Presence Of Undesirable Outputs Research Articles

Malmquist–Luenberger Productivity Index for a Two-Stage Structure in the Presence of Undesirable Outputs and Uncertainty

Network Data Envelopment Analysis (NDEA) models assess the processes of the underlying system at a certain moment and disregard the dynamic effects in the production process. Hence, distorted efficiency evaluation is gained that might give misleading information to decision-making units (DMUs). Malmquist–Luenberger Productivity Index (MPI) assesses efficiency changes over time, which are measured as the product of recovery and frontier-shift terms, both coming from the DEA framework. In this study, a form of MPI involving network structure for evaluating DMUs in the presence of uncertainty and undesirable outputs in two periods of time is presented. To cope with uncertainty, we use the stochastic p-robust approach and the weak disposability of Kuosmanen (American Journal Agricultural Economics 87 (4):1077–1082, 2005) proposed to take care of undesirable outputs. The proposed fractional models for stages and overall system are linearized by applying the Charnes and Cooper transformation. Finally, the proposed models are applied to evaluate the efficiency of 11 petroleum wells to identify the main factors determining their productivity, utilizing the data from the 2020 to 2021 period. The results show that the management of resource consumption, especially equipment and capital, is not appropriate and investment is inadequate. Although the depreciation rate of capital facilities in this industry is high, the purpose of the investment is not to upgrade the level of technology.

Accuracy of Deterministic Nonparametric Frontier Models with Undesirable Outputs

The accuracy of deterministic nonparametric frontier models with desirable outputs has been extensively investigated. However, research on the models’ accuracy in the presence of undesirable outputs is almost nonexistent, though applications in this regard are abundant. This paper evaluates the accuracy of seven representative deterministic nonparametric frontier models in dealing with undesirable outputs. The experimental design employs Monte Carlo simulation and translog production functions across a wide range of settings. We find that the integration of undesirable outputs lowers model accuracy. All seven models display robust performance under different returns-to-scale assumptions. Outputs correlation has a positive effect on model performance. Using a large sample can improve the models’ accuracy except for the range-adjusted measure model. The models’ accuracy is most sensitive to noise at low noise levels. Endogeneity has a negative effect on the models’ accuracy, but depreciation of accuracy is minor at low to medium endogeneity levels. Heteroskedasticity leads to improved performance. Overall, the experimental results support the usage of the by-production approach and strongly disfavor the range-adjusted measure approach and the hyperbolic approach. The directional distance function method has an edge for large samples, if the objective is to identify top and bottom units. Another approach, treating undesirable outputs as inputs, is dominated by other methods. The ranking of the methods is generally robust to the variations of returns-to-scale, sample size, noise, outputs correlation, endogeneity, and heteroskedasticity. We also show that the slacks-based measure under the by-production framework has better performance than the Färe–Grosskopf–Lovell index proposed in literature.

Common-weights fuzzy DEA model in the presence of undesirable outputs with ideal and anti-ideal points: development and prospects

AbstractIn the literature, fuzzy arithmetic approach has been used for solving fuzzy data envelopment analysis (DEA) model in the presence of undesirable outputs by use of ideal and anti-ideal decision-making units (DMUs). In order to obtain the best and the worst fuzzy efficiencies, such an approach allows each DMU to choose the most favorable weights via optimizing its own evaluation that needs to solve various mathematical models. On the one hand, solving one mathematical model to find the best fuzzy efficiency and solving another mathematical model to find the worst fuzzy efficiency for each DMU increase the computational complexity significantly. On the other hand, the fully flexibility of weights leads to the different set of weights that may not be desirable. This paper proposes a common-weight method from two optimistic and pessimistic perspectives in fuzzy environment to determine the common sets of weights (CWS) to compute the best and the worst fuzzy efficiencies of all DMUs. The advantages of using common-weight DEA method based upon fuzzy arithmetic approach are reduction of the computational complexities and evaluation of equitably the best and the worst fuzzy efficiencies on the same base. The proposed approach first solves one linear programming model to compute each of the best and the worst fuzzy efficiencies of all DMUS, and then combines them to find a relative closeness index for the overall assessment. The developed approach is illustrated by a numerical example form the literature and the obtained results are compared with those from the existing ones.

Stochastic data envelopment analysis in the presence of undesirable outputs

In contrast to traditional efficiency analysis models in the field of data envelopment analysis (DEA) with undesirable outputs, this paper proposes efficiency models with the joint use of weak and managerial disposability assumptions. First, we develop a deterministic efficiency analysis model to deal with undesirable outputs in a production process. Due to the importance of data variability and uncertainty, the technical efficiency analysis is sensitive to these variations. Using chance-constrained programming theory, we extend our proposed deterministic model to a stochastic production system. To demonstrate the real-world applicability of our proposed models, we employ an empirical application based on actual Iranian gas distribution company data. Although this empirical application is illustrative, our proposed scheme could be used to evaluate the relative efficiency of many real-life production units whose underlying production systems are frequently stochastic.

A two-stage structure with undesirable outputs: slacks-based and additive slacks-based measures DEA models

The slacks-based measure (SBM) and additive SBM (ASBM) models are two widely used DEA models acting based on inputs and outputs slacks and giving efficiency scores between zero and unity. In this paper, we use both models with the application of the weak disposability axiom for outputs to evaluate efficiency in a two-stage structure in the presence of undesirable outputs. In the external evaluation, the SBM model is reformulated as a linear program and the ASBM model is reformulated as a second-order cone program (SOCP) that is a convex programming problem. In the internal evaluation, the SBM model for a specific choice of weights is linearized while the ASBM model is presented as an SOCP for arbitrary choice of weights. Finally, the proposed models are applied on a real dataset for which efficiency comparison and Pearson correlation coefficients analysis show advantages of the ASBM model to the SBM model.

Radial eco‐efficiency in the presence of weakly disposable undesirable outputs: Evaluating agricultural sectors

AbstractData envelopment analysis (DEA) is a popular technique for evaluating relative efficiency. In many real‐world applications, undesirable outputs must be considered, and evaluating eco‐efficiency instead of operational efficiency is demanded. Unfortunately, eco‐efficiency models in DEA are problematic, especially in variable returns‐to‐scale (VRS) and weak disposability conditions. In this paper, the shortcomings of the available models are discussed and a new method is proposed to provide a valid eco‐efficiency measurement. The proposed model is capable of assessing radial efficiency which is not straightforward in the presence of undesirable outputs. Weak disposability condition plays an important role in modelling undesirable outputs. The proposed model also offers a new formulation for weak disposability in VRS technology. Compared to conventional DEA models with a large number of decision making units evaluated as efficient, the performance scores in the proposed model are much more dispersed, leading to a deeper assessment. None of the operational and environmental efficiencies is overlooked by the new method. The proposed model is used to evaluate the eco‐efficiency of the agriculture sector in 62 countries. The results confirm that poverty and extreme weather have negative impacts on environmental efficiency.

Influence Paths and Spillover Effects of Agricultural Agglomeration on Agricultural Green Development

Analyzing the impact of agricultural industrial agglomeration (AIG) on agricultural green development (AGD) is of a great significance to realizing the sustainable and high-quality development of agriculture. Panel data of 31 provinces in China from 2009 to 2019 were analysed. For measuring efficiency, a non-parametric DEA approach in the presence of undesirable outputs, a slack-based measure (SBM) was used. From the perspective of the spatial spillover analysis and heterogeneity analysis, Moran’s I index and the Spatial Durbin Model (SDM) were used to empirically analyze the impact of AIG on AGD to alleviate conflicts between agricultural sustainable development and environmental pollution and further explore the regional heterogeneity of AIG on AGD-efficiency due to the vast territory of China. The mediation model is constructed to explore the paths of AIG affecting AGD. The results show that: (1) Chinese efficiency of AGD was raised continuously and the high efficiency was mainly located in the southeastern coastal areas. (2) AIG not only has a significant U-shaped impact on the AGD, but also has a nonlinear U-shaped spatial spillover effect in related regions, which shows that the “siphon effect” will be triggered in the early stage of AIG and the “diffusion effect” will be evoked in the later stage of AIG. (3) From the perspective of heterogeneity analysis, AIG significantly promotes the efficiency of AGD in the central region of mainland China. In the eastern region, the AIG has an inverted U-shaped effect on the efficiency of AGD from positive to negative. On the contrary, the AIG has a U-shaped impact on the efficiency of AGD from negative to positive in the western region. (4) The analysis of the mediation model plays a partial positive mediating role for AGD to persist in promoting technology innovation and increasing the speed of talent agglomeration. Accordingly, suggestions are provided to strengthen the coordination and cooperation in sustainable agricultural development among provinces, to drive the efficiency of science and technology through the scale knowledge spillover effect, and to conduct a scientific layout of agricultural industry development.

Estimating Capacity Utilization in Network DEA in the Presence of Undesirable Outputs

Estimating Capacity Utilization in Network DEA in the Presence of Undesirable Outputs

A Modified Russell Measure for Estimating Efficiency Changes in the Presence of the Undesirable Outputs and Stochastic Data

Although data envelopment analysis (DEA) assumes deterministic data, a great volume of data might be stochastic. The global Malmquist productivity index (GMPI) is a highly effective instrument for productivity analysis in DEA. This paper extends GMPI in the presence of stochastic data. Our new stochastic DEA model is a chance-constrained programming model, which is converted to a deterministic programming problem with a linear objective function and quadratic constraints. For efficiency evaluation purposes, in this paper, the weak disposability principle is used to model Russell’s measure in the presence of undesirable outputs. The main contribution of this paper is to develop a global Russell model with stochastic data. A case study is presented to illustrate the applicability of the proposed models.

Developing two dynamic Malmquist-Luenberger productivity indices: An illustrated application for assessing productivity performance of Indian banks

In the presence of undesirable output(s) in the production process, the Malmquist-Luenberger productivity index (MLPI) has emerged as a standard tool to measure total factor productivity change and its distinct components, namely efficiency change and technical change. Notwithstanding, the standard version of MLPI has certain genuine downsides, particularly the commonness of infeasibility while computing cross-period directional distance functions with negative data values and the black-box representation of the production technology. For overcoming these downsides, this paper advances two extensions of the standard MLPI. Specifically, we propose dynamic Malmquist-Luenberger and dynamic sequential Malmquist-Luenberger productivity indices to measure the productivity change in a system that can be represented by a dynamic network production structure. The proposed indices take a holistic view of production technology that connects several divisions internally by intermediate processes and use the carryovers flow over time to add a temporal dimension to it. To exhibit the capability of the proposed extensions of MLPI, we model a three-stage dynamic network structure for Indian banks and compute the indices of productivity change, efficiency change, and technical change for forty-two banks for the period from 2010 to 2017. The empirical findings elucidate that the observed productivity growth in the Indian banking industry is primarily driven by technical progress.

Green productivity and undesirable outputs in agriculture: a systematic review of DEA approach and policy recommendations

Measuring efficiency in the presence of undesirable outputs could be difficult depending on how to treat these outputs; thus, undesirable outputs modelling has been an exciting subject of several studies in the Data envelopment analysis (DEA) literature in the last two decades. The present study aims to illustrate a thorough overlook of studies in which DEA has applied for measuring efficiency with undesirable outputs. Fifty-eight articles were published from 2000 to 2020 have been systematically reviewed through PRISMA protocol. The results indicated that "Journal of Cleaner Production" ranked first with six published articles, and Chinese scholars have the most contributions to this field, with twenty-third articles. Also, almost a quarter of the published articles' scope was related to agricultural pollution, and thirteen articles were published in 2016, the highest number of published articles annually. Taken together, the theoretical and empirical implications of research in the field of Green Productivity are discussed, and some policies were recommended.

Evaluating radial efficiency considering environmental factors: A generalization of classical DEA

Environmental issues are becoming a significant and serious worldwide problem. Undesirable outputs like waste and pollution are by-products of desirable outputs in a production system. To motivate environment-friendly production, undesirable outputs should be included in the performance assessment of firms, organizations and countries. Data Envelopment Analysis (DEA) is one of the most successful methods of efficiency evaluation. Unfortunately, there is no reliable radial efficiency measure for environmental assessment in DEA. In this paper, the conventional modeling in DEA is extended to develop a new radial model for efficiency assessment in the presence of undesirable outputs. This method enables more accurate modeling of the problem. It opens a new door to the issue, and shows more reliabilities than the existing methods. The new efficiency measure is more rigorous, and provides higher discriminating power. Evaluating divisional efficiency is another advantage of the model. It also provides credible targets with greater practical accessibility for each inefficient decision making unit. The model is studied by an axiomatic approach and employed to evaluate the performance of 28 countries in economic, social and environmental dimensions. The results show that only one country achieves efficiency, and the average environmental efficiency is considerably lower than the operational efficiency among the studied countries.

Efficiency of rice production and CO2 emissions: A study of selected Asian countries using DDF and SBM-DEA

The present study aims to measure the efficiency of desirable output (Rice) in the presence of undesirable output (CO2), for selected Asian countries. An attempt has also been made to identify how great a reduction in CO2 emission is required to make agricultural practices efficient and sustainable. DDF and SBM-DEA are used to calculate the efficiency of 28 Asian countries for the period 2002 to 2014. To compare the efficiency of the models with and without the presence of undesired output and to calculate bias, if any, in model selection, the Mann-Whitney U test was applied. Results indicate that the exclusion of undesired output leads to biased estimates. The efficiency scores show that in eleven countries rice production was environmentally efficient. For the remaining seventeen inefficient countries, a considerable amount of reduction in CO2 emissions and fertilizer use are required to make the production process efficient and environmentally sustainable.

Efficiency evaluation with cross-efficiency in the presence of undesirable outputs in stochastic environment

Data envelopment analysis (DEA) is a useful tool for efficiency evaluation of decision making units (DMUs). The classical DEA models deal with exact data while in real world problems we concern with uncertain data such as fuzzy, stochastic and etc. In this paper, using input oriented CCR model (ICCR) in the presence of undesirable outputs with specific risk (α), a new stochastic model called Expected Ranking Criterion is proposed. Based on this, the stochastic cross-efficiency evaluation is presented for robust ranking and discrimination of DMUs. Given the non-uniqueness of resulting optimal solutions, a model is introduced for ranking by which stochastic cross-efficiency is performed using aggressive approach. The proposed model provides ranking of all DMUs whereas current stochastic DEA models in literature fail in this regard. Finally, the proposed models are implemented for 32 thermal power plants with stochastic inputs and undesirable outputs. The results show the applicability of proposed models.

An investigation of the undesirable outputs congestion in data envelopment analysis

Congestion is one of the most important subjects in Data Envelopment Analysis (DEA) which helps the Decision Maker (DM) to decide about changing the size of units. The estimation of congestion has attractive advantages from different perspectives. For example, the total cost of a partiular DMU, in which the congestion occurs, can be reduced by the decreases in inputs. On the other hand, the output of units can be increased by the recognizing and eliminating the congestion of DMUs and so, the total profit of decision making units can be increased. Hence, the management is eager to know how to recognize and eliminate the congestion of units. Most of the existing methods to estimation of the congestion in the literature consider only the desirable outputs. This study focuses on the evaluation of congestion in the presence of undesirable outputs and proposes an approach to recognize the congestion of units. The method is demonstrated on a numerical example to illustrate the validity of the proposed method.

Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

Data envelopment analysis (DEA) is a prominent technique for evaluating relative efficiency of a set of entities called decision making units (DMUs) with homogeneous structures. In order to implement a comprehensive assessment, undesirable factors should be included in the efficiency analysis. The present study endeavors to propose a novel approach for solving DEA model in the presence of undesirable outputs in which all input/output data are represented by triangular fuzzy numbers. To this end, two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into proposed fuzzy DEA framework. Then, a lexicographic approach is used to find the best and the worst fuzzy efficiencies of FIDMU and FADMU, respectively. Moreover, the resulting fuzzy efficiencies are used to measure the best and worst fuzzy relative efficiencies of DMUs to construct a fuzzy relative closeness index. To address the overall assessment, a new approach is proposed for ranking fuzzy relative closeness indexes based on which the DMUs are ranked. The developed framework greatly reduces the complexity of computation compared with commonly used existing methods in the literature. To validate the proposed methodology and proposed ranking method, a numerical example is illustrated and compared the results with an existing approach.

Towards greener petrochemical production: Two-stage network data envelopment analysis in a fully fuzzy environment in the presence of undesirable outputs

Traditional Data Envelopment Analysis (DEA) models usually consider decision-making units (DMU) as black boxes that consume a set of inputs to produce a set of outputs and ignore the units’ internal structure. In literature, two-stage DEA models have been introduced and developed to deal with the inner workings of such DMUs; however, models in the extant literature can only be used to assess technologies with precise inputs and outputs. In this study we present an innovative two-stage DEA model for DMU evaluation in the presence of imprecise data, which are modeled using triangular fuzzy values in this study. We also innovate by including the treatment of undesirable outputs. We propose some alternative two-stage DEA network models with undesirable outputs in a full-fuzzy mode that are either directional or radial and are embedded within a multi-objective linear planning structure based on fuzzy triangular numbers. We also propose a method to solve fuzzy programming models in the presence of undesirable pollutant outputs from production processes such as greenhouse gas emissions, harmful effluents, among others. Our proposed model is then applied to a real case of 15 ammonia-manufacturing units in the Iranian petrochemical sector. The promising results that we obtained in our research and their implications for theory and practice are then presented and discussed.

Measuring and Improving Eco-efficiency

As energy and environmental issues continue to generate social concerns, firms are pushed to alleviate their energy and environmental externalities from economic activities and network operations while pursuing economic interests. A comprehensive performance evaluation involving both productive and environmental factors is therefore desired by firms to aggregate multiple aspects into condensed information to facilitate decision-making. In this study, we develop a new eco-efficiency measure for energy-intensive economic activities, which integrates productive and environmental factors in the presence of undesirable outputs. The proposed measure has the following merits in comparison with a majority of existing ones that have been widely used in energy- and environment-related areas. It guarantees Pareto-Koopmans eco-efficiency because only non-dominated entities are measured as eco-efficient. It also captures any actual fluctuations in inputs, desirable outputs, and undesirable outputs, as it proves to be strongly monotonic in all input and output dimensions. It has a positive significance for promoting undesirable output abatement, because it stimulates scale improvement for entities in pursuit of economies of scale. It also provides great flexibility of improvement for individual inputs and outputs to achieve eco-efficiency. The marginal abatement costs of undesirable outputs are estimated to facilitate managing the potential tradeoff between undesirable output abatement and desirable output production. We also extend it to weighted eco-efficiency measures for specific situations wherever necessary. Its practicability and comparison with existing models are illustrated by an empirical example.

A two-stage model for monitoring the green supplier performance considering dual-role and undesirable factors

PurposeThe 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.Design/methodology/approachThe 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.FindingsThe 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.Research limitations/implicationsThe 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.Originality/valueEvaluating 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.

A fuzzy multi-objective multi-period network DEA model for efficiency measurement in oil refineries

We define a fuzzy multi-objective multi-period network DEA model customized to evaluate the dynamic performance of oil refineries in the presence of undesirable outputs. In particular, we use a standard fuzzy operator to define the efficiency levels so as to integrate multiple objectives and periods of time within a unique maximization framework. Managers and decision makers are provided with a model characterized by its operational simplicity that allows for the straightforward implementation of standard spreadsheet software. The model is applied to a real-life case study, where the capacity of refineries to optimize their performance through the refining process is analyzed together with the introduction of value-added products that preserve and enhance the environmental dimensions of the refining process. The inclusion of a real-life case study aims at illustrating the efficacy and applicability of the proposed method relative to those of more conventional models. Moreover, the range of the time period covered allows us to analyze the evolution of efficiency beyond the standard two-period Malmquist framework generally considered in the literature dealing with the behavior of refineries.