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Imre Dobos Department of Economics, Budapest University of Technology and Economics, Budapest, Hungary

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Gyöngyi Vörösmarty Department of Supply Chain Management, Corvinus University of Budapest, Budapest, Hungary

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https://orcid.org/0000-0003-3845-2021
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Abstract

Considering ecological issues in supplier evaluation and management alongside business considerations is getting more recognition among firms. Data envelopment analysis (DEA) is one of those methods, which is frequently suggested by the literature to support management decisions. However, the data requirements of the method should be an important consideration. The literature often addresses the issue of desirable outputs and undesirable input as an important data related problem in case of the ecological use of DEA. This paper will present a new solution to manage these data problems along with connecting the evaluation of management criteria, environmental criteria and total cost aspects. The proposed environmental supplier selection problem is an extension of a former paper. The new model examines the effect of inventory related costs, such as EOQ costs of inventory holding or ordering costs on the selected supplier, extended with newly introduced scaled values of input and output indicators. The usage of scaled values is motivated by the problem of invariance to data alteration. In addition to the uncertainty of the data, the paper looks for a functional relationship between the input and output criterion values and the efficiency that can be assigned to them using DEA.

Abstract

Considering ecological issues in supplier evaluation and management alongside business considerations is getting more recognition among firms. Data envelopment analysis (DEA) is one of those methods, which is frequently suggested by the literature to support management decisions. However, the data requirements of the method should be an important consideration. The literature often addresses the issue of desirable outputs and undesirable input as an important data related problem in case of the ecological use of DEA. This paper will present a new solution to manage these data problems along with connecting the evaluation of management criteria, environmental criteria and total cost aspects. The proposed environmental supplier selection problem is an extension of a former paper. The new model examines the effect of inventory related costs, such as EOQ costs of inventory holding or ordering costs on the selected supplier, extended with newly introduced scaled values of input and output indicators. The usage of scaled values is motivated by the problem of invariance to data alteration. In addition to the uncertainty of the data, the paper looks for a functional relationship between the input and output criterion values and the efficiency that can be assigned to them using DEA.

1 Introduction

Suppliers are considered the key resource of an enterprise. Good supplier management and improved supplier performance contribute to the business success of organisations (Kannan − Tan, 2002; Tracey − Leng Tan 2001; Nair et al. 2015; Liu et al. 2017; Ahmed et al. 2022). Moreover, in today's globally competitive markets, increased need for flexibility and innovation lead to much higher complexity regarding management decisions. Therefore, there is a need for more transparent and systematic methods to support the evaluation of suppliers. However, in line with the growing importance of the purchasing function, the criteria system of supplier evaluation has become complex. While earlier the challenge was to compare short-term performance data against each other to define the best supplier, now large databases are handled together with expert judgements to ensure the availability of proper suppliers to reach low total costs, avoid risks and consider environmental effects.

The tasks of purchasers are very diverse from supplier pre-qualification, through supplier evaluation, to post-qualification (Roodhooft − Konings, 1997; Wu − Barnes 2011; Igarashi et al. 2013; Luzzini et al. 2014; Cole − Aitken 2019). One of the important problems of this is supplier selection. The choice of supplier in decision theory belongs to the topic of ranking. This implies that the decision-making units are sorted into a given set of considerations. This arrangement is available in a variety of methods, including TOPSIS, AHP, or data envelopment analysis (DEA), which is recommend in this paper. Each method has its own data requirements. This paper aims to focus on some data related issues of using DEA. It will address within one model the following:

  1. -the problem of data scaling (the scaling or the range of criteria may be an influencing factor in the selection process) and data preference (whether lower or the higher values are preferred). This paper proposes to solve these two elementary practical problems by recalculating the starting data, which is also suggested in the literature (Lovell − Pastor 1995; Seiford − Zhu 2002).
  2. -data uncertainty. Though many papers address data uncertainty, our paper has is based on a novel parametrized approach. The paper also looks for a functional relationship between the input and output criterion values and the efficiency that can be assigned to them using DEA. In the literature, this is called production frontier analysis. Sengupta (1987, 1992) and Tone and Sahoo (2003) examined the problem in detail.

The suggested model is a multilevel model which connects supplier evaluation with inventory control. The advantage of the proposed method is that it extends DEA in a TCO approach. The literature mostly does not include inventory costs in the DEA model among the criteria. This model interprets the inventory costs on the basis of the classic EOQ, i.e. it consists of two cost elements: inventory and order cost (Dobos − Vörösmarty 2021). The supplier is often unable to deliver the optimal batch size, so the purchasing manager should know the effectiveness of the proposed batch size. Since DEA determines efficiency, the parameterization can also provide answers to the results of the sensitivity analysis besides the uncertainty of the data (Xu et al. 2021).

The paper will be structured as follows: first it will provide a brief literature review presenting the challenges posed by the data required for supply management. In the next section, a DEA model will be developed based on an earlier method to investigate the effect of the data scaling problem in supply management. The scaling problem is extended with a transformation of different criteria to similar long intervals. This section ends with a numerical example. Then a production frontier analysis is supplied to express green criteria with other ones. Section 4 summarises the managerial implications of the paper. The concluding remarks are discussed in Sections 5.

2 Literature review

In previous studies various methods have been proposed for supplier selection (Agarwal et al. 2011; Ho et al. 2010; Chai − Ngai 2020). However, as the purchasing function moved from a traditional transactional to a strategic approach, the task became getting more complex. In line with this the criteria system applied in supply management broadened.

Dickson's (1966) often cited study presented 23 supplier evaluation criteria. Later studies investigating the criteria identified that most of them were relevant for a long period: Weber et al. (1991) revealed that price/costs, delivery and quality were the most important and some later studies (e.g. Ho et al. 2010) proved that they are still the most relevant aspects. However, the way high (acceptable) quality, delivery and price/costs are achieved and measured has changed much and are often supplemented with the aspect of risk (Giunipero − Eltentawy 2004).

Compared to the Dickson's (1966) criteria, sustainability criteria have emerged as new ones and have become increasingly important in recent decades (Kony 2019; Dutta et al. 2022). In addition to business considerations (price, quality, delivery), environmental and social responsibility aspects are increasingly indispensable in business relationships.

Formerly selection was a decision made after comparing bids. It was an important issue to handle the trade-offs and to measure the criteria against each other. Weber et al. (1991) reviewed the literature to reinvestigate Dickson's criteria, and to identify methodologies. They found that the vast majority of published methodologies were linear weighting models, mathematical models and a few probabilistic models. These at that time were suitable means to handle the identified criteria in a simple decision making process to choose the best supplier from among the bidders.

Since then the evaluation process has been transformed into a multistage process (Glock et al. 2017). It is still relevant to aim for achieving low cost, delivery and quality, but in this multistage process the evaluation became more systematic and thorough. Not only short-term measures count (e.g. price of the product, promised delivery date), but capabilities that allow long-term good performance are also considered (e.g. available capacity, technology level, financial stability) (Braglia − Petroni 2000; Sarkar − Mohapatra 2006; Kuo et al. 2010). This complex evaluation of suppliers indicates a development of methodology. As literature reviews on supplier evaluation revealed, Multi Attribute Decision Making (MADM) techniques (e.g. Analytic Hierarchy Process, AHP; Analytic Network Process, ANP; Technique for Order of Preference by Similarity to Ideal Solution, TOPSIS; Multi-Attribute Utility Theory, MAUT), mathematical programming models (Linear Programming, LP; Multiple Objective Linear Programming, MOLP; Mixed-integer Linear Programming, MILP and DEA, etc.) and artificial intelligence methods (case-based reasoning, neural network, decision tree, association rules, cluster analysis) were used (Setak et al. 2012) along with qualitative methods (Zimmer et al. 2016).

This paper will highlight DEA as one of the most frequently used techniques of supplier evaluation (Ho et al. 2010; Soheilirad et al. 2018; Sultana et al. 2016; Vörösmarty − Dobos 2021). DEA was first proposed by Charnes et al. (1978); it is a mathematical programming method for assessing the relative efficiency of homogenous decision making units (DMU). DEA has certain data requirements and a number of pitfalls have been identified. Dyson et al. (2001) describe four key assumptions with respect to the input/output set selected: it covers the full range of resources used, captures all activity levels and performance measures, the set of factors are common to all DMUs, and environmental variations has been assessed and captured if necessary. In addition, among the data requirements, homogeneity of data, the ratio of factors to DMUs, non-negative numbers and complete data have been highlighted (Dyson et al. 2001; Sarkis 2007; Kohl et al. 2019).

Papers presenting solutions for supplier evaluation with DEA highlight several issues in comparing criteria against each other. The most often addressed data handling problems are the following.

2.1 Cardinal and ordinal data

Traditionally, criteria were measured in their natural weights (e.g. price in euros, delivery in days). These are metrics, which reflect the ranking of the supplier, and it shows which supplier is better and by how much. In recent supplier evaluation systems ordinal data appears more frequently instead of cardinal data (Saen 2007; Azizi 2013; Toloo − Nalchigar 2011; Ebrahimi et al. 2021). In this case such data should be compared to each other, which does not reflect meaningful differences between the values.

2.2 Negative data

Positive numbers can measure traditional criteria. However, as new criteria about capabilities came into consideration, sometimes negative data (e.g. growth rate, or profit/loss) appears (Izadikhah − Saen 2016; Mohamad − Said 2012; Soltanifar − Sharafi 2022).

2.3 Imprecise data

Sometimes supplier evaluation faces the situation of imprecise data. It is often relevant in case of evaluating new suppliers. Uncertain information or imprecise data can be expressed in interval or fuzzy numbers (Chen et al. 2006; Wang et al. 2005; Karsak − Dursun 2014; Azadeh et al. 2017; Hatefi 2017; Dobos − Vörösmarty 2019b; Rashidi − Cullinane 2019; Wen et al. 2018).

2.4 Qualitative and quantitative data

Traditional offers mostly consisted of hard data, which could have been easily expressed in quantities (e.g. delivery in days). However, when capabilities are analysed, often soft data can only be used which are difficult to quantify (e.g. quality of equipment). Experts often evaluate this soft data. One of the problems is that it reflects subjective judgements (Shi et al. 2015). Consistency also needs to be ensured. Qualitative variables are often handled with other methods (He − Zhang 2018; Zeydan et al. 2011), which also helps to overcome the limitations of DEA. A critical drawback of DEA models is the use of different weights for effective DMUs. A further drawback in the decision process is that DMUs are usually divided as efficient and inefficient in DEA, while the decision losses of individual DMUs are not regarded. A third limitation of DEA is the number of DMUs. Cooper et al. (2007) recommended that the number of DMUs analyzed should be at least the maximum of the multiplication of numbers of input and output, or three times the sum of the number of input and number of output criteria.

2.5 Undesirable output

To implement DEA, the input and output criteria must be defined. Criteria where smaller values are considered better are inputs, and the criteria where larger is better should be considered as outputs to increase the efficiency (Amindoust et al. 2013). However, in the presence of undesirable outputs, DMUs with more good (desirable) outputs and less bad (undesirable) outputs (e.g. waste, rejected products) relative to lower inputs should be recognized as efficient. However, as sustainability considerations appear among supplier evaluation criteria, undesirable outputs need to be handled in DEA framework more frequently (Azadi et al. 2017; Mahdiloo et al. 2015; Saen 2010).

2.6 Total costs of ownership (TCO) data

In traditional supplier selection, price was one among the criteria, in a more strategic approach to purchasing, the costs of managing a relationship with a supplier are considered. The challenge here is to grasp the important cost elements. Visani et al. (2016) used applied activity-based costing (ABC) to define a supplier performance index for each supplier. Ramanathan (2007) and Mohamady Garfamy (2006) used four groups of costs to address the most important costs of the relationship. Dobos and Vörösmarty (2019a) used an EOQ model to describe the most important logistic costs. Their paper highlighted that it is not possible to handle non-linear functions in DEA.

2.7 Data scaling

The natural measure of supplier selection criteria differs. For example, delivery lead time may be measured in hours or in days. This scaling difference may alter the result of the evaluation process (see the data alteration problem in Cook and Seiford 2009). Another problem is how to compare lead-times given in days and product quality measured using the defect rate.

This review revealed that methodology development addressed several problems of the data. Many of them are properly solved by methodologies as it was indicated before. However, there are two problems which are less often addressed.

First, a series of DEA methods use imprecise, or uncertain type of information. DEA models for stochastic and fuzzy data are available to treat them (e.g., Alikhani et al. 2019; Park et al. 2018; Rashidi – Cullinane 2019; Wen et al. 2018). A potential drawback is that they require knowledge and software that is less likely to be available to purchasing managers in SMEs or even for many larger companies. From a practical point of view, it would be important to have a methodology that can be solved with a software easily accessible and known to use, e.g. Microsoft Excel.

Second, the distorting effect of different measuring scales to the result of evaluation is seldom addressed. Some of the above-mentioned data handling issues and their solutions manage this problem: for example, TCO logic converts the criteria to cost, or for comparing expert opinions the same scale may be used to evaluate each criterion. The problem of scaling is well known in the literature, but only a limited number of contributions has focused on this issue. This is a complex problem, as scaling is often associated with the problem of imprecise data and is important to investigate it as it may have an effect on the result of the evaluation.

In the next section, this problem will be handled in a two-level solution. In the first level, a solution will be offered for the data alteration problem with the introduction of a similar scaling of an evaluation criterion in a similar range. In the second level, the imprecise data will be investigated by parametrizing the criteria. In addition to the uncertainty of the data, the paper looks for a functional relationship between the input and output criterion values and the efficiency that can be assigned to them using DEA. In the literature, this is called production frontier analysis. Sengupta (1987, 1992) examined the statistical side of this problem in detail, while Tone and Sahoo (2003) studied the linear algebraic side of the production function within the framework of the DEA. Daraio et al. (2019) collected and presented software solutions available for production frontier analysis. We use the statistical method proposed by Sengupta (1987, 1992), as after estimation, it is possible to express one or all of the green output criteria using the other input and/or output criterion values and the DEA efficiency.

3 A DEA model with utilities for green supplier selection under lot sizing

In this section a DEA model to support supplier evaluation will be developed. The model will address the weaknesses of the current literature. The data will be analysed with parametrical linear programming. The parametrizing is presented through the inventory costs. With the parametrical linear programming, the data accurateness was tested and the results can be interpreted as sensitivity analyses in a DEA model. The consequences of data alteration can be revealed by comparing the results of the former evaluation and the offered novel method with utility values.

3.1 The extension of the green DEA method with inventory costs

Dobos and Vörösmarty (2019a) constructed a DEA model with EOQ-type inventory costs. Inventory related costs were involved in DEA-type supplier selection problems with raw data. In this case, the suppliers' ability to supply an ordered quantity is examined in an inventory cost saving way. It is assumed that the firm knows the setup and inventory holding costs of its suppliers, i.e., (Sj;hj), j=0,1,2,,p are known. The inventory costs for a known lot size can be calculated as (1)
xj(q)=SjDq+hjq2,
where parameter D is the yearly demand of the firm, and q is a given lot size (Dobos – Vörösmarty 2021).

The management indicators are now vector (xi;xi(q)), and the green indicators yi. As it can be seen, the management indicators are parametrized with lot size q.

Let us introduce a new weight for the inventory costs vn+1. The new weight vector is extended with the weight of the inventory costs (v;vn+1) for all suppliers. The new model has the following form
uy0max
s.t.
vx0+vn+1x0(q)=1,
uyj(vxj+vn+1xj(q))0;j=0,1,2,,p.
u0,(v;vn+1)0.

The parametric problem (2)(5) is a linear programming one. A numerical solution of this model is available in Dobos and Vörösmarty (2019a).

The basic problem in DEA models is the range of criteria. The criteria are often transformed on a similar normalised measure, i.e. the criteria have the same interval length. We offer the following linear normalisation functions. The offered normalisation functions of criteria have a range between 1 and 20. The choice of scale range is, of course, always subjective. The choice of 20 was for clarity. For managerial data, i.e. for the input, we have used the function
Xij=19xjmaxxjminxij19xjmaxxjmaxxjmin1,
where value xjmin is the worst value of criterion j, and value xjmax is the best value of this criterion. For the output, i.e. green data, we have applied
Yij=19yjmaxyjminyij19yjmaxyjmaxyjmin+20,
where value yjmax is the best value of criterion j, and value yjmin is the worst value of this criterion. The transformation used is an affine transformation, as analysed by Färe and Grosskopf (2013).
The transformed model has the following form (2’)(5’)
uY0max
s.t.
vX0+vn+1X0(q)=1,
uYj(vXj+vn+1Xj(q))0;j=0,1,2,,p.
u0,(v;vn+1)0.

The model (2’)(5’) is analysed as a parametrised linear programming problem numerically. The results are then compared in dependence of the lot sizes.

3.2 Numerical example for the green supplier selection method extended with lot sizing

A numerical example is shown below. The assumption is that the firm has information about all the criteria, i.e. the management criteria of its suppliers, such as lead-time, quality of the products, offered price, and the EOQ-related costs of vendors in dependence on the lot sizes. The green criteria of the analysis are the reusability level of the supplied products and the CO2 emission level during their production. Data in Table 1 are constructed for illustration purposes. The criteria reflect management considerations on the one hand and incorporate environmental aspects into the assessment on the other. Among the suppliers, there is no supplier that is the best in all criteria.

Table 1.

Data for numerical example (q = 50)

Management criteriaEnvironmental criteria
SupplierLead-time (Day, LT)Quality (%, QU)Price ($, PR)EOQ ($, EOQ)Reusability (%, RU)CO2 emission (g, CO2)
12802457030
2170387.55010
33905132.56015
41.585142.54020
52.5752.5146.256535
629541309025
73801.5103.757515
81.5853.5188.758520
91703.568.755510
102.5754904510
113.5902.5126.258025
122651.5103.755020
133853167.57515
141.5704.5151.258520
1516521257515
162705152.58010
17190182.58515
183852.5126.257520

Source: authors.

The basic data of the example is represented in Table 1 in the case of a lot size q = 50, interest rate k = 0.1, and demand D = 100 in a year. The example fulfils the general rule for the number of decision-making units (suppliers), to obtain proper results. The number of vendors is equal to 18, where p=max{mn;3(m+n)}, and p is the number of vendors, m is the number of outputs, and n the number of inputs (Cooper et al. 2007).

Table 1 presents a parametrisation of vendors in the lot size. A number of data tables are constructed in dependence of the lot sizes. The EOQ related cost parameters are shown in Table 2. The bold numbers in the tables indicate the best, preferred values in the following.

Table 2.

EOQ costs parameters

SupplierOrdering ($)Inventory holding ($)EOQ ($)
1200.245
2400.387.5
3600.5132.5
4200.142.5
5700.25146.25
6600.4130
7500.15103.75
8900.35188.75
9300.3568.75
10400.490
11600.25126.25
12500.15103.75
13800.3167.5
14700.45151.25
15600.2125
16700.5152.5
17400.182.5
18600.25126.25

Source: authors.

The EOQ costs for suppliers 1, to 3, etc. are calculated as follows:
x1(50)=2010050+2502=90,
x2(50)=4010050+3502=155,
x3(50)=6010050+5502=245,
etc.

The optimal lot sizes of these vendors are 89.44, 154.92, and 244.95 units. Transforming the data of Table 1 in this form means that a better result of a criterion is has a higher value than that of a worse one. If a better criterion has a higher value, than the evaluation of that criterion is unchanged (this is the case for e.g., reusability, lead-time and price). If the better criterion receives a lower value, then two methods are available to build: a negative sign is chosen before either the given data, or the inverse of the data. In the analysis, the first solution is chosen to handle this problem. The new, transformed data is presented in Table 3.

Table 3.

The transformed data with utility values for q = 50

Management criteriaEnvironmental criteria
SupplierLead time (LT)Quality (QU)Price (PR)EOQ (EOQ)Reusability (RU)CO2 emission (CO2)
1−8.6−10.5−5.75−1.32512.44.8
2−1−16.833−10.5−6.8464.820
3−16.2−4.167−20−12.6928.616.2
4−4.8−7.333−1−1112.4
5−12.4−13.667−8.125−14.47910.51
6−8.6−1−15.25−12.368208.6
7−16.2−10.5−3.375−8.95714.316.2
8−4.8−7.333−12.875−2018.112.4
9−1−16.833−12.875−4.4106.720
10−12.4−13.667−15.25−7.1712.920
11−20−4.1667−8.125−11.88016.28.6
12−8.6−20−3.375−8.9574.812.4
13−16.2−7.333−10.5−17.23914.316.2
14−4.8−16.833−17.625−15.12818.112.4
15−1−20−5.75−11.71814.316.2
16−8.6−16.833−20−15.29116.220
17−1−4.167−1−6.19718.116.2
18−16.2−7.333−8.125−11.88014.312.4

Source: authors.

The optimal efficiency indicators for the vendors are represented in Table 4, in dependence on the lot sizes.

Table 4.

Parametrical solution of the DEA model for the supplier 1 with utility values (DEA and cross efficiencies)

No. of supplier/Lot size255075100125150175200225250275300
11.0001.0001.0001.0001.0001.0000.8370.6850.5760.4950.4330.385
20.1570.1560.1530.1490.1440.1370.1210.1060.0940.0840.0760.073
30.2800.2590.2300.1970.1640.1340.1150.1010.0890.0800.0720.066
40.1090.1130.1220.1380.1680.2380.2440.2170.1940.1750.1600.147
50.2320.2290.2250.2190.2120.2020.1900.1790.1690.1600.1510.144
60.7260.6750.6020.5190.4360.3580.3110.2780.2490.2260.2060.190
70.4740.4740.4760.4770.4800.4830.4690.4530.4360.4210.4060.393
80.3520.3420.3240.3020.2750.2460.2270.2120.1980.1860.1750.165
90.2720.2660.2570.2440.2280.2100.1770.1490.1270.1110.0980.088
100.1050.1010.0940.0870.0780.0680.0580.0500.0430.0380.0340.031
110.5350.5170.4900.4540.4120.3670.3360.3130.2910.2720.2550.240
120.1220.1240.1280.1340.1430.1580.1580.1520.1460.1410.1360.132
130.3160.3070.2930.2750.2530.2290.2190.1980.1860.1750.1650.156
140.3720.3610.3440.3220.2950.2660.2360.2120.1910.1730.1590.146
150.3160.3180.3210.3270.3340.3450.3340.3170.3010.2870.2730.261
160.3320.3210.3030.2800.2540.2250.1980.1760.1570.1420.1290.119
171.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.000
180.4290.4190.4030.3800.3530.3220.2970.2760.2570.2400.2250.212

Source: authors.

In the numerical example, two sets of criteria were formulated: management (traditional purchasing criteria extended with EOQ related costs) and green criteria. The results show that the 17th and first suppliers are efficient in a wide range of lot sizes if the chosen lot size of the buyer is smaller than 150. If the lot size is not smaller than 150, then the best supplier is the 17th one. If the basic information is studied, it is obvious that the 17th supplier has the best lead time, quality, and price. It shows that this supplier is Pareto optimal in a decision theory context.

The weights vectors of this numerical example suggest that the weights of lead-time, price, and CO2 emissions should be neglected in the evaluation of the suppliers. The EOQ aspect received a higher weight than other criteria. In this evaluation situation, the logistic subsystem, i.e. logistical costs of the supplier, should receive a strong weight to influence the selection decision.

3.3 Comparison of results with raw data and utility values

Dobos and Vörösmarty (2019b) used transformed raw data. The question is now whether the model with utility values gives similar results of efficiency indicators or whether it provides different results. The efficiency indicators in dependence of the lot sizes of the model without utility values are presented in Table 5.

Table 5.

Parametrical solution of the DEA model for supplier 1 without utility values (DEA and cross efficiencies)

No. of supplier/lot size255075100125150175200225250275300
11.0000.9610.7360.7240.7200.7180.7160.7150.7140.7140.7140.713
20.5240.3980.3220.4410.4400.4390.4380.4380.4370.4370.4370.437
30.3630.3030.2400.6190.6180.6170.6170.6170.6170.6160.6160.616
40.6870.7600.6660.4510.4490.4480.4470.4470.4470.4460.4460.446
50.4000.3970.3710.6090.6100.6110.6120.6120.6120.6120.6120.613
60.6120.5050.4181.0001.0001.0001.0001.0001.0001.0001.0001.000
70.5750.6740.6520.7740.7740.7740.7750.7750.7750.7750.7750.775
80.4520.3930.3620.8570.8610.8640.8660.8670.8680.8690.8690.869
90.6760.4610.3430.4820.4790.4770.4760.4760.4750.4750.4750.475
100.3740.3090.2360.4120.4100.4090.4090.4080.4080.4080.4070.407
110.5030.5410.4920.8870.8890.8900.8910.8910.8910.8910.8920.892
120.4260.4490.4350.4250.4240.4240.4240.4240.4240.4240.4240.424
130.3980.3940.3660.7710.7740.7760.7770.7780.7790.7790.7800.780
140.5320.4160.3470.7140.7140.7130.7130.7130.7130.7130.7130.713
150.6070.5450.5170.6270.6270.6270.6270.6270.6270.6270.6270.627
160.4730.3730.3040.6650.6640.6630.6630.6630.6630.6630.6630.662
171.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.000
180.4920.5080.4610.7910.7920.7920.7930.7930.7930.7930.7930.793

Source: authors.

As it was seen, the 17th supplier is an efficient supplier in both cases, independent of the data transformations and values of lot sizes. So it can be concluded that this supplier can be chosen as a potential supplier independent of the measure system. Without utility values, the sixth supplier is an efficient supplier for lot sizes between 100 and 300, however, with utility values this supplier is no longer an efficient one. Without utility values, the first supplier is efficient only in case of a lot size of 25. In the new DEA model, i.e. with utility values, the first supplier is an efficient one if the lot sizes lie between 25 and 150.

3.4 Estimations of production frontiers for some lot sizes

After comparing the efficiency values calculated using the raw and utility values, we turn to how the effect of environmental aspects on efficiency can be functionally determined. The least squares method, well known from descriptive statistics, is used to perform the tests. As data obtained from non-statistical studies are available in our case, we cannot give more importance to the indicators known from the statistics, but rather the values show fitness.

In these studies, we look for functional relationships, which can be interpreted as production functions. In the general study, we look for a function where efficiency depends on the input x and output criteria y, i.e., the goal is to find an efficiency function ε(x,y)=f(x,y) relationship that best fits our data. To test the relationships, we consider three functions f(x,y):

  1. linear: ε(x,y)=a0+ax+by,

  2. hyperboloid: ε2(x,y)=a0+axTx+byTy+b, and

  3. Cobb-Douglas (C-D): ε(x,y)=α0i=1mxiαij=1nxjβj, type functions.

Since in our previous analysis we calculated the DEA efficiency only for the first DMU, while for the other DMUs we determined only the cross-efficiencies, and on the other hand we examined the former efficiencies depending on the lot sizes, we have to determine the DEA efficiencies for each DMU and put this to lot size. So that the reader is not burdened with unnecessary details, we illustrate the results through the lot sizes of q = 25 and q = 150. DEA efficiencies for two lot sizes are shown in Table 6.

Table 6.

DEA efficiencies ε (x, y) for the two lot sizes 25 and 150 (percents)

Supplierq = 25q = 150
1100.0100.0
2100.026.5
386.379.4
4100.0100.0
523.220.2
6100.0100.0
756.151.5
848.248.2
9100.0100.0
1065.346.1
1163.563.5
1231.931.0
1351.851.8
1440.626.6
1594.394.3
1641.630.8
17100.0100.0
1843.641.8

Source: authors.

For the two batch sizes, we estimated three possible production functions each. Next, we call the type of function with the largest coefficient of determination, i.e. R2, the most appropriate production function for our given data. In the analysis, we disregard the significance level of the estimated parameters because the shape of the functions is important to us and not the level of acceptance. Table 7 presents the possible functions along with their estimated coefficients.

Table 7.

Estimation of the DEA efficiencies in dependence of criteria values for the two lot sizes

ModelsLot sizesEquations
Linear modelq = 25εlin,25=125.3172.068LT2.403QU+0.723PR3.573EOQ+0.500RU+0.917CO2
q = 150εlin,150=120.4791.587LT2.665QU+2.313PR4.999EOQ+1.363RU+0.290CO2
Quadratic modelq = 25(εqua,25)2=11,173.67416.506LT213.879QU2+0.700PR221.995EOQ2+2.378RU2+3.945CO22
q = 150(εqua,150)2=10,419.44314.406LT213.479QU2+14.441PR227.998EOQ2+7.700RU22.706CO22
Cobb-Douglas modelq = 25εCD,25=157.591LT0.192QU0.321PR0.119EOQ0.366RU0.049CO20.225
q = 150εCD,150=149.605LT0.096QU0.365PR0.238EOQ0.728RU0.257CO20.222

Source: authors.

For both lot sizes, the Cobb-Douglas type production function gave the highest coefficient of determination. At a lot size of 25, the highest square of R2 is 0.866, which is extremely high. For a lot size of 150, this value was 0.681, which is considered medium but still adequate. ANOVA analysis was found to be significant for all six studies. The results are shown in Table 8.

Table 8.

Coefficient of Determination and ANOVA tests for the two lot sizes

q = 25q = 150
Coefficient of Determination (R2)Significance of ANOVACoefficient of Determination (R2)Significance of ANOVA
Linear model0.7720.0050.6310.048
Quadratic model0.6830.0240.5890.078
Cobb-Douglas model0.8660.0000.6810.024

Source: authors.

The result that neither linear nor hyperboloid regression yielded a more convincing result than the Cobb-Douglas type production function stems from the fact that for constant inputs the Cobb-Douglas production function is concave, while for constant outputs the inputs give a convex function. This also draws attention to the fact that DEA efficiencies as outcome variables can be successfully explained by Cobb-Douglas-type functions of input and output criteria.

Next it was examined how output criteria, i.e., one of the environmental criteria, say reuse (RU), can be expressed as a function of other input and output criteria and efficiency. We convert the production function for a batch size of 25. After the transformation, we get the following:
RU=1044.857ε20.408LT3.918QU6.551PR2.429EOQ7.469CO24.592.

Equality shows that if we examine the iso-reuse curve, lead-time, quality, and inventory costs, we get a convex, increasing function, while DEA efficiency, price, and CO2 are concave monotonically decreasing functions. The same results are obtained when the batch size is 150.

4 Managerial implications

The paper's managerial implications can be traced to three issues related to supplier evaluation criteria. A critical element of supplier evaluation is the choice of criteria (Dickson 1966; Weber et al. 1991). As the size of the company increases, it becomes important that the purchasing decision becomes more formalised. As part of this process, the criteria for the stakeholders in the sourcing decision need to be formulated and then the supplier performance ranked during the evaluation. For a more complex set of criteria, the ranking requires the use of a decision support methodology. This article has addressed the data requirements of the DEA methodology, highlighting the following managerial implications.

The first issue highlighted is that the application of the DEA method also raises the difficulty of how to interpret the input and output data. The available data depend on the direction of the optimum. We expect output data to be as good as possible. At the same time, there may be some output information for which it is better to get a lower value in our DEA tables. In our numerical example, we have defined the CO2 emissions value as output variable where it is better to get lower value. This means that its value must be transformed. In the case of inputs, it is optimal if the value of the input variable is as small as possible. In our numerical example, however, in the case of quality, it is better to have a higher value, so we need to transform it to a scale where the smaller transformed value corresponds to the higher value in original data.

The other problem concerns the scale range of input and output variables. In many cases, variables are defined on different scales. In the numerical example, the maximum range of lead time was given in days between 1 and 3.5. At the same time, quality ranges between 65 and 90 percent. This may refer to the great difference in weights that can be overcome by transforming all variables, both inputs and outputs into the same scale, in our case between 1 and 20. This also translates to variables on the same scales.

The third advantage of the proposed method is of interpreting stochastic and fuzzy DEA methods for managers. Because these methods assume deep mathematical, IT and programming skills in DEA, it is almost a “research” challenge for managers with little time to solve such problems. We have recommended the application of parametric DEA because partial DEA models can be solved with commercial software, like Microsoft Solver. To do this, only one column of the DEA table must be modified with the values of the lot size. This sensitivity test can also answer the question of which vendors will be efficient at each value of the lot size, i.e. they can be selected for delivery.

Finally, production frontier estimation allows us to express output, green criteria as a function of management, input criteria. This econometric estimation represents the green criteria as a function.

5 Conclusion and further research

In this paper a new method is offered to handle the data processing problem of supplier selection and evaluation. The literature review highlighted the research gap: data scaling or alteration and imprecise data are seldom examined and solutions fail to connect the two problems. In the supplier selection and evaluation procedure, DEA models are applied to handle the two problems. Mathematically the problem is too difficult to solve with analytical methods. To avoid this difficulty, numerical examples were presented to gain insight into the functioning of such a system.

Data scaling problems are not addressed in literature properly, but as the numerical example of this paper presented, it has an effect on the result of the evaluation. Further simulation studies are required to deepen knowledge in this context.

Following the suggestion of Sengupta (1987, 1992), DEA efficiencies were estimated using input and output criteria. The best approximation was given by the Cobb-Douglas type production function. This function makes it possible to express green output criteria with input declines and DEA efficiency.

The solutions for the scaling problem are likely to be connected to imprecise data. The literature offers several techniques to solve data uncertainty problems such as fuzzy and interval methodology, but the parametrization of data can be a suitable procedure as well.

An additional research option is how to combine the solution presented in this article with DEA cross-efficiency. This makes it possible to use DEA cross-efficiency during selection.

Throughout our investigation, we aimed at proposing solutions that are easily available and can be applied with known software. Further research could investigate what attitudes other than the available software influence the openness of decision makers to use decision support methods in business decisions.

References

  • Agarwal, P.Sahai, M.Mishra V.Bag M.Singh V. (2011): A Review of Multi-Criteria Decision Making Techniques for Supplier Evaluation and Selection. International Journal of Industrial Engineering Computations 2(4): 801810. https://doi.org/10.5267/j.ijiec.2010.06.004.

    • Search Google Scholar
    • Export Citation
  • Ahmed, M. U.Shafiq, A.Mahmoodi F. (2022): The Role of Supply Chain Analytics Capability and Adaptation in Unlocking Value from Supply Chain Relationships. Production Planning & Control 33(8): 774789. https://doi.org/10.1080/09537287.2020.1836416.

    • Search Google Scholar
    • Export Citation
  • Alikhani, R.Torabi A. S.Altay N. (2019): Strategic Supplier Selection under Sustainability and Risk Criteria. International Journal of Production Economics 208: 6982. https://doi.org/10.1016/j.ijpe.2018.11.018.

    • Search Google Scholar
    • Export Citation
  • Amindoust, A.Shamsuddin, A.Saghafinia, A. (2013): Using Data Envelopment Analysis for Green Supplier Selection in Manufacturing under Vague Environment. Advanced Materials Research 62216821685. https://doi.org/10.4028/www.scientific.net/AMR.622-623.1682.

    • Search Google Scholar
    • Export Citation
  • Azadeh, A.Siadatian, R.Rezaei-Malek M.Rouhollah, F. (2017): Optimization of Supplier Selection Problem by Combined Customer Trust and Resilience Engineering under Uncertainty. International Journal of System Assurance Engineering and Management 8(2): 15531566. https://doi.org/10.1007/s13198-017-0628-2.

    • Search Google Scholar
    • Export Citation
  • Azadi, M.Mirhedayatian, S. M.Saen, R. F.Hatamzad, M.Momeni, E. (2017): Green Supplier Selection: a Novel Fuzzy Double Frontier Data Envelopment Analysis Model to Deal with Undesirable Outputs and Dual-Role Factors. International Journal of Industrial and Systems Engineering 25(2): 160181. https://doi.org/10.1504/IJISE.2017.081516.

    • Search Google Scholar
    • Export Citation
  • Azizi, H. (2013): A Note on “A Decision Model for Ranking Suppliers in the Presence of Cardinal and Ordinal Data, Weight Restrictions, and Nondiscriminatory Factors. Annals of Operations Research 211(1): 4954. https://doi.org/10.1007/s10479-009-0556-x.

    • Search Google Scholar
    • Export Citation
  • Braglia, M.Petroni, A. (2000): A Quality Assurance-Oriented Methodology for Handling Trade-Offs in Supplier Selection. International Journal of Physical Distribution & Logistics Management 30(2): 96112. https://doi.org/10.1108/09600030010318829.

    • Search Google Scholar
    • Export Citation
  • Chai, J.Ngai, E. W. (2020): Decision-making Techniques in Supplier Selection: Recent Accomplishments and what Lies Ahead. Expert Systems with Applications 140: 112903. https://doi.org/10.1016/j.eswa.2019.112903.

    • Search Google Scholar
    • Export Citation
  • Charnes, A.Cooper, W. W.Rhodes, E. (1978): Measuring the Efficiency of Decision Making Units. European Journal of Operational Research 2(6): 429444. http://dx.doi.org/10.1016/0377-2217(78)90138-8.

    • Search Google Scholar
    • Export Citation
  • Chen, C. T.Lin, C. T.Huang, S. F. (2006): A Fuzzy Approach for Supplier Evaluation and Selection in Supply Chain Management. International Journal of Production Economics 102(2): 289301. https://doi.org/10.1016/j.ijpe.2005.03.009.

    • Search Google Scholar
    • Export Citation
  • Cole, R.Aitken, J. (2019): Selecting Suppliers for Socially Sustainable Supply Chain Management: Post-exchange Supplier Development Activities as Pre-selection Requirements. Production Planning & Control 30(14): 11841202. https://doi.org/10.1080/09537287.2019.1595208.

    • Search Google Scholar
    • Export Citation
  • Cook, W. D.Seiford, L. M. (2009): Data Envelopment Analysis (DEA)–Thirty Years On. European Journal of Operational Research 192(1): 117. https://doi.org/10.1016/j.ejor.2008.01.032.

    • Search Google Scholar
    • Export Citation
  • Cooper, W. W.Seiford, L. M.Tone, K. (2007): Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. New York: Springer.

    • Search Google Scholar
    • Export Citation
  • Daraio, C.Kerstens, K. H.Nepomuceno, T. C. C.Sickles, R. (2019): Productivity and Efficiency Analysis Software: an Exploratory Bibliographical Survey of the Options. Journal of Economic Surveys 33(1): 85100. https://doi.org/10.1111/joes.12270.

    • Search Google Scholar
    • Export Citation
  • Dickson, G. W. (1966): An Analysis of Vendor Selection Systems and Decisions. Journal of Purchasing 2(1): 517. https://doi.org/10.1111/j.1745-493X.1966.tb00818.x.

    • Search Google Scholar
    • Export Citation
  • Dobos, I.Vörösmarty, G. (2019a): Inventory-related Costs in Green Supplier Selection Problems with Data Envelopment Analysis (DEA). International Journal of Production Economics 209: 374380. https://doi.org/10.1016/j.ijpe.2018.03.022.

    • Search Google Scholar
    • Export Citation
  • Dobos, I.Vörösmarty, G. (2019b): Evaluating Green Suppliers: Improving Supplier Performance with DEA in the Presence of Incomplete Data. Central European Journal of Operations Research 27(2): 483495. https://doi.org/10.1007/s10100-018-0544-9.

    • Search Google Scholar
    • Export Citation
  • Dobos, I.Vörösmarty, G. (2021): Green Supplier Selection Using a Common Weights Analysis of DEA and EOQ Types of Order Allocation. Managerial and Decision Economics 42(3): 612621. https://doi.org/10.1002/mde.3258.

    • Search Google Scholar
    • Export Citation
  • Dyson, R. G.Allen, R.Camanho, A. S.Podinovski, V. V.Sarrico, C. S.Shale, E. A. (2001). Pitfalls and Protocols in DEA. European Journal of Operational Research 132(2): 245259. https://doi.org/10.1016/S0377-2217(00)00149-1.

    • Search Google Scholar
    • Export Citation
  • Dutta, P.Jaikumar, B.Arora, M. S. (2022): Applications of Data Envelopment Analysis in Supplier Selection between 2000 and 2020: a Literature Review. Annals of Operations Research 315(2): 13991454. https://doi.org/10.1007/s10479-021-03931-6.

    • Search Google Scholar
    • Export Citation
  • Ebrahimi, B.Dellnitz, A.Kleine, A.Tavana, M. (2021): A Novel Method for Solving Data Envelopment Analysis Problems with Weak Ordinal Data Using Robust Measures. Expert Systems with Applications 164: 113835. https://doi.org/10.1016/j.eswa.2020.113835.

    • Search Google Scholar
    • Export Citation
  • Färe, R.Grosskopf, S. (2013): DEA, Directional Distance Functions and Positive, Affine Data Transformation. Omega 41(1): 2830. https://doi.org/10.1016/j.omega.2011.07.011.

    • Search Google Scholar
    • Export Citation
  • Giunipero, L. C.Aly Eltantawy, R. (2004): Securing the Upstream Supply Chain: a Risk Management Approach. International Journal of Physical Distribution & Logistics Management 34(9): 698713. https://doi.org/10.1108/09600030410567478.

    • Search Google Scholar
    • Export Citation
  • Glock, C. H.Grosse, E. H.Ries, J. M. (2017): Reprint of “Decision Support Models for Supplier Development: Systematic Literature Review and Research Agenda”. International Journal of Production Economics 194: 246260. https://doi.org/10.1108/09600030410567478.

    • Search Google Scholar
    • Export Citation
  • Hatefi, S. M. (2017): A Multi-Objective Model for Supplier Evaluation and Selection in the Presence of Both Cardinal and Imprecise Data. International Journal of Integrated Engineering 9(2): 917.

    • Search Google Scholar
    • Export Citation
  • He, X.Zhang, J. (2018): Supplier Selection Study under the Respective of Low-Carbon Supply Chain: A Hybrid Evaluation Model Based on FA-DEA-AHP. Sustainability 10(2): 564. https://doi.org/10.3390/su10020564.

    • Search Google Scholar
    • Export Citation
  • Ho, W.Xu, X.Dey, P. K. (2010): Multi-criteria Decision Making Approaches for Supplier Evaluation and Selection: A Literature Review. European Journal of Operational Research 202(1): 1624. https://doi.org/10.1016/j.ejor.2009.05.009.

    • Search Google Scholar
    • Export Citation
  • Igarashi, M.de Boer, L.Fet, A. M. (2013): What Is Required for Greener Supplier Selection? A Literature Review and Conceptual Model Development. Journal of Purchasing and Supply Management 19(4): 247263. https://doi.org/10.1016/j.pursup.2013.06.001.

    • Search Google Scholar
    • Export Citation
  • Izadikhah, M.Saen, R. F. (2016): Evaluating Sustainability of Supply Chains by Two-Stage Range Directional Measure in the Presence of Negative Data. Transportation Research Part D: Transport and Environment 49: 110126. https://doi.org/10.1016/j.trd.2016.09.003.

    • Search Google Scholar
    • Export Citation
  • Kannan, V. R.Tan, K. C. (2002): Supplier Selection and Assessment: Their Impact on Business Performance. Journal of Supply Chain Management 38(3): 1121. https://doi.org/10.1111/j.1745-493X.2002.tb00139.x.

    • Search Google Scholar
    • Export Citation
  • Karsak, E. E.Dursun, M. (2014): An Integrated Supplier Selection Methodology Incorporating QFD and DEA with Imprecise Data. Expert Systems with Applications 41(16): 69957004. https://doi.org/10.1016/j.eswa.2014.06.020.

    • Search Google Scholar
    • Export Citation
  • Kohl, S.Schoenfelder, J.Fügener, A.Brunner, J. O. (2019). The Use of Data Envelopment Analysis (DEA) in Healthcare with a Focus on Hospitals. Health Care Management Science 22(2): 245286. https://doi.org/10.1007/s10729-018-9436-8.

    • Search Google Scholar
    • Export Citation
  • Konys, A. (2019): Green Supplier Selection Criteria: from a Literature Review to a Comprehensive Knowledge Base. Sustainability 11(15): 4208. https://doi.org/10.3390/su11154208.

    • Search Google Scholar
    • Export Citation
  • Kuo, R. J.Wang, Y. C.Tien, F. C. (2010): Integration of Artificial Neural Network and MADA Methods for Green Supplier Selection. Journal of Cleaner Production 18(12): 11611170. https://doi.org/10.1016/j.jclepro.2010.03.020.

    • Search Google Scholar
    • Export Citation
  • Liu, Y.Zhu, Q.Seuring, S. (2017): Linking Capabilities to Green Operations Strategies: The Moderating Role of Corporate Environmental Proactivity. International Journal of Production Economics 187: 182195. https://doi.org/10.1016/j.ijpe.2017.03.007.

    • Search Google Scholar
    • Export Citation
  • Lovell, C. K.Pastor, J. T. (1995): Units Invariant and Translation Invariant DEA Models. Operations Research Letters 18(3): 147151. https://doi.org/10.1016/0167-6377(95)00044-5.

    • Search Google Scholar
    • Export Citation
  • Luzzini, D.Caniato, F.Spina, G. (2014): Designing Vendor Evaluation Systems: An Empirical Analysis. Journal of Purchasing and Supply Management 20(2): 113129. https://doi.org/10.1016/j.pursup.2014.03.002.

    • Search Google Scholar
    • Export Citation
  • Mahdiloo, M.Saen, R. F.Lee, K. H. (2015): Technical, Environmental and Eco-Efficiency Measurement for Supplier Selection: An Extension and Application of Data Envelopment Analysis. International Journal of Production Economics 168: 279289. https://doi.org/10.1016/j.ijpe.2015.07.010.

    • Search Google Scholar
    • Export Citation
  • Mohamad, N. H.Said, F. (2012): Using Super-efficient DEA Model to Evaluate the Business Performance in Malaysia. World Applied Sciences Journal 17(9): 11671177.

    • Search Google Scholar
    • Export Citation
  • Mohammady Garfamy, R. (2006): A Data Envelopment Analysis Approach Based on Total Cost of Ownership for Supplier Selection. Journal of Enterprise Information Management 19(6): 662678. https://doi.org/10.1108/17410390610708526.

    • Search Google Scholar
    • Export Citation
  • Nair, A.Jayaram, J.Das, A. (2015): Strategic Purchasing Participation, Supplier Selection, Supplier Evaluation and Purchasing Performance. International Journal of Production Research 53(20): 62636278. https://doi.org/10.1080/00207543.2015.1047983.

    • Search Google Scholar
    • Export Citation
  • Park, S.Ok, C.Ha, C. (2018): A Stochastic Simulation-Based Holistic Evaluation Approach with DEA for Vendor Selection. Computers & Operations Research 100: 368378. https://doi.org/10.1016/j.cor.2017.08.005.

    • Search Google Scholar
    • Export Citation
  • Ramanathan, R. (2007): Supplier Selection Problem: Integrating DEA with the Approaches of Total Cost of Ownership and AHP. Supply Chain Management: An International Journal 12(4): 258261. https://doi.org/10.1108/13598540710759772.

    • Search Google Scholar
    • Export Citation
  • Rashidi, K.Cullinane, K. (2019): A Comparison of Fuzzy DEA and Fuzzy TOPSIS in Sustainable Supplier Selection: Implications for Sourcing Strategy. Expert Systems with Applications 121: 266281. https://doi.org/10.1016/j.eswa.2018.12.025.

    • Search Google Scholar
    • Export Citation
  • Roodhooft, F.Konings, J. (1997): Vendor Selection and Evaluation an Activity Based Costing Approach. European Journal of Operational Research 96(1): 97102. https://doi.org/10.1016/0377-2217(95)00383-5.

    • Search Google Scholar
    • Export Citation
  • Saen R. F. (2007): Supplier Selection in the Presence of Both Cardinal and Ordinal Data. European Journal of Operational Research 183: 741747. https://doi.org/10.1016/j.ejor.2006.10.022.

    • Search Google Scholar
    • Export Citation
  • Saen, R. F. (2010): Developing a New Data Envelopment Analysis Methodology for Supplier Selection in the Presence of Both Undesirable Outputs and Imprecise Data. The International Journal of Advanced Manufacturing Technology 51(9–12): 12431250. https://doi.org/10.1007/s00170-010-2694-3.

    • Search Google Scholar
    • Export Citation
  • Sarkar, A.Mohapatra, P. K. (2006): Evaluation of Supplier Capability and Performance: A Method for Supply Base Reduction. Journal of Purchasing and Supply Management 12(3): 148163. https://doi.org/10.1016/j.pursup.2006.08.003.

    • Search Google Scholar
    • Export Citation
  • Sarkis, J (2007) Preparing Your Data for DEA. In: Zhu, J.Cook, W. D. (eds): Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Boston, MA: Springer, pp. 305320. https://doi.org/10.1007/978-0-387-71607-7_17.

    • Search Google Scholar
    • Export Citation
  • Seiford, L. M.Zhu, J. (2002): Modeling Undesirable Factors in Efficiency Evaluation. European Journal of Operational Research 142(1): 1620. https://doi.org/10.1016/S0377-2217(01)00293-4.

    • Search Google Scholar
    • Export Citation
  • Sengupta, J. K. (1987): Production Frontier Estimation to Measure Efficiency: A Critical Evaluation in Light of Data Envelopment Analysis. Managerial and Decision Economics 8(2): 9399. https://doi.org/10.1002/mde.4090080203.

    • Search Google Scholar
    • Export Citation
  • Sengupta, J. K. (1992): The Maximum Entropy Approach in Production Frontier Estimation. Mathematical Social Sciences 25(1): 4157. https://doi.org/10.1016/0165-4896(92)90024-Y.

    • Search Google Scholar
    • Export Citation
  • Setak, M.Samaneh S.Alimohammadian A. (2012): Supplier Selection and Order Allocation Models in Supply Chain Management: A Review. World Applied Sciences Journal 18(1): 5572. https://doi.org/10.5829/idosi.wasj.2012.18.01.3258.

    • Search Google Scholar
    • Export Citation
  • Shi, P.Yan, B.Shi, S.Ke, C. (2015): A Decision Support System to Select Suppliers for a Sustainable Supply Chain Based on a Systematic DEA Approach. Information Technology and Management 16(1): 3949. https://doi.org/10.1007/s10799-014-0193-1.

    • Search Google Scholar
    • Export Citation
  • Soheilirad, S.Govindan, K.Mardani, A.Zavadskas, E. K.Nilashi, M.Zakuan, N. (2018): Application of Data Envelopment Analysis Models in Supply Chain Management: A Systematic Review and Meta-Analysis. Annals of Operations Research 271: 915969. https://doi.org/10.1007/s10479-017-2605-1.

    • Search Google Scholar
    • Export Citation
  • Soltanifar, M.Sharafi, H. (2022): A Modified DEA Cross Efficiency Method with Negative Data and its Application in Supplier Selection. Journal of Combinatorial Optimization 43: 265296. https://doi.org/10.1007/s10878-021-00765-7.

    • Search Google Scholar
    • Export Citation
  • Sultana, M. N.Rahman, M. H.Al Mamun, A. (2016): Multi Criteria Decision Making Tools for Supplier Evaluation and Selection: A Review. European Journal of Advances in Engineering and Technology 3(5): 5665.

    • Search Google Scholar
    • Export Citation
  • Toloo, M.Nalchigar, S. (2011): A New DEA Method for Supplier Selection in Presence of Both Cardinal and Ordinal Data. Expert Systems with Applications 38(12): 1472614731. https://doi.org/10.1016/j.eswa.2011.05.008.

    • Search Google Scholar
    • Export Citation
  • Tone, K.Sahoo, B. K. (2003): Scale, Indivisibilities and Production Function in Data Envelopment Analysis. International Journal of Production Economics 84(2): 165192. https://doi.org/10.1016/S0925-5273(02)00412-7.

    • Search Google Scholar
    • Export Citation
  • Tracey, M.Leng Tan, C. (2001): Empirical Analysis of Supplier Selection and Involvement, Customer Satisfaction, and Firm Performance. Supply Chain Management: An International Journal 6(4): 174188. https://doi.org/10.1108/EUM0000000005709.

    • Search Google Scholar
    • Export Citation
  • Visani, F.Barbieri, P.Di Lascio, F. M. L.Raffoni, A.Vigo, D. (2016): Supplier’s Total Cost of Ownership Evaluation: a Data Envelopment Analysis Approach. Omega 61: 141154. https://doi.org/10.1016/j.omega.2015.08.001.

    • Search Google Scholar
    • Export Citation
  • Vörösmarty, G.Dobos, I. (2020): A Literature Review of Sustainable Supplier Evaluation with Data Envelopment Analysis. Journal of Cleaner Production 264: 121672. https://doi.org/10.1016/j.jclepro.2020.121672.

    • Search Google Scholar
    • Export Citation
  • Wang, Y. M.Greatbanks, R.Yang, J. B. (2005): Interval Efficiency Assessment Using Data Envelopment Analysis. Fuzzy Sets and Systems 153(3): 347370. https://doi.org/10.1016/j.fss.2004.12.011.

    • Search Google Scholar
    • Export Citation
  • Weber, C. A.Current, J. R.Benton, W. C. (1991): Vendor Selection Criteria and Methods. European Journal of Operational Research 50(1): 218. https://doi.org/10.1016/0377-2217(91)90033-R.

    • Search Google Scholar
    • Export Citation
  • Wen, M.Zu, T.Guo, M.Kang, R.Yang, Y. (2018): Optimization of Spare Parts Varieties Based on Stochastic DEA Model. IEEE Access 6: 2217422183. https://doi.org/10.1109/ACCESS.2018.2829480.

    • Search Google Scholar
    • Export Citation
  • Wu, C.Barnes, D. (2011): A Literature Review of Decision-Making Models and Approaches for Partner Selection in Agile Supply Chains. Journal of Purchasing and Supply Management 17(4): 256274. https://doi.org/10.1016/j.pursup.2011.09.002.

    • Search Google Scholar
    • Export Citation
  • Xu, H.Chen, L.Li, Q.Yang, J. (2021): A Multi-Attribute Decision Method under Uncertainty Environment Conditions – the Green Supplier Evaluation Perspective. International Journal of Environmental Research and Public Health 18(1): 344. https://doi.org/10.3390/ijerph18010344.

    • Search Google Scholar
    • Export Citation
  • Zeydan, M.Çolpan, C.Çobanoğlu, C. (2011): A Combined Methodology for Supplier Selection and Performance Evaluation. Expert Systems with Applications 38(3): 27412751. https://doi.org/10.1016/j.eswa.2010.08.064.

    • Search Google Scholar
    • Export Citation
  • Zimmer, K.Fröhling, M.Schultmann, F. (2016): Sustainable Supplier Management–A Review of Models Supporting Sustainable Supplier Selection, Monitoring and Development. International Journal of Production Research 54(5): 14121442. https://doi.org/10.1080/00207543.2015.1079340.

    • Search Google Scholar
    • Export Citation
  • Agarwal, P.Sahai, M.Mishra V.Bag M.Singh V. (2011): A Review of Multi-Criteria Decision Making Techniques for Supplier Evaluation and Selection. International Journal of Industrial Engineering Computations 2(4): 801810. https://doi.org/10.5267/j.ijiec.2010.06.004.

    • Search Google Scholar
    • Export Citation
  • Ahmed, M. U.Shafiq, A.Mahmoodi F. (2022): The Role of Supply Chain Analytics Capability and Adaptation in Unlocking Value from Supply Chain Relationships. Production Planning & Control 33(8): 774789. https://doi.org/10.1080/09537287.2020.1836416.

    • Search Google Scholar
    • Export Citation
  • Alikhani, R.Torabi A. S.Altay N. (2019): Strategic Supplier Selection under Sustainability and Risk Criteria. International Journal of Production Economics 208: 6982. https://doi.org/10.1016/j.ijpe.2018.11.018.

    • Search Google Scholar
    • Export Citation
  • Amindoust, A.Shamsuddin, A.Saghafinia, A. (2013): Using Data Envelopment Analysis for Green Supplier Selection in Manufacturing under Vague Environment. Advanced Materials Research 62216821685. https://doi.org/10.4028/www.scientific.net/AMR.622-623.1682.

    • Search Google Scholar
    • Export Citation
  • Azadeh, A.Siadatian, R.Rezaei-Malek M.Rouhollah, F. (2017): Optimization of Supplier Selection Problem by Combined Customer Trust and Resilience Engineering under Uncertainty. International Journal of System Assurance Engineering and Management 8(2): 15531566. https://doi.org/10.1007/s13198-017-0628-2.

    • Search Google Scholar
    • Export Citation
  • Azadi, M.Mirhedayatian, S. M.Saen, R. F.Hatamzad, M.Momeni, E. (2017): Green Supplier Selection: a Novel Fuzzy Double Frontier Data Envelopment Analysis Model to Deal with Undesirable Outputs and Dual-Role Factors. International Journal of Industrial and Systems Engineering 25(2): 160181. https://doi.org/10.1504/IJISE.2017.081516.

    • Search Google Scholar
    • Export Citation
  • Azizi, H. (2013): A Note on “A Decision Model for Ranking Suppliers in the Presence of Cardinal and Ordinal Data, Weight Restrictions, and Nondiscriminatory Factors. Annals of Operations Research 211(1): 4954. https://doi.org/10.1007/s10479-009-0556-x.

    • Search Google Scholar
    • Export Citation
  • Braglia, M.Petroni, A. (2000): A Quality Assurance-Oriented Methodology for Handling Trade-Offs in Supplier Selection. International Journal of Physical Distribution & Logistics Management 30(2): 96112. https://doi.org/10.1108/09600030010318829.

    • Search Google Scholar
    • Export Citation
  • Chai, J.Ngai, E. W. (2020): Decision-making Techniques in Supplier Selection: Recent Accomplishments and what Lies Ahead. Expert Systems with Applications 140: 112903. https://doi.org/10.1016/j.eswa.2019.112903.

    • Search Google Scholar
    • Export Citation
  • Charnes, A.Cooper, W. W.Rhodes, E. (1978): Measuring the Efficiency of Decision Making Units. European Journal of Operational Research 2(6): 429444. http://dx.doi.org/10.1016/0377-2217(78)90138-8.

    • Search Google Scholar
    • Export Citation
  • Chen, C. T.Lin, C. T.Huang, S. F. (2006): A Fuzzy Approach for Supplier Evaluation and Selection in Supply Chain Management. International Journal of Production Economics 102(2): 289301. https://doi.org/10.1016/j.ijpe.2005.03.009.

    • Search Google Scholar
    • Export Citation
  • Cole, R.Aitken, J. (2019): Selecting Suppliers for Socially Sustainable Supply Chain Management: Post-exchange Supplier Development Activities as Pre-selection Requirements. Production Planning & Control 30(14): 11841202. https://doi.org/10.1080/09537287.2019.1595208.

    • Search Google Scholar
    • Export Citation
  • Cook, W. D.Seiford, L. M. (2009): Data Envelopment Analysis (DEA)–Thirty Years On. European Journal of Operational Research 192(1): 117. https://doi.org/10.1016/j.ejor.2008.01.032.

    • Search Google Scholar
    • Export Citation
  • Cooper, W. W.Seiford, L. M.Tone, K. (2007): Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. New York: Springer.

    • Search Google Scholar
    • Export Citation
  • Daraio, C.Kerstens, K. H.Nepomuceno, T. C. C.Sickles, R. (2019): Productivity and Efficiency Analysis Software: an Exploratory Bibliographical Survey of the Options. Journal of Economic Surveys 33(1): 85100. https://doi.org/10.1111/joes.12270.

    • Search Google Scholar
    • Export Citation
  • Dickson, G. W. (1966): An Analysis of Vendor Selection Systems and Decisions. Journal of Purchasing 2(1): 517. https://doi.org/10.1111/j.1745-493X.1966.tb00818.x.

    • Search Google Scholar
    • Export Citation
  • Dobos, I.Vörösmarty, G. (2019a): Inventory-related Costs in Green Supplier Selection Problems with Data Envelopment Analysis (DEA). International Journal of Production Economics 209: 374380. https://doi.org/10.1016/j.ijpe.2018.03.022.

    • Search Google Scholar
    • Export Citation
  • Dobos, I.Vörösmarty, G. (2019b): Evaluating Green Suppliers: Improving Supplier Performance with DEA in the Presence of Incomplete Data. Central European Journal of Operations Research 27(2): 483495. https://doi.org/10.1007/s10100-018-0544-9.

    • Search Google Scholar
    • Export Citation
  • Dobos, I.Vörösmarty, G. (2021): Green Supplier Selection Using a Common Weights Analysis of DEA and EOQ Types of Order Allocation. Managerial and Decision Economics 42(3): 612621. https://doi.org/10.1002/mde.3258.

    • Search Google Scholar
    • Export Citation
  • Dyson, R. G.Allen, R.Camanho, A. S.Podinovski, V. V.Sarrico, C. S.Shale, E. A. (2001). Pitfalls and Protocols in DEA. European Journal of Operational Research 132(2): 245259. https://doi.org/10.1016/S0377-2217(00)00149-1.

    • Search Google Scholar
    • Export Citation
  • Dutta, P.Jaikumar, B.Arora, M. S. (2022): Applications of Data Envelopment Analysis in Supplier Selection between 2000 and 2020: a Literature Review. Annals of Operations Research 315(2): 13991454. https://doi.org/10.1007/s10479-021-03931-6.

    • Search Google Scholar
    • Export Citation
  • Ebrahimi, B.Dellnitz, A.Kleine, A.Tavana, M. (2021): A Novel Method for Solving Data Envelopment Analysis Problems with Weak Ordinal Data Using Robust Measures. Expert Systems with Applications 164: 113835. https://doi.org/10.1016/j.eswa.2020.113835.

    • Search Google Scholar
    • Export Citation
  • Färe, R.Grosskopf, S. (2013): DEA, Directional Distance Functions and Positive, Affine Data Transformation. Omega 41(1): 2830. https://doi.org/10.1016/j.omega.2011.07.011.

    • Search Google Scholar
    • Export Citation
  • Giunipero, L. C.Aly Eltantawy, R. (2004): Securing the Upstream Supply Chain: a Risk Management Approach. International Journal of Physical Distribution & Logistics Management 34(9): 698713. https://doi.org/10.1108/09600030410567478.

    • Search Google Scholar
    • Export Citation
  • Glock, C. H.Grosse, E. H.Ries, J. M. (2017): Reprint of “Decision Support Models for Supplier Development: Systematic Literature Review and Research Agenda”. International Journal of Production Economics 194: 246260. https://doi.org/10.1108/09600030410567478.

    • Search Google Scholar
    • Export Citation
  • Hatefi, S. M. (2017): A Multi-Objective Model for Supplier Evaluation and Selection in the Presence of Both Cardinal and Imprecise Data. International Journal of Integrated Engineering 9(2): 917.

    • Search Google Scholar
    • Export Citation
  • He, X.Zhang, J. (2018): Supplier Selection Study under the Respective of Low-Carbon Supply Chain: A Hybrid Evaluation Model Based on FA-DEA-AHP. Sustainability 10(2): 564. https://doi.org/10.3390/su10020564.

    • Search Google Scholar
    • Export Citation
  • Ho, W.Xu, X.Dey, P. K. (2010): Multi-criteria Decision Making Approaches for Supplier Evaluation and Selection: A Literature Review. European Journal of Operational Research 202(1): 1624. https://doi.org/10.1016/j.ejor.2009.05.009.

    • Search Google Scholar
    • Export Citation
  • Igarashi, M.de Boer, L.Fet, A. M. (2013): What Is Required for Greener Supplier Selection? A Literature Review and Conceptual Model Development. Journal of Purchasing and Supply Management 19(4): 247263. https://doi.org/10.1016/j.pursup.2013.06.001.

    • Search Google Scholar
    • Export Citation
  • Izadikhah, M.Saen, R. F. (2016): Evaluating Sustainability of Supply Chains by Two-Stage Range Directional Measure in the Presence of Negative Data. Transportation Research Part D: Transport and Environment 49: 110126. https://doi.org/10.1016/j.trd.2016.09.003.

    • Search Google Scholar
    • Export Citation
  • Kannan, V. R.Tan, K. C. (2002): Supplier Selection and Assessment: Their Impact on Business Performance. Journal of Supply Chain Management 38(3): 1121. https://doi.org/10.1111/j.1745-493X.2002.tb00139.x.

    • Search Google Scholar
    • Export Citation
  • Karsak, E. E.Dursun, M. (2014): An Integrated Supplier Selection Methodology Incorporating QFD and DEA with Imprecise Data. Expert Systems with Applications 41(16): 69957004. https://doi.org/10.1016/j.eswa.2014.06.020.

    • Search Google Scholar
    • Export Citation
  • Kohl, S.Schoenfelder, J.Fügener, A.Brunner, J. O. (2019). The Use of Data Envelopment Analysis (DEA) in Healthcare with a Focus on Hospitals. Health Care Management Science 22(2): 245286. https://doi.org/10.1007/s10729-018-9436-8.

    • Search Google Scholar
    • Export Citation
  • Konys, A. (2019): Green Supplier Selection Criteria: from a Literature Review to a Comprehensive Knowledge Base. Sustainability 11(15): 4208. https://doi.org/10.3390/su11154208.

    • Search Google Scholar
    • Export Citation
  • Kuo, R. J.Wang, Y. C.Tien, F. C. (2010): Integration of Artificial Neural Network and MADA Methods for Green Supplier Selection. Journal of Cleaner Production 18(12): 11611170. https://doi.org/10.1016/j.jclepro.2010.03.020.

    • Search Google Scholar
    • Export Citation
  • Liu, Y.Zhu, Q.Seuring, S. (2017): Linking Capabilities to Green Operations Strategies: The Moderating Role of Corporate Environmental Proactivity. International Journal of Production Economics 187: 182195. https://doi.org/10.1016/j.ijpe.2017.03.007.

    • Search Google Scholar
    • Export Citation
  • Lovell, C. K.Pastor, J. T. (1995): Units Invariant and Translation Invariant DEA Models. Operations Research Letters 18(3): 147151. https://doi.org/10.1016/0167-6377(95)00044-5.

    • Search Google Scholar
    • Export Citation
  • Luzzini, D.Caniato, F.Spina, G. (2014): Designing Vendor Evaluation Systems: An Empirical Analysis. Journal of Purchasing and Supply Management 20(2): 113129. https://doi.org/10.1016/j.pursup.2014.03.002.

    • Search Google Scholar
    • Export Citation
  • Mahdiloo, M.Saen, R. F.Lee, K. H. (2015): Technical, Environmental and Eco-Efficiency Measurement for Supplier Selection: An Extension and Application of Data Envelopment Analysis. International Journal of Production Economics 168: 279289. https://doi.org/10.1016/j.ijpe.2015.07.010.

    • Search Google Scholar
    • Export Citation
  • Mohamad, N. H.Said, F. (2012): Using Super-efficient DEA Model to Evaluate the Business Performance in Malaysia. World Applied Sciences Journal 17(9): 11671177.

    • Search Google Scholar
    • Export Citation
  • Mohammady Garfamy, R. (2006): A Data Envelopment Analysis Approach Based on Total Cost of Ownership for Supplier Selection. Journal of Enterprise Information Management 19(6): 662678. https://doi.org/10.1108/17410390610708526.

    • Search Google Scholar
    • Export Citation
  • Nair, A.Jayaram, J.Das, A. (2015): Strategic Purchasing Participation, Supplier Selection, Supplier Evaluation and Purchasing Performance. International Journal of Production Research 53(20): 62636278. https://doi.org/10.1080/00207543.2015.1047983.

    • Search Google Scholar
    • Export Citation
  • Park, S.Ok, C.Ha, C. (2018): A Stochastic Simulation-Based Holistic Evaluation Approach with DEA for Vendor Selection. Computers & Operations Research 100: 368378. https://doi.org/10.1016/j.cor.2017.08.005.

    • Search Google Scholar
    • Export Citation
  • Ramanathan, R. (2007): Supplier Selection Problem: Integrating DEA with the Approaches of Total Cost of Ownership and AHP. Supply Chain Management: An International Journal 12(4): 258261. https://doi.org/10.1108/13598540710759772.

    • Search Google Scholar
    • Export Citation
  • Rashidi, K.Cullinane, K. (2019): A Comparison of Fuzzy DEA and Fuzzy TOPSIS in Sustainable Supplier Selection: Implications for Sourcing Strategy. Expert Systems with Applications 121: 266281. https://doi.org/10.1016/j.eswa.2018.12.025.

    • Search Google Scholar
    • Export Citation
  • Roodhooft, F.Konings, J. (1997): Vendor Selection and Evaluation an Activity Based Costing Approach. European Journal of Operational Research 96(1): 97102. https://doi.org/10.1016/0377-2217(95)00383-5.

    • Search Google Scholar
    • Export Citation
  • Saen R. F. (2007): Supplier Selection in the Presence of Both Cardinal and Ordinal Data. European Journal of Operational Research 183: 741747. https://doi.org/10.1016/j.ejor.2006.10.022.

    • Search Google Scholar
    • Export Citation
  • Saen, R. F. (2010): Developing a New Data Envelopment Analysis Methodology for Supplier Selection in the Presence of Both Undesirable Outputs and Imprecise Data. The International Journal of Advanced Manufacturing Technology 51(9–12): 12431250. https://doi.org/10.1007/s00170-010-2694-3.

    • Search Google Scholar
    • Export Citation
  • Sarkar, A.Mohapatra, P. K. (2006): Evaluation of Supplier Capability and Performance: A Method for Supply Base Reduction. Journal of Purchasing and Supply Management 12(3): 148163. https://doi.org/10.1016/j.pursup.2006.08.003.

    • Search Google Scholar
    • Export Citation
  • Sarkis, J (2007) Preparing Your Data for DEA. In: Zhu, J.Cook, W. D. (eds): Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. Boston, MA: Springer, pp. 305320. https://doi.org/10.1007/978-0-387-71607-7_17.

    • Search Google Scholar
    • Export Citation
  • Seiford, L. M.Zhu, J. (2002): Modeling Undesirable Factors in Efficiency Evaluation. European Journal of Operational Research 142(1): 1620. https://doi.org/10.1016/S0377-2217(01)00293-4.

    • Search Google Scholar
    • Export Citation
  • Sengupta, J. K. (1987): Production Frontier Estimation to Measure Efficiency: A Critical Evaluation in Light of Data Envelopment Analysis. Managerial and Decision Economics 8(2): 9399. https://doi.org/10.1002/mde.4090080203.

    • Search Google Scholar
    • Export Citation
  • Sengupta, J. K. (1992): The Maximum Entropy Approach in Production Frontier Estimation. Mathematical Social Sciences 25(1): 4157. https://doi.org/10.1016/0165-4896(92)90024-Y.

    • Search Google Scholar
    • Export Citation
  • Setak, M.Samaneh S.Alimohammadian A. (2012): Supplier Selection and Order Allocation Models in Supply Chain Management: A Review. World Applied Sciences Journal 18(1): 5572. https://doi.org/10.5829/idosi.wasj.2012.18.01.3258.

    • Search Google Scholar
    • Export Citation
  • Shi, P.Yan, B.Shi, S.Ke, C. (2015): A Decision Support System to Select Suppliers for a Sustainable Supply Chain Based on a Systematic DEA Approach. Information Technology and Management 16(1): 3949. https://doi.org/10.1007/s10799-014-0193-1.

    • Search Google Scholar
    • Export Citation
  • Soheilirad, S.Govindan, K.Mardani, A.Zavadskas, E. K.Nilashi, M.Zakuan, N. (2018): Application of Data Envelopment Analysis Models in Supply Chain Management: A Systematic Review and Meta-Analysis. Annals of Operations Research 271: 915969. https://doi.org/10.1007/s10479-017-2605-1.

    • Search Google Scholar
    • Export Citation
  • Soltanifar, M.Sharafi, H. (2022): A Modified DEA Cross Efficiency Method with Negative Data and its Application in Supplier Selection. Journal of Combinatorial Optimization 43: 265296. https://doi.org/10.1007/s10878-021-00765-7.

    • Search Google Scholar
    • Export Citation
  • Sultana, M. N.Rahman, M. H.Al Mamun, A. (2016): Multi Criteria Decision Making Tools for Supplier Evaluation and Selection: A Review. European Journal of Advances in Engineering and Technology 3(5): 5665.

    • Search Google Scholar
    • Export Citation
  • Toloo, M.Nalchigar, S. (2011): A New DEA Method for Supplier Selection in Presence of Both Cardinal and Ordinal Data. Expert Systems with Applications 38(12): 1472614731. https://doi.org/10.1016/j.eswa.2011.05.008.

    • Search Google Scholar
    • Export Citation
  • Tone, K.Sahoo, B. K. (2003): Scale, Indivisibilities and Production Function in Data Envelopment Analysis. International Journal of Production Economics 84(2): 165192. https://doi.org/10.1016/S0925-5273(02)00412-7.

    • Search Google Scholar
    • Export Citation
  • Tracey, M.Leng Tan, C. (2001): Empirical Analysis of Supplier Selection and Involvement, Customer Satisfaction, and Firm Performance. Supply Chain Management: An International Journal 6(4): 174188. https://doi.org/10.1108/EUM0000000005709.

    • Search Google Scholar
    • Export Citation
  • Visani, F.Barbieri, P.Di Lascio, F. M. L.Raffoni, A.Vigo, D. (2016): Supplier’s Total Cost of Ownership Evaluation: a Data Envelopment Analysis Approach. Omega 61: 141154. https://doi.org/10.1016/j.omega.2015.08.001.

    • Search Google Scholar
    • Export Citation
  • Vörösmarty, G.Dobos, I. (2020): A Literature Review of Sustainable Supplier Evaluation with Data Envelopment Analysis. Journal of Cleaner Production 264: 121672. https://doi.org/10.1016/j.jclepro.2020.121672.

    • Search Google Scholar
    • Export Citation
  • Wang, Y. M.Greatbanks, R.Yang, J. B. (2005): Interval Efficiency Assessment Using Data Envelopment Analysis. Fuzzy Sets and Systems 153(3): 347370. https://doi.org/10.1016/j.fss.2004.12.011.

    • Search Google Scholar
    • Export Citation
  • Weber, C. A.Current, J. R.Benton, W. C. (1991): Vendor Selection Criteria and Methods. European Journal of Operational Research 50(1): 218. https://doi.org/10.1016/0377-2217(91)90033-R.

    • Search Google Scholar
    • Export Citation
  • Wen, M.Zu, T.Guo, M.Kang, R.Yang, Y. (2018): Optimization of Spare Parts Varieties Based on Stochastic DEA Model. IEEE Access 6: 2217422183. https://doi.org/10.1109/ACCESS.2018.2829480.

    • Search Google Scholar
    • Export Citation
  • Wu, C.Barnes, D. (2011): A Literature Review of Decision-Making Models and Approaches for Partner Selection in Agile Supply Chains. Journal of Purchasing and Supply Management 17(4): 256274. https://doi.org/10.1016/j.pursup.2011.09.002.

    • Search Google Scholar
    • Export Citation
  • Xu, H.Chen, L.Li, Q.Yang, J. (2021): A Multi-Attribute Decision Method under Uncertainty Environment Conditions – the Green Supplier Evaluation Perspective. International Journal of Environmental Research and Public Health 18(1): 344. https://doi.org/10.3390/ijerph18010344.

    • Search Google Scholar
    • Export Citation
  • Zeydan, M.Çolpan, C.Çobanoğlu, C. (2011): A Combined Methodology for Supplier Selection and Performance Evaluation. Expert Systems with Applications 38(3): 27412751. https://doi.org/10.1016/j.eswa.2010.08.064.

    • Search Google Scholar
    • Export Citation
  • Zimmer, K.Fröhling, M.Schultmann, F. (2016): Sustainable Supplier Management–A Review of Models Supporting Sustainable Supplier Selection, Monitoring and Development. International Journal of Production Research 54(5): 14121442. https://doi.org/10.1080/00207543.2015.1079340.

    • Search Google Scholar
    • Export Citation
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2022  
Web of Science  
Total Cites
WoS
not indexed
Journal Impact Factor not indexed
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not indexed
not indexed

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without
Journal Self Cites
not indexed
5 Year
Impact Factor
not indexed
Journal Citation Indicator not indexed
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not indexed

Scimago  
Scimago
H-index
15
Scimago
Journal Rank
0.217
Scimago Quartile Score

Business and International Management Q3
Economics, Econometrics and Finance (miscellaneous) Q3
Industrial Relations Q3
Public Administration Q3
Sociology and Political Science Q3
Strategy and Management Q4

Scopus  
Scopus
Cite Score
1.5
Scopus
Cite Score Rank
Sociology and Political Science 602/1415 (57th PCTL)
General Economics, Econometrics and Finance 131/279 (53rd PCTL)
Industrial Relations 31/57 (46th PCTL)
Public Administration 3126/213 (41th PCTL)
Business and International Management 302/436 (30th PCTL)
Strategy and Management 343/473 (27th PCTL)
Scopus
SNIP
0.468

 

2021  
Web of Science  
Total Cites
WoS
not indexed
Journal Impact Factor not indexed
Rank by Impact Factor

not indexed

Impact Factor
without
Journal Self Cites
not indexed
5 Year
Impact Factor
not indexed
Journal Citation Indicator not indexed
Rank by Journal Citation Indicator

not indexed

Scimago  
Scimago
H-index
13
Scimago
Journal Rank
0,196
Scimago Quartile Score Economics, Econometrics and Finance (miscellaneous) (Q3)
Industrial Relations (Q3)
Sociology and Political Science (Q3)
Business and International Management (Q4)
Public Administration (Q4)
Strategy and Management (Q4)
Scopus  
Scopus
Cite Score
1,2
Scopus
CIte Score Rank
Sociology and Political Science 626/1345 (Q2)
General Economics, Econometrics and Finance 131/260 (Q3)
Industrial Relations 35/57 (Q3)
Public Administration 120/190 (Q3)
Business and International Management 292/423 (Q3)
Strategy and Management 340/456 (Q3)
Scopus
SNIP
0,270

2020  
Scimago
H-index
11
Scimago
Journal Rank
0,157
Scimago
Quartile Score
Business and International Management Q4
Economics, Econometrics and Finance (miscellaneous) Q4
Industrial Relations Q4
Public Administration Q4
Sociology and Political Science Q3
Strategy and Management Q4
Scopus
Cite Score
103/117=0,9
Scopus
Cite Score Rank
Business and International Management 305/399 (Q4)
General Economics, Econometrics and Finance 137/243 (Q3)
Industrial Relations 40/54 (Q3)
Public Administration 116/165 (Q3)
Sociology and Political Science 665/1269 (Q3)
Strategy and Management 351/440 (Q4)
Scopus
SNIP
0,171
Scopus
Cites
157
Scopus
Documents
24
Days from submission to acceptance 148
Days from acceptance to publication 50

 

2019  
Scimago
H-index
10
Scimago
Journal Rank
0,228
Scimago
Quartile Score
Business and International Management Q3
Economics, Econometrics and Finance (miscellaneous) Q3
Industrial Relations Q3
Public Administration Q3
Sociology and Political Science Q3
Strategy and Management Q3
Scopus
Cite Score
87/110=0,8
Scopus
Cite Score Rank
Business and International Management 286/394 (Q3)
General Economics, Econometrics and Finance 125/228 (Q3)
Industrial Relations 38/58 (Q3)
Public Administration 114/157 (Q3)
Sociology and Political Science 645/1243 (Q3)
Strategy and Management 330/427 (Q4)
Scopus
SNIP
0,308
Scopus
Cites
132
Scopus
Documents
22

 

Society and Economy
Publication Model Gold Open Access
Submission Fee none
Article Processing Charge 900 EUR/article with enough waivers
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Sufficient number of full waiver available. Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription Information Gold Open Access

Society and Economy
Language English
Size B5
Year of
Foundation
1972
Volumes
per Year
1
Issues
per Year
4
Founder Budapesti Corvinus Egyetem
Founder's
Address
H-1093 Budapest, Hungary Fővám tér 8.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 1588-9726 (Print)
ISSN 1588-970X (Online)