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Each production unit is responsible for the protection of the environment. The restricted undesirable production effects lower environmental damage. This paper emphasizes a proportional reduction of the undesirable outputs, and it supports the growth of desirable outputs as much as possible as well. The two-stage proposed model not only considers the viewpoint of the managers to follow the environmental regulations but also it assigns some bounds on producing undesirable factors according to international environmental protocols. Additionally, the restricted bounds on the undesirable outputs, in both stages, enhance the discriminatory ability of the model.

Two-stage network structure based on Data Envelopment Analysis (DEA) is applied as the main methodology for this paper. The advantages of the proposed model are appointed to assess the environmental units.

Comparing with the existing models, the proposed approach presents a new two-stage model to deal with the environmental issues. Furthermore, the discriminatory ability of the efficiency scores is improved. The distribution of this model is greater than the existing ones.

This paper is fully written, submitted and revised during limitations caused by coronavirus .

The proposed method is employed in two different cases. The efficiency scores of 25 power plants and 13 poultry farms are determined. In fact, the undesirable outputs never meet zero in the process of production but they can be reduced. The results of this research support the effect of the undesirable factors' restriction on the reduction scenario. Both of the examples show that imposing the upper bounds for the undesirable products provide low-efficiency results in comparison with the existing model. On the other hand, the results cover the arguments of sustainability in the evaluation of environmental efficiency.

In the production process, desirable outputs and undesirable factors are produced jointly so undesirable factors never meet zero. This paper develops a new two-stage method to reduce the undesirable outputs at each stage. First, the model confirms the reduction of undesirable outputs. Second, this model imposes restrictions on intermediate and final undesirable outputs according to environmental rights and the concerns of the managers. The model increases the discrimination of the efficiency assessment of real-life two-stage environmental systems as well. Then it focuses on the production of desirable outputs. The new objective function is defined according to the aim of the proposed model that not only declares better efficiency decomposition to the individual system but also the efficiency score is evaluated for each stage.

The purpose of this paper is to monitor the environmental efficiency of suppliers in the presence of undesirable output and dual-role factors with static and dynamic aspects. Meanwhile, it also aims to explain the main reason for the low efficiency of suppliers.

The authors propose a modified data model considering undesirable output and dual-role factors. The study integrates the modified data envelopment analysis model into the distance function of the Malmquist–Luenberger index. Moreover, this study uses the global benchmark technology to formulate a two-stage model. To verify the validity of this model, a model application is conducted on an automotive spare components company in China.

The results identify the unique status of dual-role factors based on the global optimality of the model and then categorize inefficient suppliers in an individual evaluation cycle. In addition, each supplier is projected on a frontier curve after obtaining the improved data. Furthermore, through the status plot of M-L and its components, this paper concludes that efficiency scale change is the main reason for the gap in ecological performance between different suppliers.

The proposed model considers both undesirable output and dual-role factors; however, variables with different features, such as imprecise, fuzzy and qualitative characteristics, can be embedded into the presented two-stage model.

Evaluating green suppliers through multiple consecutive evaluation cycles will aid a company in effectively managing its key suppliers. Furthermore, the evaluation provides policy guidance for further improvement of suppliers.

The determination of input and output factors is a well-known source of pitfalls when applying data envelopment analysis (DEA). The purpose of this paper is to contribute to overcome the respective problems of input/output factor determination related to factor selection, dual-role factors and undesirable factors.

The problems of input/output factor determination are discussed from a goal-oriented perspective, shedding a new light on the role of input/output factors in DEA. This is exemplified by the case of measuring pharmacy stores’ efficiency concerning their goal of customer retention.

The findings suggest to applying a generalized DEA (GDEA). The three steps of this approach include the development of a system of objectives, the derivation of corresponding performance criteria as well as the construction of cost and benefit functions. These functions build the basis for GDEA models, of which one is exemplarily described and applied to the customer retention case.

While traditional DEA implicitly assumes linear cost and benefit functions, GDEA requires to explicitly specifying these functions. In doing so, the approach contributes to solve the problem of factor selection, the problem of dual-role factors and the problem of undesirable factors.

For determining input/output factors in a consistent and transparent manner, it is recommended to apply GDEA in practical benchmarking studies.

GDEA integrates well-known concepts of multi-criteria decision making into traditional DEA. The new approach helps to cope with the challenges of input/output factor determination in DEA.

The aim of this paper is to show current position of domestic airports and provide an improvement scheme through the comparative analysis of efficiency and social efficiency. We used SBM (Slack Based Measure) for efficiency and undesirable output model that is extended from SBM for social efficiency. In addition, window analysis is used for analyzing the trend of the values. For the scope of this study, we analyzed fourteen airports in Korea from 2004 to 2009. In the models, we considered the length of runway, the number of employees and terminal area as input factors, and the number of passengers, the amount of cargo and the number of flights as desirable outputs and directly controllable CO2 emissions from airports as undesirable output. The results show that all of the efficiencies are higher than the social efficiencies and both of them are decreasing by years. To improve social efficiency in 2009, the average amounts of reduced CO2 emissions which account for 48.3% of the total emissions are required.

Data envelopment analysis (DEA) is a significant method for measuring the relative efficiency of decision making units (DMUs) that use the least inputs, produce the most desirable outputs and emit the least undesirable outputs in order to maximize their profits. In DEA, detecting an optimal scale size (OSS) is also vital and could be more applicable in economic activities when there are integer and undesirable measures. The purpose of this research is to measure average-profit efficiency (APE) and OSSs with integer data and undesirable outputs.

This study presents an alternative concept of APE using the concepts of most productive scale size (MPSS), profit efficiency and scales, containing desirable and undesirable outputs along with integer and non-integer measures. In fact, the OSS minimizes APE as the optimal scale, which is the ratio of the profit efficiency to the radial average output. Considering the prices of the inputs and desirable outputs, as well as the lack of any specific weight for the undesirable outputs, a two-step model for the numerical calculation of OSS is presented. In addition, the proposed approach is applied to a real data set of Iranian gas companies while there are integer measures and undesirable outputs.

The results show the introduced approach is beneficial to estimate OSSs from the aspect of maximizing profits of firms with undesirable outputs and integer values.

Estimating OSSs is the significant issue for managers, but its investigation in the presence of integer measures and undesirable outputs is presently under-considered.

Resource scheduling is the study of how to effectively measure, evaluate, analyze, and dispatch resources in order to meet the demands of corresponding tasks. Aiming at the problem of resource scheduling in the private cloud environment, the purpose of this paper is to propose a resource scheduling approach from an efficiency priority point of view.

To measure the computational efficiencies for the resource nodes in a private cloud environment, the data envelopment analysis (DEA) approach is incorporated and a suitable DEA model is proposed. Then, based on the efficiency scores calculated by the proposed DEA model for the resource nodes, the 0-1 programming technique is introduced to build a simple resource scheduling model.

The proposed DEA model not only has the ability of ranking all the decision-making units into different positions but also can handle non-discretionary inputs and undesirable outputs when evaluating the resource nodes. Furthermore, the resource scheduling model can generate for the calculation tasks an optimal resource scheduling scheme that has the highest total computational efficiency.

The proposed method may also be used in studies of resource scheduling studies in the environments of public clouds and hybrid clouds.

The proposed approach can achieve the goal of resource scheduling in private cloud computing platforms by attaining the highest total computational efficiency, which is very significant in practice.

This paper uses an efficiency priority point of view to solve the problem of resource scheduling in private cloud environments.

This study aims to examine how environmental, social and governance (ESG) initiatives and ISO 14001, which is an internationally agreed standard to set out the requirements for an environmental management system, affect firm performance in the context of the Industry 4.0 supply chain.

The authors develop a new chance-constrained network data envelopment analysis (DEA) in the presence of non-positive data to estimate innovation, operational and profitability performances for three main relation groups (suppliers, partners and customers) in Microsoft's supply chain.

Results of this study show the following: (1) the application of ISO 14001 will reduce profitability but increase overall performance (OP); (2) ESG implementation has a convex U-shaped influence on profitability and OP, which means that firms will benefit when ESG investment goes beyond a particular level; (3) the nonlinear U-shape is presented in the E and G components, but not in the S of the individual ESG initiatives, and (4) only specific subcomponents of S and G in the subcomponent of individual ESG initiatives are nonlinearly connected to OP. Research's results reveal that the customer group has a higher performance value than the other two groups, which suggests that this group will create competitive advantages for Microsoft.

Overall, the authors provide an insightful viewpoint into supply chain management by examining the ESG initiatives, ISO 14001 and performances of Microsoft's supply chain.

This study aims to make investment decisions in stock markets using forecasting-Markowitz based decision-making approaches.

The authors’ approach offers the use of time series prediction methods including autoregressive, autoregressive moving average and artificial neural network, rather than calculating the expected rate of return based on distribution.

The results show that using time series prediction methods has a significant effect on improving investment decisions and the performance of the investments.

In this study, in contrast to previous studies, the alteration in the Markowitz model started with the investment expected rate of return. For this purpose, instead of considering the distribution of returns and determining the expected returns, time series prediction methods were used to calculate the future return of each asset. Then, the results of different time series methods replaced the expected returns in the Markowitz model. Finally, the overall performance of the method, as well as the performance of each of the prediction methods used, was examined in relation to nine stock market indices.

The purpose of this paper is to combine the uncertain methods of type-2 fuzzy sets and data envelopment analysis (DEA) evaluation model together. A new type-2 fuzzy DEA efficiency assessment method is established. Then the proposed procedure is applied to the poverty alleviation problem.

The research method is the DEA model, which is an effective method for efficiency assessment of social–economic systems. Considering the existence of the same efficiency values that cannot be ranked in the proposed DEA model, the balance index is introduced to solve the ranking problem of decision-making units effectively.

The results show that the proposed method can not only measure the efficiency of the existence of uncertain information but also deal with the ranking of multiple efficient decision-making units.

This paper selects type-2 fuzzy DEA model to express a lot of uncertain information in efficiency evaluation problems. We use the parameter decomposition method of type-2 fuzzy programming or the type-2 expectation values indirectly. The balance index is proposed to further distinguish the multiple effective decision-making units. Furthermore, this paper selects rural poverty alleviation in Hainan Province as a case study to verify the feasibility of the method. The relative efficiency values in different years are calculated and analyzed.

The purpose of this paper is introducing an alternative model to measure the relative efficiency of observations with undesirable products. Describing the reference set and benchmarking.

In this paper, an alternative definition of weak disposability assumption is introduced to handle undesirable outputs. Actually, two types of undesirable outputs are addressed and a substitute definition of weak disposability is presented.

Using this assumption a linear production technology set along with a performance analysis model is constructed to assess the relative efficiency of the decision-making units. To illustrate the radial application of the proposed approach, a real case on transportation system of USA during 1992-2009 is given.

To date, data envelopment analysis studies have investigated undesirable outputs by the assumption of weak disposability, defined as the proportional contraction of good and bad products, which leads to the null-joint assumption between good and bad outputs. Therefore, the only way to produce no undesirable outputs is producing zero desirable outputs. So the production process should be stopped while it is not economically cost-effective. However, in some processes there are some undesirable outputs, which are decreased with non-same percentages. So these undesirable outputs can be stopped while the good outputs have a strictly positive value. In this situation, the good outputs are not null-joint with this type of bad outputs. In the current paper, a new definition of the weak disposability of outputs was represented while two groups of undesirable outputs were considered. Hence, desirable outputs and the first kind of undesirable outputs were decreased proportionally. However, the reduction value was different for the second kind of undesirable outputs. Hence, the null-joint assumption is removed from the production technology. Then, a new technology was proposed based on five postulates as inclusion of observations, free disposability of desirable outputs and inputs, new weak disposability, convexity and minimum extrapolation.