1 q g r y r 0 = 1 g r , f i ε > 0

3.3.2. Banker–Charnes–Cooper Model (BCC Model)

Banker et al. proposed the input-oriented BBC model (BCC-I) [30], which is able to assess the efficiency of DMU0 by solving the following linear program [76]:
γ B = m i n γ S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q k = 1 n β k = 1 β k 0 , k = 1 , 2 , , n
We avoid the weakly efficient frontier point by invoking the linear program as follows [76]:
m a x i = 1 m d i + r = 1 d d r + S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q k = 1 n β k = 1 β k 0 ,   k = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
Therefore, this is the first multiplier form to solve the problem as follows [76]:
m i n γ ε ( i = 1 m d i + r = 1 d d r + ) S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q k = 1 n β k = 1 β k 0 ,   k = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
The linear program in Equation (17) gives us the second multiplier form, which is expressed as [76]:
max g . f , f 0   γ B = f V y 0 f 0 S . t g V x 0 = 1 f V y j g V x j f 0 0 ,   j = 1 ,   2 , , n g 0 f 0
If g and f, which are mentioned in Equation (22), are vectors, the scalar v 0 may be positive or negative (or zero). Thus, the equivalent BCC fractional program is obtained from the dual program in Equation (22) as [76]:
max g . f   γ = f V y 0 f 0 g V x 0 S . t f V y j f 0 g V x j 1 ,   j = 1 ,   2 , , n g 0 f 0
The DMU0 can be called BCC-efficient if an optimal solution ( γ B * ,   d * , d + * )   is claimed in this two-phase process for Equation (17) satisfies γ B * = 1 and has no slack d * =   d + * = 0, then. The improved activity ( γ * x   d * , y + d + * ) also can be illustrated as BCC-efficient [76].
The output-oriented BCC model (BCC–O) is:
max η S . t j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = η y r 0 ,   r = 1 ,   2 , , q k = 1 n β k = 1 β k 0 ,   k = 1 ,   2 , , n
From Equation (24), we have the associate multiplier form, which is expressed as [76]:
min g . f , g 0 f V y 0 f 0 S . t f V y 0 = 1 g V x j f V y j f 0 0 ,   j = 1 ,   2 , , n g 0 f 0
f0 is the scalar associated with k = 1 n β k = 1 . In conclusion, the authors achieve the equivalent (BCC) fractional programming formulation for Equation (25) [76]:
min g . f , g 0 g V x 0 f 0 f V y 0 S . t f V x j f 0 f V y j 1 ,   j = 1 ,   2 , , n g 0 f 0

3.3.3. Slacks-Based Measure Model (SBM Model)

The SBM model was introduced by Tone [78] (see also Pastor et al. [79]).

Input-Oriented SBM (SBM-I-C)

The input-oriented SBM under a constant-returns-to-scale assumption [76] is described as follows:
ρ I * =   min β ,   d , d + 1   1 m i = 1 m d i x i h S . t x i c = j = 1 m x i c β i +   d i   ,   i = 1 ,   2 ,   m y r c = j = 1 m y r c β i   d r +   ,   i = 1 ,   2 ,   d β j 0 ,   k   ( j ) ,   d i 0   ( j ) , d r + 0   ( j )
The DMUs in the reference set R of ( x c ,   y c ) are SBM-input-efficient. In addition, the SBM-input-efficiency score must is lower than the CCR efficiency score.

Output-Oriented SBM (SBM-O-C)

The output-oriented SBM efficiency ρ O * of DMUc = (xc, yc) is defined by [SBM-O-C] [76]:
1 ρ O * = max λ , s , s + 1 + 1 s r = 1 s s r + y r h S . t . x i c = j = 1 n x i j β j +   d j ( i = 1 , . . m ) y i c = j = 1 n y i j β j + d i + ( i = 1 , m ) β j 0 ( j ) ,   d i 0 ( i ) ,   d i + 0   ( r ) The   optimal   solution of   [ SBM - O - C ] β * , d * , d + * ) .

3.3.4. Super-Slacks-Based Measure Model (Super SBM Model)

Tone’s super SBM model [78] has proposed a slacks-based measure of efficiency (SBM model) that measures the efficiency of the units under evaluation using slack variables only. The super efficiency SBM model removes the evaluated unit DMUq from the set of units and looks for a DMU* with inputs xi*, i = 1, ..., m, and outputs yk*, k = 1, ..., r, being SBM (and CCR) efficient after this removal. The super SBM model is formulated as follow:
minimize   θ q S B M = 1 p i = 1 m x i * / x i 0 1 q k = 1 r y k * / y k 0 S . t
j = 1 n x i j β j + d i = γ x i 0 ,   i = 1 ,   2 , , p j = 1 n y r j β j d r + = y r 0 ,   r = 1 ,   2 , , q x i * x i 0 ,   i = 1 ,   2 , , n y k * y k 0 ,   k = 1 ,   2 , , n β k 0 ,   k = 1 ,   2 , , n d i 0 , i = 1 , 2 , , p d r + 0 , r = 1 , 2 , , q
The numerator in the ratio in Equation (29) can be explained as the distance of units DMUq and DMU* in input space and the average reduction rate of inputs of DMU* to inputs of DMUq.

4. Case Study

In this research, the authors collected 25 suppliers (DMU) in Vietnam. Information about the suppliers is shown in Table 4.
The data collection of the FANP and hierarchical structure are introduced in Figure 4.
A fuzzy comparison matrix for all criteria is shown in Table 5.
During the defuzzification, we obtain the coefficients α = 0.5 and β = 0.5 (Tang and Beynon) [80]. In it, α represents the uncertain environment conditions, and β represents the attitude of the evaluator is fair.
g 0.5 , 0.5 ( a E M S , F S ¯ )   =   [ ( 0.5   ×   6.5 )   +   ( 1     0.5 )   ×   7.5 ]   =   7 f 0.5 ( L E M S , F S )   =   ( 7     6 )   × 0.5   +   6     =   6.5 f 0.5 ( U E M S , F S )   =   8     ( 8     7 )   × 0.5   =   7.5 g 0.5 , 0.5 ( a E M S , F S ¯ )   =   1 / 7
The remaining calculations are similar to the above, as well as the fuzzy number priority points. The real number priorities when comparing the main criteria pairs are presented in Table 6.
We calculate the maximum individual values as follows:
G M 1 = ( 1 × 1 / 7 × 1 / 8 × 1 / 2 ) 1 / 4 = 0.03073 G M 2 = ( 7 × 1 × 1 / 6 × 2 ) 1 / 4 = 1.2359 G M 3 = ( 8 × 6 × 1 × 5 ) 1 / 4 = 3.9359 G M 4 = ( 2 × 1 / 2 × 1 / 5 × 1 ) 1 / 4 = 0.6687 G M = G M 1 + G M 2 + G M 3 + G M 4 = 6.1478
ω 1 = 0.3073 6.1478 = 0.0499 ω 2 = 1.2359 6.1478 = 0.2010 ω 3 = 3.9359 6.1478 = 0.6402 ω 4 = 0.6687 6.1478 = 0.1087
[ 1 1 / 7 1 / 8 1 / 2 7 1 1 / 6 2 8 6 1 5 2 1 / 2 1 / 5 1 ] × [ 0.0499 0.2010 0.6402 0.1087 ] = [ 0.2129 0.8744 2.7889 0.4370 ] [ 0.2129 0.8744 2.7889 0.4370 ] / [ 0.0499 0.2010 0.6402 0.1087 ] = [ 4.2665 4.3502 4.3562 4.0202 ]
with the number of criteria is 4, we obtain n = 4, and λmax and CI are calculated as follows:
λ m a x = 4.2665 + 4.3502 + 4.3562 + 4.0202 4 = 4.2482
C I = 4.2482 4 4 1 = 0.0827
For CR, with n = 4 we obtain RI = 0.9:
C R = 0.0827 1.12 = 0.0919
We have CR = 0.0919 ≤ 0.1, so the pairwise comparison data is consistent and does not need to be re-evaluated. The results of the pair comparison between the main criteria are presented in Table 7, Table 8, Table 9, Table 10 and Table 11.
Based on how the hierarchical structure was built, the pairwise comparison matrix was built through completing a questionnaire. Then, the received data to calculate the weight of supplier’s indices and to ensure the accuracy of judged inconsistency rate and other constraints are presented.
In summary, a graphic of the DEA model for analysis of DMUs (suppliers) along with three inputs and three outputs is shown in Figure 4. The results of the FANP model for the ranking of various suppliers on qualitative attributes are utilized in the output qualitative benefits of the DEA model [71,81]. In our situation, inputs are those factors that organizations would consider as an improvement if they were decreased in value (i.e., smaller values are better), whereas outputs are those factors that organizations would consider as improvements if they were increased in value (i.e., larger is better). This is a standard approach when seeking to use DEA as a discrete alternative multiple criteria decision-making tool [71]. There are three inputs and three outputs, as shown in Figure 5.
To aid in reducing scaling errors associated with the mathematical programming software packages, the dataset is mean normalized for each factor, i.e., each value in each column is divided by that column’s mean score. This normalization procedure does not change the efficiency scores of the ratio-based DEA models. As previously mentioned, to help model the analysis as inputs and outputs, instead of the standard productivity efficiency measurement approach, assume that the inputs are those factors that improve as their values decrease and the outputs are those values that improve as their values increase [71]. Raw data are provided by the case organization, as shown in Table 12.

4.1. Isotonicity Test

The variables of input and output for the correlation coefficient matrix should comply with the isotonicity premise. In other words, the increase of an input will not cause the decreasing output of another item. The results of the Pearson correlation coefficient test are shown in Table 13.
Based on the results of Pearson correlation test, the results of all correlation coefficients are positive, thus meeting a basic assumption of the DEA model. Hence, we do not to change the input and output.

4.2. Results and Discussion

Supplier evaluation and selection have been identified as important issues that could affect the efficiency of a supply chain. It can be seen that selecting a supplier is complicated in that decision-makers must understand qualitative and quantitative features for assessing the symmetrical impact of the criteria to reach the most accurate result.
For the performance in an empirical study, the authors collected data from 25 suppliers in Vietnam. A hierarchical structure to select the best suppliers is built with four main criteria (including 15 sub-criteria). Completion of a questionnaire for analyzing the FANP model is done by interviewing experts, and surveying the managers and company’s databases. The ANP model is combined with a fuzzy set, to evaluate the supplier selection criteria and define the priorities of each supplier, which are able to be utilized to clarify important criteria that directly affect the profitability of the business. Then, several DEA models are proposed for ranking suppliers. As a result, DMU 1, DMU 5, DMU 10, DMU 16, DMU 19, DMU 22, and DMU 23 are identified as efficient in all nine models, as shown in Table 7 [78], which have a conditioned response to the enterprises’ supply requirements. Whereas for other DMUs, there were differences in the results, so the next research should include an improvement or review of data inputs to produce appropriate outputs, so that suppliers remain efficient. This integration model supports a great deal of corporate decision-making because of the effectiveness and the complication of this model, for exactly choosing the most suitable supplier. The ranking list of 25 DMUs as shown in Table 14.
The optimal weights and the slacks for each DMU using nine DEA models (CCR, BCC, and SBM, Super SBM) are shown from Table A1, Table A2, Table A3, Table A4, Table A5, Table A6, Table A7, Table A8, Table A9, Table A10, Table A11, Table A12, Table A13, Table A14, Table A15, Table A16, Table A17 and Table A18 in appendix section.

5. Conclusions

Many studies have applied the MCDM approach to various fields of science and engineering, and their numbers have been increasing over the past years. The fuzzy MCDM model has been applied to supplier selection problems. Although some studies have considered a review of applications of MCDM approaches in this field, little work has focused on this problem in a fuzzy environment. This is a reason why hybrid ANP with fuzzy logic and DEA is proposed in this study.
Initially, we proposed the ANP model combined with a fuzzy set, to evaluate supplier selection criteria and define a priority of each supplier, which are able to be utilized to clarify important criteria that directly affect the profitability of the business. The FANP can be used for ranking suppliers but the number of supplier selections is practically limited because of the number of pairwise comparisons that need to be made, and a disadvantage of the FANP approach is that input data, expressed in linguistic terms, depend on the experience of decision-makers and, thus, involves subjectivity. This is a reason why several DEA models are proposed for ranking suppliers in the final stage. The DEA model can handle hundreds of suppliers with multiple inputs and outputs for the best supplier rating. The FANP-DEA integration model supports a great deal of corporate decision-making because of the effectiveness and complication of this model, for exactly choosing the most suitable supplier. Finally, this research will provide a potential suppliers list, which has a conditioned response to the enterprises’ supply requirements.
The main contribution of this research is to develop complete approaches for supplier evaluation and selection of the rice supply chain as a typical example. This is a useful proposed model on an academic and practical front. The FANP-DEA method not only provides reasonable results but also allows the decision-maker to visualize the impact of different criteria in the final result. Furthermore, this integrated model may offer valuable insights, as well as provide methods for other sectors to select and evaluate suppliers. This model can also be applied to many different industries for future research directions.
For improving these MCDM model, outlier detection and the curse of dimensionality of the DEA model will be considered in future research. Moreover, different methodologies, such as the preference ranking organization method for enrichment of evaluations (PROMETHEE), fuzzy data envelopment analysis (FDEA), etc., can also been combined for different scenarios.

Author Contributions

In this research, C.-N.W. contributed to generating the research ideas and designing the theoretical verifications, and reviewed the manuscript; V.T.N. contributed the research ideas, designed the framework, collected data, analyzed the data, and summarized and wrote the manuscript; D.H.D. collected data, analyzed the data, wrote the manuscript; and H.T.D. wrote and formatted the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. The optimal weights for each DMU using the CCR-I model.
Table A1. The optimal weights for each DMU using the CCR-I model.
DMUScoreRankV (1)V (2)V (3)U (1)U (2)U (3)
DMU 1110.31244601.25 × 10 3 4.57 × 10 2 01.41 × 10 2
DMU 20.4245259.96 × 10 2 1.25 × 10 3 2.05 × 10 3 01.68 × 10 2 0
DMU 30.5329230.1210821.51 × 10 3 2.49 × 10 4 02.05 × 10 2 0
DMU 40.48762402.12 × 10 3 7.97 × 10 3 00.0212460
DMU 5117.31 × 10 3 4.55 × 10 3 05.74 × 10 2 01.76 × 10 2
DMU 60.6428220.1240621.57 × 10 3 2.79 × 10 4 6.24 × 10 4 2.11 × 10 2 0
DMU 70.9708902.02 × 10 3 7.59 × 10 3 02.02 × 10 2 0
DMU 80.79210.1058651.37 × 10 3 02.51 × 10 3 1.78 × 10 2 0
DMU 90.7934200.333333000.106561.37 × 10 2 0
DMU 10110.30364102.97 × 10 3 0.0971771.41 × 10 2 1.34 × 10 3
DMU 110.952911003.33 × 10 2 0.1862936.31 × 10 3 0
DMU 12110.1363881.71 × 10 3 002.27 × 10 2 0
DMU 130.8941130.1188191.54 × 10 3 02.82 × 10 3 2.00 × 10 2 0
DMU 140.8845168.30 × 10 2 01.67 × 10 2 0.1397194.74 × 10 3 0
DMU 150.8357191.53 × 10 2 2.29 × 10 3 2.72 × 10 3 2.77 × 10 2 1.64 × 10 2 0
DMU 16110.1127671.49 × 10 3 6.21 × 10 4 02.00 × 10 2 0
DMU 170.9683108.09 × 10 2 2.11 × 10 3 02.32 × 10 2 1.88 × 10 2 0
DMU 180.8581802.33 × 10 3 3.91 × 10 3 2.59 × 10 2 1.67 × 10 2 0
DMU 191103.18 × 10 3 00.13481100
DMU 200.89671202.44 × 10 3 4.10 × 10 3 2.71 × 10 2 1.75 × 10 2 0
DMU 210.89091402.53 × 10 3 4.25 × 10 3 2.81 × 10 2 0.0181090
DMU 22110.25000.14570700
DMU 231101.20 × 10 4 1.92 × 10 2 0.108724.31 × 10 3 0
DMU 240.8906151.85 × 10 3 2.69 × 10 3 03.52 × 10 2 4.82 × 10 3 7.86 × 10 3
DMU 250.87051702.36 × 10 3 3.96 × 10 3 2.62 × 10 2 1.69 × 10 2 0
Table A2. The slacks for each DMU using the CCR-I model.
Table A2. The slacks for each DMU using the CCR-I model.
DMUScoreRankLTUPPCQBNIRE
DMU 111000000
DMU 20.4245250000.01200.001
DMU 30.5329230000.55800.006
DMU 40.4876240.064000.53103.114
DMU 511000000
DMU 60.642822000000.275
DMU 70.970890.995002.58802.98
DMU 80.7921002.474000.221
DMU 90.793420019.8262.518000.001
DMU 1011000000
DMU 110.9529111.90669.610003.945
DMU 1211000000
DMU 130.894113003.512004.416
DMU 140.884516016.8960001.959
DMU 150.835719000000.231
DMU 1611000000
DMU 170.9683100022.934001.983
DMU 180.858180.22200003.722
DMU 1911000000
DMU 200.8967120.03400006.509
DMU 210.8909140.48900003.554
DMU 2211000000
DMU 2311000000
DMU 240.8906150013.043000
DMU 250.8705170.11600002.629
Table A3. The optimal weights for each DMU using the CCR-O model.
Table A3. The optimal weights for each DMU using the CCR-O model.
DMUScoreRankV (1)V (2)V (3)U (1)U (2)U (3)
DMU 1110.2193769.79 × 10 4 3.76 × 10 5 02.27 × 10 2 0
DMU 20.4245250.2346782.93 × 10 3 4.82 × 10 4 03.97 × 10 2 0
DMU 30.5329230.2271952.84 × 10 3 4.66 × 10 4 03.84 × 10 2 0
DMU 40.48762404.35 × 10 3 1.63 × 10 2 04.36 × 10 2 0
DMU 5119.80 × 10 2 2.85 × 10 3 0001.87 × 10 2
DMU 60.6428220.1930112.44 × 10 3 4.34 × 10 4 9.71 × 10 4 3.28 × 10 2 0
DMU 70.9708902.08 × 10 3 7.82 × 10 3 02.08 × 10 2 0
DMU 80.79210.1340061.74 × 10 3 03.18 × 10 3 2.26 × 10 2 0
DMU 90.7934200.420146000.1343121.73 × 10 2 0
DMU 10110.33333300001.69 × 10 2
DMU 110.952911003.50 × 10 2 0.1954976.63 × 10 3 0
DMU 12110.1363881.71 × 10 3 002.27 × 10 2 0
DMU 130.8941130.1328861.72 × 10 3 03.16 × 10 3 2.24 × 10 2 0
DMU 140.884516002.83 × 10 2 0.1579595.35 × 10 3 0
DMU 150.8357191.83 × 10 2 2.74 × 10 3 3.26 × 10 3 0.0331781.97 × 10 2 0
DMU 16110.1169631.52 × 10 3 02.78 × 10 3 1.97 × 10 2 0
DMU 170.9683108.36 × 10 2 2.18 × 10 3 02.40 × 10 2 1.94 × 10 2 0
DMU 180.8581802.72 × 10 3 4.56 × 10 3 3.02 × 10 2 1.94 × 10 2 0
DMU 191103.18 × 10 3 00.13481100
DMU 200.89671202.72 × 10 3 4.57 × 10 3 3.02 × 10 2 0.0194680
DMU 210.89091402.84 × 10 3 4.77 × 10 3 3.16 × 10 2 2.03 × 10 2 0
DMU 22118.23 × 10 2 2.15 × 10 3 02.36 × 10 2 1.91 × 10 2 0
DMU 23116.40 × 10 2 1.37 × 10 4 1.27 × 10 2 0.11455602.49 × 10 3
DMU 240.8906152.08 × 10 2 3.02 × 10 3 03.96 × 10 2 5.41 × 10 3 8.82 × 10 3
DMU 250.87051702.71 × 10 3 4.54 × 10 3 3.01 × 10 2 1.94 × 10 2 0
Table A4. The slacks for each DMU using the CCR-O model.
Table A4. The slacks for each DMU using the CCR-O model.
No.DMUScoreRankLTUPPCQBNIRE
1DMU 111000000
2DMU 20.4245250000.02900.002
3DMU 30.5329230001.04700.012
4DMU 40.4876240.131001.0906.387
5DMU 511000000
6DMU 60.642822000000.428
7DMU 70.970891.025002.66503.07
8DMU 80.7921003.132000.279
9DMU 90.793420024.9893.174000.002
10DMU 1011000000
11DMU 110.952911273.0490004.14
12DMU 1211000000
13DMU 130.894113003.928004.939
14DMU 140.884516019.1020002.214
15DMU 150.835719000000.277
16DMU 1611000000
17DMU 170.9683100023.686002.048
18DMU 180.858180.25900004.338
19DMU 1911000000
20DMU 200.8967120.03700007.259
21DMU 210.8909140.54900003.989
22DMU 2211000000
23DMU 2311000000
24DMU 240.8906150014.645000
25DMU 250.8705170.13300003.019
Table A5. The optimal weights for each DMU using the BBC-I model.
Table A5. The optimal weights for each DMU using the BBC-I model.
DMUScoreRankV (1)V (2)V (3)U (0)U (1)U (2)U (3)
DMU 1110.3333330009.02 × 10 2 01.13 × 10 2
DMU 20.7047250.1206089.27 × 10 4 4.87 × 10 4 0.7047000
DMU 30.8647220.1480011.14 × 10 3 5.97 × 10 4 0.8647000
DMU 40.9274152.67 × 10 2 1.57 × 10 3 9.71 × 10 3 0.9274000
DMU 51104.68 × 10 3 005.84 × 10 2 01.76 × 10 2
DMU 60.8847200.1514111.16 × 10 3 6.11 × 10 4 0.8847000
DMU 70.97921201.81 × 10 3 9.41 × 10 3 0.236401.55 × 10 2 0
DMU 80.792240.1064131.36 × 10 3 00.0377201.88 × 10 2 0
DMU 9110.1654861.47 × 10 3 00.96361.12 × 10 2 00
DMU 10110.1326331.68 × 10 3 2.98 × 10 4 06.68 × 10 4 2.25 × 10 2 0
DMU 1111003.33 × 10 2 0.14480.1796714.14 × 10 3 0
DMU 12110.2447537.67 × 10 4 0003.06 × 10 3 1.47 × 10 2
DMU 130.9087160.107881.53 × 10 3 9.40 × 10 4 0.2971.77 × 10 2 1.23 × 10 2 0
DMU 14114.61 × 10 2 7.35 × 10 4 1.46 × 10 2 0.56768.40 × 10 2 00
DMU 150.8389230.0176212.74 × 10 3 00.349733.02 × 10 2 2.44 × 10 2 0
DMU 16117.04 × 10 2 2.05 × 10 3 00001.35 × 10 2
DMU 170.9747130.1153651.68 × 10 3 00.20371.85 × 10 2 1.49 × 10 2 0
DMU 180.88112101.76 × 10 3 7.86 × 10 3 0.51742.40 × 10 2 5.68 × 10 3 0
DMU 191103.18 × 10 3 000.13481100
DMU 200.9679141.71 × 10 2 1.79 × 10 3 7.96 × 10 3 0.64040.0272254.53 × 10 3 0
DMU 210.89981801.87 × 10 3 0.0083560.55012.55 × 10 2 6.04 × 10 3 0
DMU 22117.72 × 10 2 2.21 × 10 3 000.14570700
DMU 2311002.00 × 10 2 00.11719902.15 × 10 3
DMU 240.8989192.05 × 10 2 2.66 × 10 3 00.60470.0448500
DMU 250.9038171.23 × 10 2 1.68 × 10 3 7.35 × 10 3 0.57342.54 × 10 2 4.40 × 10 3 0
Table A6. The slacks for each DMU using the BCC-I model.
Table A6. The slacks for each DMU using the BCC-I model.
DMUScoreRankLTUPPCQBNIRE
DMU 111000000
DMU 20.7047250000.71711.73615.648
DMU 30.8647220001.33113.96218.622
DMU 40.9274150000.7417.79323.721
DMU 511000000
DMU 60.8847200000.3819.55112.733
DMU 70.9792121.076002.02101.311
DMU 80.79224008.4790.78202.928
DMU 91100000.0010.001
DMU 1011000000
DMU 111100.0020000
DMU 1211000000
DMU 130.908716000001.281
DMU 141100000.0010.001
DMU 150.838923001.157000.626
DMU 1611000000
DMU 170.9747130019.705000.379
DMU 180.8811210.03300002.897
DMU 1911000000
DMU 200.967914000002.287
DMU 210.8998180.42400003.248
DMU 2211000000
DMU 2311000000
DMU 240.8989190012.92300.5460.724
DMU 250.903817000001.467
Table A7. The optimal weights for each DMU using the BBC-O model.
Table A7. The optimal weights for each DMU using the BBC-O model.
DMUScoreRankV (0)V (1)V (2)V (3)U (1)U (2)U (3)
DMU 11100.333333000.1065782.16 × 10 3 8.66 × 10 3
DMU 20.504241.9841300003.97 × 10 2 0
DMU 30.5349230.07690.2169382.78 × 10 3 003.84 × 10 2 0
DMU 40.492825-0.665805.08 × 10 3 2.65 × 10 2 04.36 × 10 2 0
DMU 511002.49 × 10 3 9.37 × 10 3 02.50 × 10 2 0
DMU 60.6448220.065730.1854482.38 × 10 3 003.28 × 10 2 0
DMU 70.972712-0.318302.43 × 10 3 1.27 × 10 2 02.08 × 10 2 0
DMU 80.8909200.5584601.64 × 10 3 002.27 × 10 2 0
DMU 90.999711-26.4354.5400954.02 × 10 2 00.30863200
DMU 101100.1335271.67 × 10 3 2.74 × 10 4 02.26 × 10 2 0
DMU 1111-0.1694003.90 × 10 2 0.21014.84 × 10 3 0
DMU 121100.2425627.86 × 10 4 002.27 × 10 2 0
DMU 130.8958180.045370.1279891.64 × 10 3 002.27 × 10 2 0
DMU 1411-1.31280.1066911.70 × 10 3 3.38 × 10 2 0.19423500
DMU 150.8909200.3899502.20 × 10 3 02.11 × 10 2 2.10 × 10 2 0
DMU 1611002.81 × 10 3 3.35 × 10 4 3.48 × 10 2 01.09 × 10 2
DMU 170.96831300.0835822.18 × 10 3 02.40 × 10 2 1.94 × 10 2 0
DMU 180.8911190.3807702.15 × 10 3 02.06 × 10 2 2.05 × 10 2 0
DMU 1911001.92 × 10 4 0.0187920.13481100
DMU 200.910616-1.95545.23 × 10 2 5.47 × 10 3 0.024318.31 × 10 2 1.38 × 10 2 0
DMU 210.9374150.5569401.64 × 10 3 002.27 × 10 2 0
DMU 221107.72 × 10 2 2.21 × 10 3 00.14570700
DMU 231106.11 × 10 2 1.20 × 10 4 1.31 × 10 2 0.108724.31 × 10 3 0
DMU 240.9456141.057470004.77 × 10 2 1.59 × 10 2 0
DMU 250.8987171.112660005.02 × 10 2 1.68 × 10 2 0
Table A8. The slacks for each DMU using the BCC-O model.
Table A8. The slacks for each DMU using the BCC-O model.
DMUScoreRankLTUPPCQBNIRE
DMU 111000000
DMU 20.50424140.546302.79207.633
DMU 30.534923008.6523.32106.618
DMU 40.4928250.219000.38704.289
DMU 511000000
DMU 60.644822007.2111.7305.505
DMU 70.9727121.042002.52902.679
DMU 80.8909201029.4172.94707.185
DMU 90.99971100000.0140.018
DMU 1011000000
DMU 111100.0030000
DMU 1211000000
DMU 130.895818009.2490.64107.057
DMU 141100000.0010.002
DMU 150.8909200.883017.796005.95
DMU 1611000000
DMU 170.9683130023.686002.048
DMU 180.8911190.99109.472007.238
DMU 1911000000
DMU 200.910616000006.369
DMU 210.937415107.0810.69405.413
DMU 2211000000
DMU 2311000000
DMU 240.9456140.24614.50622.457001.871
DMU 250.8987170.6352.6426.353004.847
Table A9. The optimal weights for each DMU using the SBM-I-C model.
Table A9. The optimal weights for each DMU using the SBM-I-C model.
DMUScoreRankV (1)V (2)V (3)U (1)U (2)U (3)
DMU 11115.134169.60 × 10 4 6.67 × 10 3 0.58315200.747719
DMU 20.3666256.67 × 10 2 8.52 × 10 4 4.76 × 10 3 09.58 × 10 3 3.73 × 10 3
DMU 30.4732238.33 × 10 2 1.00 × 10 3 6.67 × 10 3 01.82 × 10 2 0
DMU 40.4537248.33 × 10 2 1.04 × 10 3 8.33 × 10 3 2.58 × 10 2 1.78 × 10 2 0
DMU 5118.33 × 10 2 6.08 × 10 3 6.67 × 10 3 003.68 × 10 2
DMU 60.569228.33 × 10 2 1.07 × 10 3 6.67 × 10 3 01.17 × 10 2 5.22 × 10 3
DMU 70.893496.67 × 10 2 1.88 × 10 3 8.33 × 10 3 02.52 × 10 2 0
DMU 80.6873206.67 × 10 2 1.43 × 10 3 4.76 × 10 3 01.92 × 10 2 0
DMU 90.6775210.1111119.70 × 10 4 6.67 × 10 3 3.08 × 10 2 1.77 × 10 2 0
DMU 10110.1111119.41 × 10 4 5.47904610.578181.5777781.061762
DMU 110.7471186.67 × 10 2 1.04 × 10 3 1.11 × 10 2 9.77 × 10 2 1.09 × 10 2 0
DMU 120.9036817.935970.1116464.76 × 10 3 01.1111110.747719
DMU 130.8148138.33 × 10 2 9.79 × 10 4 6.67 × 10 3 2.21 × 10 2 1.65 × 10 2 0
DMU 140.8334128.33 × 10 2 1.06 × 10 3 8.33 × 10 3 0.0816911.18 × 10 2 0
DMU 150.7229196.67 × 10 2 1.00 × 10 3 5.56 × 10 3 1.30 × 10 2 1.54 × 10 2 0
DMU 16118.33 × 10 2 9.50 × 10 4 3.5758277.9336350.8239440.796321
DMU 170.8534118.33 × 10 2 1.04 × 10 3 4.69 × 10 3 5.55 × 10 2 0.0116730
DMU 180.7683176.67 × 10 2 9.67 × 10 4 6.67 × 10 3 1.7 × 10 2 1.56 × 10 2 0
DMU 19116.67 × 10 2 0.2808936.67 × 10 3 6.3469080.9466670
DMU 200.8856108.33 × 10 2 9.74 × 10 4 8.33 × 10 3 2.73 × 10 2 1.72 × 10 2 0
DMU 210.8027156.67 × 10 2 1.67 × 10 3 6.67 × 10 3 02.24 × 10 2 0
DMU 22113.7410931.07 × 10 3 0.7052146.34690800.119497
DMU 23116.67 × 10 2 9.75 × 10 4 8.86 × 10 2 0.68323800
DMU 240.789166.67 × 10 2 9.87 × 10 4 4.76 × 10 3 5.19 × 10 2 0.01040
DMU 250.8106146.67 × 10 2 9.80 × 10 4 6.67 × 10 3 6.56 × 10 2 1.04 × 10 2 0
Table A10. The slacks for each DMU using the SBM-I-C model.
Table A10. The slacks for each DMU using the SBM-I-C model.
DMUScoreRankLTUPPCQBNIRE
DMU 111000000
DMU 20.3666253.293189.98752.9290.40100
DMU 30.4732232.237124.28932.3680.97900.005
DMU 40.4537242.393142.19423.93000.652
DMU 511000000
DMU 60.569221.93769.16629.3730.50600
DMU 70.893491.26602.6592.32401.809
DMU 80.6873201.903039.0311.41401.419
DMU 90.6775210.486105.98824.86003.722
DMU 1011000000
DMU 110.7471182.27889.210.732003.636
DMU 120.903680020.2380.81200
DMU 130.8148130.71611.39217.161003.672
DMU 140.8334120.89567.6052.466000.982
DMU 150.7229191.5729.52325.705006.417
DMU 1611000000
DMU 170.8534110.178.52426.32002.441
DMU 180.7683171.50432.31515.037006.328
DMU 1911000000
DMU 200.8856100.50930.415.088006.305
DMU 210.8027151.48014.81.53406.598
DMU 2211000000
DMU 2311000000
DMU 240.789161.11631.37822.191000.565
DMU 250.8106141.35836.4979.463003.803
Table A11. The optimal weights for each DMU using the SBM-O-C model.
Table A11. The optimal weights for each DMU using the SBM-O-C model.
DMUScoreRankV (1)V (2)V (3)U (1)U (2)U (3)
DMU 111272.1957007.0064457.57 × 10 3 13.45895
DMU 20.2795240.715473000.2476661.32 × 10 2 9.92 × 10 3
DMU 30.2564250.975128000.4043841.28 × 10 2 9.61 × 10 3
DMU 40.40892304.22 × 10 3 2.72 × 10 2 0.1892761.45 × 10 2 1.09 × 10 2
DMU 51102.67 × 10 2 00.3325688.32 × 10 3 9.42 × 10 2
DMU 60.4189220.47761709.54 × 10 3 0.2077231.09 × 10 2 8.21 × 10 3
DMU 70.71042001.74 × 10 3 2.01 × 10 2 0.129466.94 × 10 3 4.89 × 10 3
DMU 80.4919210.0877464.65 × 10 3 00.1658797.57 × 10 3 5.68 × 10 3
DMU 90.7822180.3568976.04 × 10 4 00.1028771.02 × 10 2 7.65 × 10 3
DMU 10110069.73439134.08962013.45895
DMU 110.870911003.94 × 10 2 9.18 × 10 2 1.02 × 10 2 7.63 × 10 3
DMU 1211405.57841.32041801.2200842013.45895
DMU 130.8021140.270064.89 × 10 4 00.0829317.56 × 10 3 5.67 × 10 3
DMU 140.7971153.51 × 10 2 3.06 × 10 3 3.77 × 10 3 6.47 × 10 2 9.56 × 10 3 7.17 × 10 3
DMU 150.7845173.77 × 10 2 3.27 × 10 3 07.15 × 10 2 7.75 × 10 3 5.81 × 10 3
DMU 16110060.44946134.089613.7108213.45895
DMU 170.951890.1399041.53 × 10 3 00.0544327.57 × 10 3 5.68 × 10 3
DMU 180.7918163.88 × 10 2 2.32 × 10 3 5.36 × 10 3 7.07 × 10 2 7.56 × 10 3 5.67 × 10 3
DMU 191105.9802670134.0896205.66 × 10 3
DMU 200.857123.88 × 10 2 2.33 × 10 3 5.37 × 10 3 7.09 × 10 2 7.57 × 10 3 5.67 × 10 3
DMU 210.71521909.07 × 10 3 1.29 × 10 2 0.1025745.44 × 10 2 5.66 × 10 3
DMU 221179.70503014.9138134.08967.59 × 10 3 2.457001
DMU 231105.24 × 10 4 7.74 × 10 2 0.4536767.59 × 10 3 5.69 × 10 3
DMU 240.8857102.68 × 10 2 2.95 × 10 3 05.08 × 10 2 7.73 × 10 3 5.80 × 10 3
DMU 250.838133.27 × 10 2 2.44 × 10 3 3.98 × 10 3 6.01 × 10 2 7.75 × 10 3 5.81 × 10 3
Table A12. The slacks for each DMU using the SBM-O-C model.
Table A12. The slacks for each DMU using the SBM-O-C model.
DMUScoreRankLTUPPCQBNIRE
DMU 111000000
DMU 20.27952400.957.57.23329.71239.612
DMU 30.25642502006.03917.923.87
DMU 40.4089230003.8422.7235.674
DMU 511000000
DMU 60.41892200.205.25813.4817.97
DMU 70.7104201002.9141.1754.571
DMU 80.4919210015.2815.8474.1835.569
DMU 90.782218000.880.49811.04314.979
DMU 1011000000
DMU 110.870911248.724005.33212.325
DMU 1211000000
DMU 130.802114007.3251.8184.25611.262
DMU 140.7971150000.4849.8418.013
DMU 150.784517006.9973.0363.7154.948
DMU 1611000000
DMU 170.951890022.9740.4631.1182.995
DMU 180.7918160002.5624.5328.386
DMU 1911000000
DMU 200.857120000.7994.67313.202
DMU 210.7152190.044003.87700.095
DMU 2211000000
DMU 2311000000
DMU 240.8857100016.1471.2154.3575.804
DMU 250.838130001.7444.978.617
Table A13. The optimal weights for each DMU using the Super SBM-I-C model.
Table A13. The optimal weights for each DMU using the Super SBM-I-C model.
No.DMUScoreRankV (1)V (2)V (3)U (1)U (2)U (3)
1DMU 11115.134169.60 x 10 4 6.67 x 10 3 0.58315200.747719
2DMU 20.3666256.67 × 10 2 8.52 × 10 4 4.76 × 10 3 09.58 × 10 3 3.73 × 10 3
3DMU 30.4732238.33 × 10 2 1.00 × 10 3 6.67 × 10 3 01.82 × 10 2 0
4DMU 40.4537248.33 × 10 2 1.04 × 10 3 8.33 × 10 3 2.58 × 10 2 1.78 × 10 2 0
5DMU 5118.33 × 10 2 6.08 × 10 3 6.67 × 10 3 003.68 × 10 2
6DMU 60.569228.33 × 10 2 1.07 × 10 3 6.67 × 10 3 01.17 × 10 2 5.22 × 10 3
7DMU 70.893496.67 × 10 2 1.88 × 10 3 8.33 × 10 3 02.52 × 10 2 0
8DMU 80.6873206.67 × 10 2 1.43 × 10 3 4.76 × 10 3 01.92 × 10 2 0
9DMU 90.6775210.1111119.70 × 10 4 6.67 × 10 3 3.08 × 10 2 1.77 × 10 2 0
10DMU 10110.1111119.41 × 10 4 5.47904610.578181.5777781.061762
11DMU 110.7471186.67 × 10 2 1.04 × 10 3 1.11 × 10 2 9.77 × 10 2 1.09 × 10 2 0
12DMU 120.9036817.935970.1116464.76 × 10 3 01.1111110.747719
13DMU 130.8148138.33 × 10 2 9.79 × 10 4 6.67 × 10 3 2.21 × 10 2 1.65 × 10 2 0
14DMU 140.8334128.33 × 10 2 1.06 × 10 3 8.33 × 10 3 0.0816911.18 × 10 2 0
15DMU 150.7229196.67 × 10 2 1.00 × 10 3 5.56 × 10 3 1.30 × 10 2 1.54 × 10 2 0
16DMU 16118.33 × 10 2 9.50 × 10 4 3.5758277.9336350.8239440.796321
17DMU 170.8534118.33 × 10 2 1.04 × 10 3 4.69 × 10 3 5.55 × 10 2 0.0116730
18DMU 180.7683176.67 × 10 2 9.67 × 10 4 6.67 × 10 3 1.73 × 10 2 1.56 × 10 2 0
19DMU 19116.67 × 10 2 0.2808936.67 × 10 3 6.3469080.9466670
20DMU 200.8856108.33 × 10 2 9.74 × 10 4 8.33 × 10 3 2.73 × 10 2 1.72 × 10 2 0
21DMU 210.8027156.67 × 10 2 1.67 × 10 3 6.67 × 10 3 02.24 × 10 2 0
22DMU 22113.7410931.07 × 10 3 0.7052146.34690800.119497
23DMU 23116.67 × 10 2 9.75 × 10 4 8.86 × 10 2 0.68323800
24DMU 240.789166.67 × 10 2 9.87 × 10 4 4.76 × 10 3 5.19 × 10 2 0.01040
25DMU 250.8106146.67 × 10 2 9.80 × 10 4 6.67 × 10 3 6.56 × 10 2 1.04 × 10 2 0
Table A14. The slacks for each DMU using the Super SBM-I-C model.
Table A14. The slacks for each DMU using the Super SBM-I-C model.
No.DMUScoreRankLTUPPCQBNIRE
1DMU 111000000
2DMU 20.3666253.293189.98752.9290.40100
3DMU 30.4732232.237124.28932.3680.97900.005
4DMU 40.4537242.393142.19423.93000.652
5DMU 511000000
6DMU 60.569221.93769.16629.3730.50600
7DMU 70.893491.26602.6592.32401.809
8DMU 80.6873201.903039.0311.41401.419
9DMU 90.6775210.486105.98824.86003.722
10DMU 1011000000
11DMU 110.7471182.27889.210.732003.636
12DMU 120.903680020.2380.81200
13DMU 130.8148130.71611.39217.161003.672
14DMU 140.8334120.89567.6052.466000.982
15DMU 150.7229191.5729.52325.705006.417
16DMU 1611000000
17DMU 170.8534110.178.52426.32002.441
18DMU 180.7683171.50432.31515.037006.328
19DMU 1911000000
20DMU 200.8856100.50930.415.088006.305
21DMU 210.8027151.48014.81.53406.598
22DMU 2211000000
23DMU 2311000000
24DMU 240.789161.11631.37822.191000.565
25DMU 250.8106141.35836.4979.463003.803
Table A15. The optimal weights for each DMU using the SBM-AR-C model.
Table A15. The optimal weights for each DMU using the SBM-AR-C model.
No.DMUScoreV (1) LTV (2) UPV (3) PCU (1) QBU (2) NIU (3) RE
1DMU 110.77748389.60 × 10 4 6.67 × 10 3 0.21392254.25 × 10 2 5.68 × 10 3
2DMU 20.2693266.67× 10 2 8.52 × 10 4 4.76 × 10 3 6.67 × 10 2 3.56 × 10 3 2.67 × 10 3
3DMU 30.2512358.33 × 10 2 1.00 × 10 3 6.67 × 10 3 0.10159513.22 × 10 3 2.41 × 10 3
4DMU 40.4010498.33 × 10 2 1.04 × 10 3 8.33 × 10 3 7.59 × 10 2 5.82 × 10 3 4.37 × 10 3
5DMU 518.33 × 10 2 9.26 × 10 2 6.67 × 10 3 1.15631988.32 × 10 3 0.3546177
6DMU 60.4187788.33 × 10 2 1.07 × 10 3 6.67 × 10 3 8.70 × 10 2 4.58 × 10 3 3.44 × 10 3
7DMU 70.6622416.67 × 10 2 9.65 × 10 4 8.33 × 10 3 8.57 × 10 2 4.60 × 10 3 3.24 × 10 3
8DMU 80.4482516.67 × 10 2 9.72 × 10 4 4.76 × 10 3 7.44 × 10 2 3.39 × 10 3 2.55 × 10 3
9DMU 90.6413020.11111119.70 × 10 4 6.67 × 10 3 6.60 × 10 2 6.54 × 10 3 4.90 × 10 3
10DMU 1011.20310179.41 × 10 4 1.11 × 10 2 0.35877266.42 × 10 2 5.64 × 10 3
11DMU 110.7036436.67 × 10 2 1.04 × 10 3 1.11 × 10 2 0.05857847.16 × 10 3 5.37 × 10 3
12DMU 12166.7423320.25303474.76 × 10 3 0.11438646.53156735.68 × 10 3
13DMU 130.7536828.33 × 10 2 9.79 × 10 4 6.67 × 10 3 6.25 × 10 2 5.69 × 10 3 4.27 × 10 3
14DMU 140.7711378.33 × 10 2 1.90 × 10 3 8.33 × 10 3 0.10133097.37 × 10 3 5.53 × 10 3
15DMU 150.6949236.67 × 10 2 1.00 × 10 3 5.56 × 10 3 4.97 × 10 2 5.38 × 10 3 4.04 × 10 3
16DMU 1618.33 × 10 2 9.50 × 10 4 8.33 × 10 3 6.10 × 10 2 6.67 × 10 3 4.49 × 10 3
17DMU 170.8375078.33 × 10 2 1.55 × 10 3 4.69 × 10 3 7.19 × 10 2 6.34 × 10 3 4.76 × 10 3
18DMU 180.736346.67 × 10 2 9.67 × 10 4 6.67 × 10 3 5.21 × 10 2 5.56 × 10 3 4.17 × 10 3
19DMU 1916.67 × 10 2 4.73 × 10 3 6.67 × 10 3 0.12304227.55 × 10 3 1.54 × 10 2
20DMU 200.8495818.33 × 10 2 9.74 × 10 4 8.33 × 10 3 6.02 × 10 2 6.43 × 10 3 4.82 × 10 3
21DMU 210.6695866.67 × 10 2 1.07 × 10 3 6.67 × 10 3 6.87 × 10 2 5.06 × 10 3 3.79 × 10 3
22DMU 2218.33 × 10 2 1.98 × 10 3 6.67 × 10 3 9.00 × 10 2 7.59 × 10 3 0.0056912
23DMU 2310.4287329.75E-047.86 × 10 2 0.76978597.59 × 10 3 5.69 × 10 3
24DMU 240.7690976.67 × 10 2 1.54 × 10 3 4.76 × 10 3 6.75 × 10 2 5.95 × 10 3 4.46 × 10 3
25DMU 250.7726966.67 × 10 2 1.55 × 10 3 6.67 × 10 3 8.13 × 10 2 5.99 × 10 3 4.49 × 10 3
Table A16. The slacks for each DMU using the SBM-AR-C model.
Table A16. The slacks for each DMU using the SBM-AR-C model.
No.DMUScoreExcessExcessExcessShortageShortageShortage
LTUPPCQBNIRE
S−(1)S−(2)S−(3)S+(1)S+(2)S+(3)
1DMU 11000000
2DMU 20.26932600.957.57.23297529.712539.6125
3DMU 30.25123502006.038817.923.87
4DMU 40.4010490.335138203.3513823.243543622.8607737.47481
5DMU 51000000
6DMU 60.41877800.205.258413.4817.97
7DMU 70.6622411.168.4361.62.66900803.128
8DMU 80.4482510.609475015.118445.5236534.188945.578262
9DMU 90.6413020.384114.111423.840.332244204.9922
10DMU 101000000
11DMU 110.703643256.92509.27x 10 2 4.7212.025
12DMU 121000000
13DMU 130.7536820.470430.9658414.7040.800533506.73232
14DMU 140.7711370.355088902.33015409.94040319.28401
15DMU 150.6949231.2108863022.108860.5139194.34392113.02279
16DMU 161000000
17DMU 170.8375070.1015444026.3032301.2533824.748504
18DMU 180.736341.470434.9658414.7040.108433506.74232
19DMU 191000000
20DMU 200.8495819.80E-0200.9803360.62452774.7145813.72903
21DMU 210.6695861.4571103014.57111.58838160.1361216.949176
22DMU 221000000
23DMU 231000000
24DMU 240.7690970.8652768022.1284604.6137849.059744
25DMU 250.7726961.066957409.39005305.36636213.68358
Table A17. The optimal weights for each DMU using the SBM-AR-V model.
Table A17. The optimal weights for each DMU using the SBM-AR-V model.
No.DMUScoreV (1) LTV (2) UPV (3) PCU (1) QBU (2) NIU (3) RE
1DMU 112.20558472.40 × 10 2 6.67 × 10 3 8.96 × 10 2 0.33180295.68E-03
2DMU 20.2693266.67 × 10 2 8.52 × 10 4 4.76 × 10 3 6.67 × 10 2 3.56 × 10 3 2.67 × 10 3
3DMU 30.2512358.33 × 10 2 1.00 × 10 3 6.67 × 10 3 0.10159513.22 × 10 3 2.41 × 10 3
4DMU 40.456798.33 × 10 2 5.91 × 10 3 2.56 × 10 2 8.65 × 10 2 6.63 × 10 3 4.98 × 10 3
5DMU 510.17636212.58 × 10 2 6.67 × 10 3 0.33256847.64 × 10 2 5.90 × 10 2
6DMU 60.4187788.33 × 10 2 1.07 × 10 3 6.67 × 10 3 8.70 × 10 2 4.58 × 10 3 3.44 × 10 3
7DMU 70.6774946.67 × 10 2 4.83 × 10 3 2.28 × 10 2 8.77 × 10 2 4.70 × 10 3 3.31 × 10 3
8DMU 80.4485566.67 × 10 2 9.72 × 10 4 4.76 × 10 3 7.44 × 10 2 8.89 × 10 3 2.55 × 10 3
9DMU 90.9994539.78081867.58 × 10 2 6.67 × 10 3 0.10282121.02 × 10 2 7.64 × 10 3
10DMU 1010.11111119.41 × 10 4 8.65 × 10 2 0.10862367.53 × 10 3 4.40 × 10 2
11DMU 1116.67 × 10 2 1.04 × 10 3 9.61 × 10 2 0.35502341.02 × 10 2 7.63 × 10 3
12DMU 12117.0380470.21700564.76 × 10 3 0.11438642.92865395.68 × 10 3
13DMU 130.7629438.33 × 10 2 2.10 × 10 3 6.67 × 10 3 6.33 × 10 2 5.76 × 10 3 4.32 × 10 3
14DMU 1410.22441871.37 × 10 2 5.83 × 10 2 0.21808159.56 × 10 3 7.17 × 10 3
15DMU 150.7124746.67 × 10 2 2.15 × 10 3 5.56 × 10 3 5.10 × 10 2 5.52 × 10 3 4.14 × 10 3
16DMU 1618.33 × 10 2 9.50 × 10 4 8.33 × 10 3 6.10 × 10 2 6.67 × 10 3 4.49 × 10 3
17DMU 170.8491098.33 × 10 2 2.52 × 10 3 4.69 × 10 3 4.62 × 10 2 6.43 × 10 3 4.82 × 10 3
18DMU 180.7440866.67 × 10 2 2.43 × 10 3 6.67 × 10 3 5.26 × 10 2 5.62 × 10 3 4.22 × 10 3
19DMU 1916.67 × 10 2 4.73 × 10 3 6.67 × 10 3 0.12304227.55 × 10 3 1.54 × 10 2
20DMU 200.8762998.33 × 10 2 4.66 × 10 3 1.94 × 10 2 6.21 × 10 2 6.63 × 10 3 4.97 × 10 3
21DMU 210.6933316.67 × 10 2 5.64 × 10 3 6.67 × 10 3 0.07111743.10 × 10 2 3.93 × 10 3
22DMU 2218.33 × 10 2 1.98 × 10 3 6.67 × 10 3 9.00 × 10 2 7.59 × 10 3 0.0056912
23DMU 2310.4287329.75 × 10 4 7.86 × 10 2 0.76978597.59 × 10 3 5.69 × 10 3
24DMU 240.7780436.67 × 10 2 9.87 × 10 4 4.76 × 10 3 0.08359196.02 × 10 3 4.51 × 10 3
25DMU 250.782116.67 × 10 2 2.83 × 10 3 6.67 × 10 3 4.70 × 10 2 6.06 × 10 3 4.55 × 10 3
Table A18. The slacks for each DMU using the SBM-AR-V model.
Table A18. The slacks for each DMU using the SBM-AR-V model.
No.DMUScoreExcessExcessExcessShortageShortageShortage
LTUPPCQBNIRE
S−(1)S−(2)S−(3)S+(1)S+(2)S+(3)
1DMU 11000000
2DMU 20.269326179.05205.517218.7324.97
3DMU 30.25123502006.038817.923.87
4DMU 40.456790.2190489002.199967523.61942335.781249
5DMU 51000000
6DMU 60.41877800.205.258413.4817.97
7DMU 70.6774940.9193048002.88285910.11893382.3581649
8DMU 80.448556129.8657320.164744.830522600.1191433
9DMU 90.9994530008.57 x 10 4 2.24 x 10 2 2.98 x 10 2
10DMU 101000000
11DMU 1118.79 x 10 5 00005.42 x 10 4
12DMU 121000000
13DMU 130.7629434.00 x 10 5 07.3259871.81747724.256131211.262405
14DMU 14100003.01 x 10 3 4.01 x 10 3
15DMU 150.7124741.00004015.196121.47482944.06339.3821192
16DMU 161000000
17DMU 170.8491090022.975340.46259611.1182872.9958335
18DMU 180.7440861.0000408.3649480.97983954.886780512.906691
19DMU 191000000
20DMU 200.8762996.41x 10 2 000.31942454.936605913.23423
21DMU 210.6933311.0000400.6213623.290080500.4775992
22DMU 221000000
23DMU 231000000
24DMU 240.778043116.8750122.1623402.13253784.4913542
25DMU 250.782111.0000407.1961170.30496945.277312.528119

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Figure 1. Research process.
Figure 1. Research process.
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Figure 2. A triangular fuzzy number (TFN).
Figure 2. A triangular fuzzy number (TFN).
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Figure 3. Triangular fuzzy number (TFN).
Figure 3. Triangular fuzzy number (TFN).
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Figure 4. Hierarchical structure to select best suppliers.
Figure 4. Hierarchical structure to select best suppliers.
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Figure 5. Data envelopment analysis model.
Figure 5. Data envelopment analysis model.
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Table 1. Criteria for supplier selection.
Table 1. Criteria for supplier selection.
CriteriaSub-CriteriaResearcher
FinancialCapital and financial power of supplier companyHo et al. [54], Dickson [55], Weber et al. [56]
Proposed raw material priceBanaeian et al. [50], Dickson [55], Weber et al. [56], Ho et al. [54]
Transportation cost to the geographical locationDickson [55], Weber et al. [56]
Delivery and serviceCommunication systemDickson [55], Weber et al. [56]
Lead timeHandfield [57], Choi & Hartley [58], Verma & Pullman [59], Bharadwa [60], Kannan et al. [61], Chu & Varma [62], Tam & Tummala [63], Shahgholian et al. [64]
Production capacityKannan [61], Dickson [55], Weber et al. [56]
After sales serviceDzever et al. [65], Choi & Hartley [58], Bevilacqua & Petroni [66], Bharadwaj [60], Rezaei & Ortt [67], Roshandel et al. [68]
QualitativeBusiness experience and position among competitorsBanaeian et al. [50], Dickson [55], Weber et al. [56]
Expert labor, technical capabilities and facilitiesBanaeian et al. [50], Dickson [55], Weber et al. [56]
Operational controlDickson [55], Weber et al. [56]
QualityGrover et al. [55], Dickson [55]
Environmental management systemEnvironmental friendly technologyRajesri Govindaraju et al. [69], Grover et al. [53]
Environmental planningBanaeian et al. [50], Nielsen et al. [70]
Environmentally friendly materialGrover et al. [53]
Environmental prerequisiteBanaeian et al. [50]
Table 2. The 1–9 scale for AHP [6].
Table 2. The 1–9 scale for AHP [6].
Importance IntensityDefinition
1Equally importance
3Moderate importance
5Strongly more importance
7Very strong more importance
9Extremely importance
2, 4, 6, 8Intermediate values
Table 3. The 1–9 fuzzy conversion scale [72].
Table 3. The 1–9 fuzzy conversion scale [72].
Importance IntensityTriangular Fuzzy Scale
1(1, 1, 1)
2(1, 1, 2)
3(1, 2, 3)
4(2, 3, 4)
5(3, 4, 5)
6(4, 5, 6)
7(5, 6, 7)
8(7, 8, 9)
9(9, 9, 9)
Table 4. Number of suppliers (DMU).
Table 4. Number of suppliers (DMU).
NoCompany NameAddressTurnover (USD)EmployeesMarket Geographical AreaSymbol
1An Gia Phu Food and Cereal Limited Liability CompanyVinh Long Province, Vietnam616,89425VietnamDMU 1
2VINA Fragrant Rice Limited Liability CompanyCan Tho City, Vietnam877,66239VietnamDMU 2
3Thai Hung Cereal Co-operative CompanyCan Tho City, Vietnam616,30931VietnamDMU 3
4Sang Mai Agricultural Production Limited Liability CompanyHai Phong Provice, Vietnam686,35039VietnamDMU 4
5FAS Vietnam Cereal Limited Liability CompanyVinh Long Province, Vietnam729,34924VietnamDMU 5
6S1000 Food Commercial and Service Limited Liability CompanyHo Chi Minh City, Vietnam590,81421VietnamDMU 6
7Khau Thien Thanh Phat Production and Commercial Export-Import CompanyHo Chi Minh City, Vietnam3,180,926121Vietnam, Malaysia, Japan, AustraliaDMU 7
8Gia Son Phat Commercial and Service Limited Liability CompanyKien Giang, Vietnam613,65433VietnamDMU 8
9VILACONIC Cereal Joint Stock CompanyNghe An Province, Vietnam717,78031VietnamDMU 9
10Binh Minh Cereal Joint Stock CompanyCan Tho City, Vietnam658,27226VietnamDMU 10
11Phu Thai Huong Joint Stock CompanyLong An Province, Vietnam1.347,62157VietnamDMU 11
12Long Tra Agroforestry Food Production Limited Liability CompanyHo Chi Minh City, Vietnam4,650,698234Vietnam, AsiaDMU 12
13Huong Chien Rice Production Limited Liability CompanyLong An Province, Vietnam674,38818VietnamDMU 13
14Loc Troi Joint Stock Incorporated CompanyAn Giang Province, Vietnam3,077,786179Vietnam, Lao, CambodiaDMU 14
15Ngoc Oanh Rice Private BusinessHo Chi Minh City, Vietnam502,44823VietnamDMU 15
16Khanh Tam Rice Private BusinessHo Chi Minh City Vietnam589,57716VietnamDMU 16
17Thien Ngoc Cereal Limited Liability CompanyLong An Province, Vietnam1,094,88031VietnamDMU 17
18Xuyen Giang Commercial and Service Limited Liability CompanyHo Chi Minh City, Vietnam1,475,43159VietnamDMU 18
19Viet Lam Commercial and Service Limited Liability CompanyVinh Long Province, Vietnam1,502,04342VietnamDMU 19
20Long An Export-Production Joint Stock CompanyHa Noi City, Vietnam2,125,82589Vietnam, EUDMU 20
21Phat Tai Limited Liability CompanyDong Thap Province, Vietnam1,054,15629VietnamDMU 21
22Thai Binh Rice Joint Stock CompanyThai Binh Province, Vietnam1,777,24451VietnamDMU 22
23Angimex Kitoku Limited Liability CompanyTien Giang Province, Vietnam1,098,97838VietnamDMU 23
24Hoa Lua Rice Commercial Limited Liability CompanyHo Chi Minh City, Vietnam1,029,62259VietnamDMU 24
25Phuong Quan Production Limited Liability CompanyLong An Province, Vietnam1,733,25661VietnamDMU 25
Table 5. Fuzzy comparison matrix for criteria.
Table 5. Fuzzy comparison matrix for criteria.
CriteriaFSEMSFIQU
FS(1, 1, 1)(1/8, 1/7, 1/6)(1/9, 1/8, 1/7)(1/3, 1/2, 1)
EMS(6, 7, 8)(1, 1, 1)(1/6, 1/5, 1/4)(1, 2, 3)
FI(7, 8, 9)(4, 5, 6)(1, 1, 1)(4, 5, 6)
QU(1, 2, 3)(1/3, 1/2, 1)(1/6, 1/5, 1/4)(1, 1, 1)
Table 6. Real number priority.
Table 6. Real number priority.
CriteriaFSEMSFIQU
FS11/71/81/2
EMS711/62
FI8615
QU21/21/51
Table 7. Fuzzy comparison matrices for the criteria.
Table 7. Fuzzy comparison matrices for the criteria.
CriteriaFSEMSFIQUWeight
FS(1, 1, 1)(1/8, 1/7, 1/6)(1/9, 1/8, 1/7)(1/3, 1/2, 1)0.04929
EMS(6, 7, 8)(1, 1, 1)(1/7, 1/6, 1/5)(1, 2, 3)0.20144
FI(7, 8, 9)(5, 6, 7)(1, 1, 1)(4, 5, 6)0.64816
QU(1, 2, 3)(1/3, 1/2, 1/1)(1/6, 1/5, 1/4)(1, 1, 1)0.10111
Total1
CR = 0.09480
Table 8. Comparison matrix for the financial criteria.
Table 8. Comparison matrix for the financial criteria.
CriteriaCFBRPMPTCOOLWeight
CFB(1, 1, 1)(1/5, 1/4, 1/3)(3, 4, 5)0.2290
RPMP(3, 4, 5)(1, 1, 1)(6, 7, 8)0.6955
TCOOL(1/5, 1/4, 1/3)(1/8, 1/7, 1/6)(1, 1, 1)0.0754
Total1
CR = 0.07348
Table 9. Comparison matrix for the delivery and service criteria.
Table 9. Comparison matrix for the delivery and service criteria.
CriteriaCSLTPCASSWeight
CS(1, 1, 1)(1/9, 1/8, 1/7)(1/5, 1/4, 1/3)(2, 3, 4)0.0924
LT(7, 8, 9)(1, 1, 1)(1/3, 1/2, 1)(6, 7, 8)0.3956
PC(3, 4, 5)(1, 2, 3)(1, 1, 1)(7, 8, 9)0.4672
ASS(1/4, 1/3, 1/2)(1/8, 1/7, 1/6)(1/9, 1/8, 1/7)(1, 1, 1)0.0448
Total1
CR = 0.09456
Table 10. Comparison matrix for the qualitative criteria.
Table 10. Comparison matrix for the qualitative criteria.
CriteriaPEPETCTOCQAWeight
PEP(1, 1, 1)(2, 3, 4)(4, 5, 6)(1/5, 1/4, 1/3)0.2136
ETCT(1/4, 1/3, 1/2)(1, 1, 1)(1/4, 1/3, 1/2)(1, 1, 1)0.0436
OC(1/6, 1/5, 1/4)(2, 3, 4)(1, 1, 1)(1/9, 1/8, 1/7)0.0791
QA(3, 4, 5)(1, 1, 1)(7, 8, 9)(1, 1, 1)0.6638
Total1
CR = 0.09005
Table 11. Comparison matrix for the environmental management systems criteria.
Table 11. Comparison matrix for the environmental management systems criteria.
CriteriaEFTEPEFMENRWeight
EFT(1, 1, 1)(1/9, 1/9, 1/9)(1/6, 1/5, 1/4)(1/6, 1/5, 1/4)0.0445
EP(9, 9, 9)(1, 1, 1)(1, 2, 3)(5, 6, 7)0.5345
EFM(4, 5, 6)(1/3, 1/2, 1)(1, 1, 1)(3, 4, 5)0.3009
ENR(4, 5, 6)(1/7, 1/6, 1/5)(1/5, 1/4, 1/3)(1, 1, 1)0.1201
Total1
CR = 0.0838
Table 12. Raw data provided by case organization used to assess the relative efficiency of various suppliers.
Table 12. Raw data provided by case organization used to assess the relative efficiency of various suppliers.
A Supplier (DMU)InputOutput
LT (Days)UP (USD)PC (Tons)QB (%)NI (USD)RE (USD)
DMU 13347.3503.722144.0358.71
DMU 25391.45701.345925.2033.60
DMU 34332.4500.824326.0334.70
DMU 44321.5401.761122.9530.60
DMU 54213.5501.002340.0553.40
DMU 64312.6501.604730.4540.60
DMU 75345.3402.574848.0068.20
DMU 85342.9702.009544.0358.71
DMU 93343.6503.240132.7043.60
DMU 103354.1303.068744.2959.05
DMU 115320.10304.004032.7843.70
DMU 123346.30702.914144.0258.70
DMU 134340.60504.019444.1258.83
DMU 144315.05405.148434.8846.50
DMU 155332.40604.660443.0257.36
DMU 164350.90405.462350.0074.30
DMU 174320.00716.123844.0158.68
DMU 185344.60504.711544.1258.82
DMU 195314.03507.417844.1558.86
DMU 204342.30404.703944.0658.75
DMU 215310.80503.249744.1558.86
DMU 224312.40506.863143.9358.57
DMU 235342.00507.457743.9258.56
DMU 245337.60706.560243.1157.48
DMU 255340.10505.550143.0257.36
Table 13. The results of the Pearson correlation coefficient.
Table 13. The results of the Pearson correlation coefficient.
Inputs/OutputsLTUPPCQBNIRE
LT10.024840.161490.242570.07760.07681
UP0.0248410.141050.093010.007250.03435
PC0.161490.1410510.017130.047280.00201
QB0.242570.093010.0171310.546640.51879
NI0.07760.007250.047280.5466410.98863
RE0.076810.034350.002010.518790.988631
Table 14. Ranking list of suppliers by using nine DEA models (CCR, BCC, and SBM, Super SBM).
Table 14. Ranking list of suppliers by using nine DEA models (CCR, BCC, and SBM, Super SBM).
SupplierCCR-ICCR-OBCC-IBCC-OSBM-I-CSBM-O-CSuper SBM-I-CSuper SBM-AR-CSuper SBM-AR-V
DMU 1111111111
DMU 2252525242524252424
DMU 3232322232325232525
DMU 4242415252423242321
DMU 5111111111
DMU 6222220222222222223
DMU 799121292091920
DMU 8212124202021202122
DMU 920201112118212011
DMU 10111111111
DMU 11111111181118161
DMU 12111181811
DMU 13131316181314131416
DMU 14161611121512121
DMU 15191923201917191718
DMU 16111111111
DMU 1710101313119111013
DMU 18181821191716171517
DMU 19111111111
DMU 2012121416101210912
DMU 21141418151519151819
DMU 22111111111
DMU 23111111111
DMU 24151519141610161315
DMU 25171717171413141114

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