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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 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.

The purpose of this study is to measure the technical efficiency of 20 Algerian insurance companies from 2016 to 2020, by using slacks-based measure (slacks-based measure [SBM] data envelopment analysis [DEA]) model. This research aims to provide a comprehensive assessment of this companies' efficiency, taking into account both the desirable and undesirable outputs.

The study uses a nonoriented, SBM model with the assumption of constant returns to scale to estimate the technical efficiency of commercial insurance companies over a five-year period. The inputs used are labor expense, agent expense and investments, while the outputs included are gross premiums and investment income as desirable outputs and gross claims as undesirable output.

Among 20 insurance companies evaluated, only 5 companies consistently achieved technical efficiency during the study period (Caisse Nationale de Mutualité Agricole [CNMA], MACIR, CARDIF, MUTUALISTE and AGLIC); so they represent the best practices in the Algerian insurance sector, with overall average of the technical efficiency is 81%. However, the reference sets analysis showed that CNMA and AGLIC had high robustness. Also, the results demonstrate the impact of ignoring the undesirable outputs on the accuracy of the assessment.

The sample of the study consists of the active insurance companies in Algeria, based on the Annual Insurance Reports of Algeria; there are 20 companies as shown in the table. The data are taken from the annual reports of insurance companies during the 2020 period, issued by the Algerian Ministry of Finance.

The challenge for insurance company is how to find a balance between reducing claims paid and simultaneously improving the quality of insurance services. In fact, it is observed that studies evaluating their efficiency ignore claims in the analysis process. Therefore, the study highlights the importance of considering undesirable outputs within the DEA framework; this allows for a more accurate assessment of the company's performance and helps in improvement. Furthermore, although the insurance sector plays a crucial role, it has not received enough research attention compared to other financial sectors, especially in Arab and developing countries.

The literature on efficiency assessment in the insurance companies shows a lack of addressing undesirable outputs (such as claims) within the DEA framework; so this study aims at bridging this research gap. Also, the study provides an overview of the efficiency of Algerian insurance companies.

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.

In this paper, the authors extend the goal-directed benchmarking theory proposed by Stewart for benchmarking and selecting suppliers. This extension is in recognition of the fact that benchmarking for suppliers is more than a pure monitoring process and includes a component of future planning. The paper aims to discuss these issues.

In this paper, the proposed model utilizes a goal programming structure to find points on the efficient frontier which are realistically attainable by suppliers in the presence of undesirable outputs, but at the same time achieving a closer method to long-term organizational goals (as distinct from the local performance of individual suppliers).

The contributions of the current paper are as follows: the proposed model considers undesirable outputs in the context of goal-directed benchmarking. The proposed model does not demand weights from the decision maker. The proposed model can be easily computerized, enabling it to serve as a decision making tool to assist decision makers. For the first time, the proposed model is applied for the supplier selection and benchmarking.

To the best of knowledge of the authors, there is not any reference that discusses supplier selection problem and benchmarking in the presence of undesirable outputs in the context of goal-directed benchmarking.

The objective of this paper is to propose a new data envelopment analysis (DEA) model for assessing sustainability of suppliers with partial impacts between inputs, desirable outputs and undesirable outputs.

This paper examines partial impacts of inputs on desirable and undesirable outputs and applies weak disposability assumption to propose a novel DEA model to determine the sustainability of suppliers.

This paper shows the type of resource sharing in DEA models and takes into account sustainable development and sustainability assessment concepts for sustainable supplier selection problem and develops a DEA model for selecting the most sustainable suppliers with partial sharing of resources. To select the most sustainable suppliers, this model helps managers to consider aggregate efficiency, overall efficiency and bundle efficiency. The paper introduces the supplier which is efficient at all levels as the most sustainable supplier.

For the first time, this paper suggests a new DEA model by partial impact between inputs and good outputs/bad outputs for selecting sustainable supplier and deals with the situations in which each supplier has several subunits. The new model calculates aggregate efficiency, overall efficiency and subunit efficiency of supplier. paper introduces the supplier which is efficient in all levels including aggregate efficiency, overall efficiency and subunit efficiency as the best supplier.

Comparing conventional data envelopment analysis (DEA) model with contemporary Seiford and Zhu model, this study aims to evaluate the technical efficiency (TE) of Indian banks from 1998/99 to 2016/17 in the presence of non-performing loans (NPLs).

To examine TE, this study has considered a novel approach, i.e. linear monotone decreasing transformation as suggested by Seiford and Zhu (2002), which treats undesirable output as a desirable output in the framework of Charnes, Cooper and Rhodes (CCR)-based output-oriented DEA approach. In particular, to remove the biasness from the estimated efficiency scores, Simar Wilson (1998, Algorithm #1) has been applied, which is perhaps the first attempt in this kind of literature till now. This study further tries to investigate the notion of sigma and unconditional β-convergence in TE using two-step system generalized method of moments model in dynamic panel framework.

Treatment of NPLs using conventional DEA model misinterprets the TE scores, while a true picture emerges when the NPLs are correctly accounted as an undesirable output in banks’ loans production process. Efficiency has declined during the crisis years, but it recovered immediately after the crisis years in India. However, a sudden and steep deterioration in efficiency scores has been seen from 2013 till the most recent study period. Public sector banks and old private banks have reported higher average efficiency scores than new private banks (NPBs) and foreign banks (FBs) in India. However, FBs are the only commercial banks that maintained their efficiency levels during crisis years in India. This study also saw the persistence and presence of σ-convergence phenomena in TE for Indian banks, reflecting the ability to reach up to “Catch-up” phenomenon owing to the lower dispersion and persistence of convergence in TE by the Indian banks.

The actual efficiency score can only be estimated when the NPL will be considered as an undesirable output rather than a desirable output when designing the loan production process of banks. Although the ownership clusters of all commercial banks in India need to formulate stricter policies to increase the level of assets quality and efficiency, but, NPBs need to pay some more efforts in this direction. This study’s outcome has the potential to provide useful information for regulators and policymakers, which suggests that in which direction or in which clusters improvement are needed to raise the level of asset quality and technical efficiency in the coming years.

For a long time, there has been the existence of trade-offs between researchers, like which is the best model for accounting for NPLs? Traditional or contemporary? Thus, our study aims to add knowledge to the limited stock of NPL modelling in the efficiency literature. Dynamic convergence in TE scores in Indian banks has yet not to be tested, which is another novelty of the study.

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.

Cement as one of the major components of construction activities, releases a tremendous amount of carbon dioxide (CO₂) into the atmosphere, resulting in adverse environmental impacts and high energy consumption. Increasing demand for CO₂ consumption has urged construction companies and decision-makers to consider ecological efficiency affected by CO₂ consumption. Therefore, this paper aims to develop a method capable of analyzing and assessing the eco-efficiency determining factor in Iran’s 22 local cement companies over 2015–2019.

This research uses two well-known artificial intelligence approaches, namely, optimization data envelopment analysis (DEA) and machine learning algorithms at the first and second steps, respectively, to fulfill the research aim. Meanwhile, to find the superior model, the CCR model, BBC model and additive DEA models to measure the efficiency of decision processes are used. A proportional decreasing or increasing of inputs/outputs is the main concern in measuring efficiency which neglect slacks, and hence, is a critical limitation of radial models. Thus, the additive model by considering desirable and undesirable outputs, as a well-known DEA non-proportional and non-radial model, is used to solve the problem. Additive models measure efficiency via slack variables. Considering both input-oriented and output-oriented is one of the main advantages of the additive model.

After applying the proposed model, the Malmquist productivity index is computed to evaluate the productivity of companies over 2015–2019. Although DEA is an appreciated method for evaluating, it fails to extract unknown information. Thus, machine learning algorithms play an important role in this step. Association rules are used to extract hidden rules and to introduce the three strongest rules. Finally, three data mining classification algorithms in three different tools have been applied to introduce the superior algorithm and tool. A new converting two-stage to single-stage model is proposed to obtain the eco-efficiency of the whole system. This model is proposed to fix the efficiency of a two-stage process and prevent the dependency on various weights. Converting undesirable outputs and desirable inputs to final desirable inputs in a single-stage model to minimize inputs, as well as turning desirable outputs to final desirable outputs in the single-stage model to maximize outputs to have a positive effect on the efficiency of the whole process.

The performance of the proposed approach provides us with a chance to recognize pattern recognition of the whole, combining DEA and data mining techniques during the selected period (five years from 2015 to 2019). Meanwhile, the cement industry is one of the foremost manufacturers of naturally harmful material using an undesirable by-product; specific stress is given to that pollution control investment or undesirable output while evaluating energy use efficiency. The significant concentration of the study is to respond to five preliminary questions.

This study aims to investigate environmental efficiency based on energy change by using energy-related or nonenergy-related variables by reckoning with months and years as decision-making units (DMUs) for a hospital under radial and nonradial models.

The non-oriented slack-based measures (SBM)-data envelopment analysis (DEA) model considering desirable and undesirable outputs has been embraced in this study, where its obtained results were compared with the results of other DEA models are output-oriented SBM-DEA and Banker, Charnes, & Cooper-DEA. For this purpose, this research has used a data set covering the 2012–2018 period for a reference hospital, which includes energy-related and nonenergy-related variables.

The results demonstrate that environmental efficiency based on energy reached the highest level in the winter months, whereas the summer months have the lowest efficiency values arising from the increasing electricity consumption due to high cooling needs. According to results of the non-oriented SBM model, the month with the highest efficiency in all periods is January with a 0.936 average efficiency score, the lowest month is August with a 0.406 value.

This paper differs from other studies related to energy and environmental efficiencies in the literature with some aspects. First, to the best of the authors’ knowledge, this study is the first one that takes into account time periods (months and years) as (DMUs for a single organization. Second, this study investigates environmental nonefficiencies, which are derived from energy uses and factors affecting energy use.