Classical Data Envelopment Analysis Models Research Articles

Sustainable approach towards alternatives for the use of iron ore tailings in the construction sector using Data Envelopment Analysis methodology.

Iron ore tailings (IOTs) need to be properly managed to mitigate the environmental, social, and economic impacts of mining activities. To cope with this issue, we use data envelopment analysis (DEA) to evaluate alternatives for using IOT in the construction sector. The classical and weight restriction output-oriented DEA models were used in this analysis. The results show that the ranking of alternatives depends on the aspect being evaluated. Concrete block is the most environmentally friendly alternative when analysing both models. For both social and economic aspects, ceramics produced better results in the classical model, whereas Portland cement showed better outcomes in the weight restriction model. In this sense, the results suggest great potential for the use of IOT in the construction sector, enabling the reduction of risks and social and environmental impacts of tailings dams.

The Harmonious Relationship between Energy Utilization Efficiency and Industrial Structure Development under Carbon Emission Constraints: Measurement, Quantification, and Identification

Addressing the challenge of attaining a harmonious balance between energy utilization efficiency and the level of industrial structure development is crucial for promoting regional sustainable development. Aiming at the goal of carbon neutrality, a three-stage method to analyze the relationship between energy utilization and industrial structure development is proposed. The multidimensional input–output index system was augmented with a carbon emission constraint. Additionally, two classical data envelopment analysis models were integrated to establish a dynamic measurement model for energy utilization efficiency, ensuring comparability among all decision-making units. From two perspectives of industrial structure, rational degree and advanced degree, the industrial structure development index was proposed to quantitatively characterize the level of regional industrial structure development. Drawing upon the Tapio decoupling theory, an elaborate model for identifying harmonious relationships was constructed to refine the recognition of the harmonious state between energy utilization efficiency and industrial structural development. A city-scale case study was conducted in Heilongjiang Province, a typical energy province in Northern China. The results revealed that: (a) energy utilization efficiency in various cities has exhibited a consistent upward trend, with the average efficiency rising from 0.54 in 2010 to 0.88 in 2020. Core cities like Daqing and Harbin stand out in energy utilization, and the disparity in energy utilization levels between different cities is progressively diminishing; (b) the overall level of industrial structural development has shown a weak downward trend. Harbin has the best industrial structure development level, with a quantitative index higher than 0.8. For some cities with relatively backward industrial structures, it is necessary to clarify new industrial development positioning and promote deep optimization of industrial structures; and (c) the harmonious relationship between energy utilization efficiency and industrial structural development demonstrates stage characteristics, indicating an overall negative decoupling relationship with limited dynamic coordination. These distinct findings will assist in identifying potential solutions for achieving high-quality development in traditional industrial cities under carbon emission constraints.

Evaluating efficiency and ranking of suppliers using non-radial super-efficiency data envelopment analysis with uncontrollable factors

Supply chain management (SCM) has been received much attention from academics and corporates. Effective and sustainable SCM require proper efficiency evaluation of suppliers. Such evaluation can be performed using data envelopment analysis (DEA). Classical DEA models presume all inputs and outputs are under the control of suppliers’ management, as well as the models cannot provide a complete ranking of efficient and inefficient suppliers. However, in SCM and other real-managerial problems, some inputs and/or outputs may be uncontrollable (outside management control). Thus, this paper proposes a super efficiency of slacks-based measure (SE-SBM) approach that can handle uncontrollable factors. The proposed approach can distinguish between efficient and inefficient suppliers and identify their rankings. The discriminating power of the proposed approach is due to it concurrently deals with input excesses and output shortfalls to improve inefficient suppliers, as well as input savings and output surpluses of efficient suppliers to maintain their efficient status.

Input/Output Variables Selection in Data Envelopment Analysis: A Shannon Entropy Approach

The purpose of this study is to provide an efficient method for the selection of input–output indicators in the data envelopment analysis (DEA) approach, in order to improve the discriminatory power of the DEA method in the evaluation process and performance analysis of homogeneous decision-making units (DMUs) in the presence of negative values and data. For this purpose, the Shannon entropy technique is used as one of the most important methods for determining the weight of indicators. Moreover, due to the presence of negative data in some indicators, the range directional measure (RDM) model is used as the basic model of the research. Finally, to demonstrate the applicability of the proposed approach, the food and beverage industry has been selected from the Tehran stock exchange (TSE) as a case study, and data related to 15 stocks have been extracted from this industry. The numerical and experimental results indicate the efficacy of the hybrid data envelopment analysis–Shannon entropy (DEASE) approach to evaluate stocks under negative data. Furthermore, the discriminatory power of the proposed DEASE approach is greater than that of a classical DEA model.

Fuzzy efficiency evaluation in relational network data envelopment analysis: application in gas refineries

In contrast to classical data envelopment analysis (DEA), network DEA has attention to the internal structure of a production system and reveals the relationship between the efficiency of system and efficiencies of the processes. However, the flexibility of weights and the need for crisp input and output data in the evaluation process are two major shortcomings of classical network DEA models. This paper presents a common weights approach for a relational network DEA model in a fuzzy environment to measure the efficiencies of the system and the component processes. The proposed approach first finds upper bounds on input and output weights for a given cut level and then it determines a common set of weights (CSW) for all decision-making units (DMUs). Hence, the fuzzy efficiencies of all processes and systems for all DMUs are obtained based on the resulting CSW. The developed fuzzy relational network DEA and the proposed common weights approach are illustrated with a numerical example. The obtained results confirm that the fuzzy data affects over the efficiency scores and complete ranking of DMUs. The applicability of the proposed network model is illustrated by performance evaluation of gas refineries in Iran.

Interval Cross Efficiency Measurement for General Two-Stage Systems

The data envelopment analysis (DEA), which is based on mathematical programming, is employed to measure the relative efficiency of several homogeneous decision-making units (DMUs) with multiple inputs and outputs. There has been extensive research on developing the classical DEA models for various forms and conditions. For example, ranking models such as cross efficiency have been proposed to address the shortcomings of the initial basic models. The data envelopment analysis for network systems has been developed as the network data envelopment analysis (NDEA), and models such as interval data envelopment analysis (IDEA) have been provided to take into account data uncertainty. But using this technique for issues that have all these conditions requires a single model, in which all the conditions are included. In the case study of this paper, the branches in the banking industry are ranked, and several models are presented according to different approaches to the NDEA in order to calculate the interval cross efficiency of a general two-stage network system. Finally, the results of the models are compared.

Data envelopment analysis efficiency in the public sector using provider and customer opinion: An application to the Spanish health system

Measuring the relative efficiency of a finite fixed set of service-producing units (hospitals, state services, libraries, banks,...) is an important purpose of Data Envelopment Analysis (DEA). We illustrate an innovative way to measure this efficiency using stochastic indexes of the quality from these services. The indexes obtained from the opinion-satisfaction of the customers are estimators, from the statistical view point, of the quality of the service received (outputs); while, the quality of the offered service is estimated with opinion-satisfaction indexes of service providers (inputs). The estimation of these indicators is only possible by asking a customer and provider sample, in each service, through surveys. The technical efficiency score, obtained using the classic DEA models and estimated quality indicators, is an estimator of the unknown population efficiency that would be obtained if in each one of the services, interviews from all their customers and all their providers were available. With the object of achieving the best precision in the estimate, we propose results to determine the sample size of customers and providers needed so that with their answers can achieve a fixed accuracy in the estimation of the population efficiency of these service-producing units through the use of a novel one bootstrap confidence interval. Using this bootstrap methodology and quality opinion indexes obtained from two surveys, one of doctors and another of patients, we analyze the efficiency in the health care system of Spain.

Development of a multi-objective stepwise data envelopment analysis method based on common set of weights to evaluate the agility of decision-making units: a case study

In most data envelopment analysis (DEA) models, the internal structure of production units is ignored during the evaluation process. To solve this problem, a stepwise DEA model has been considered by the researchers. Another weakness of classical DEA models is that the weights of inputs and outputs are being changed each time the model is run. In such case, the common set of weight method is one of the popular ranking methods which can well identify efficient and inefficient units based on the same criteria. In the present study, using the related studies in the literature, a conceptual model considering agility dimensions was constructed, in which the main dimensions include drivers, enablers, capabilities and agility results. Then, a model for calculating the performance weights is presented. The model was applied to evaluate the agility performance of 11 technical and vocational training centres in Kerman Province. At the end, the obtained results were analysed and suggestions were made for interested researchers for future studies in this field.

DEA METHOD AS A TOOL FOR COMPARATIVE ANALYSIS OF THE EFFICIENCY OF NATIONAL ECONOMIES

The paper deals with the theory of comparative analysis of the efficiency of national economies using the nonparametric method of data envelopment analysis (DEA).
 The main works on the use of data envelopment analysis are studied. In order to develop the ideas of F. Caselli, W. J. Coleman II., J. Growiec it is proposed to take into account that the goal of producers in modern economy is not only to increase technical efficiency, which is expressed in reducing stock and labor intensity, but also to increase economic (in a narrow sense) efficiency that is reduction of the real prices of the used production factors. The subject of the research is an adequate representation of the interdependence of these "competing" goals in the theory of the efficiency frontiers. In the study, all efficiency frontiers were constructed in a purely nonparametric way reflecting a single period (in a standard form – a year). The goal is to solve the problem of incompleteness of a purely technological approach to the world efficiency frontiers that is to supplement the classical DEA model in a way to make it possible to build the boundaries of technical and economic efficiency using both methods – the envelopments of the actual states (points) of the countries and the envelopments of their national functions of the product distribution and its price. In accordance with the content of the proposed model of Paired Efficiency Frontier Model (PEF model), the geometric method is chosen as the main method for studying and interpreting the results obtained. Therefore, it is proven that it is possible to display a frontier using the envelopment method of functions distribution (straight lines) in one coordinate system as an envelopmentl of actual states (points) in an alternative system. This, in turn, significantly simplifies the range estimation to these borders.
 In the course of the research, the following goals are set: to determine the algebraic forms of linear programming problems that adequately represent the frontiers of technical and economic efficiency; to outline the main points of view regarding the construction of a global technological frontier and to justify the feasibility of complementing it with a global economic frontier.
 The proposed model contains four efficiency frontiers – technological and economic frontiers constructed using the envelopment method of the actual states, and similar frontiers representing the envelopments of the functions of the product distribution and its price. In accordance with the content of the proposed model, the geometric method is chosen as the main method for studying the frontiers of efficiency and interpreting the results obtained. Hence, it is possible to display a frontier using the envelopment method of functions distribution (straight lines) in one coordinate system as an envelopmentl of actual states (points) in an alternative system.
  

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.

A minimax approach for selecting the overall and stage-level most efficient unit in two stage production processes

Data envelopment analysis (DEA) is a very effective management tool in assessing the performance of a set of decision making units (DMUs). In the efficiency evaluation using classic single stage DEA models, the internal processes of the DMUs are often neglected. In most real-world problems, it may be more realistic to evaluate the efficiency evaluation in two-stage production systems. In some cases: however, the decision-maker must need to identify the most efficient single unit. Numerous methods have been introduced to find the most efficient unit in single stage systems whereas no methods have been proposed for this aim in two stage production systems. Therefore, a new model based on mixed-integer programming was proposed to determine the most efficient DMU in two-stage systems and sub-stages in this study. The most important innovation of the suggested approach is that the most efficient DMUs of both stages can be found separately using only one model. Numerical examples for real world problems and a simulation study were provided for the validity of the proposed model.

Designing an Intuitionistic Fuzzy Network Data Envelopment Analysis Model for Efficiency Evaluation of Decision-Making Units with Two-Stage Structures

Data envelopment analysis (DEA) is a powerful tool for evaluating the efficiency of decision-making units for ranking and comparison purposes and to differentiate efficient and inefficient units. Classic DEA models are ill-suited for the problems where decision-making units consist of multiple stages with intermediate products and those where inputs and outputs are imprecise or nondeterministic, which is not uncommon in the real world. This paper presents a new DEA model for evaluating the efficiency of decision-making units with two-stage structures and triangular intuitionistic fuzzy data. The paper first introduces two-stage DEA models, then explains how these models can be modified with intuitionistic fuzzy coefficients, and finally describes how arithmetic operators for intuitionistic fuzzy numbers can be used for a conversion into crisp two-stage structures. In the end, the proposed method is used to solve an illustrative numerical example.

A new approach for index construction: The case of the road user behavior index

In recent years, composite indicators have become increasingly recognized as a useful tool for performance evaluation, benchmarking, and decision-making by summarizing complex and multidimensional issues. In this study, we focus on the application of data envelopment analysis (DEA) on index construction in the context of road safety and highlight the shortcomings of using the classical DEA models. The DEA method assigns a weight to each indicator by selecting the best set of weights for the unit under evaluation. The flexibility in selecting the weights in the classical DEA approach may lead to two interrelated problems: compensability and unfairness. These shortcomings are, respectively, overcome traditionally by imposing weight restrictions and applying a common weights approach. However, the problem of evaluating a layered hierarchy of indicators with a common set of weights (CSW) has not been addressed in the literature. To fill this gap, we propose a new approach for index construction to determine an optimal CSW to assess all units simultaneously while reflecting the hierarchical structure of the indicators in the model. The applicability of the suggested common-weight approach is illustrated by a case study on constructing a road user behavior index for a set of European countries. From a theoretical point of view, our approach provides a fair and identical basis for evaluation and comparison of countries in terms of driver’s behaviors and, from a practical point of view, it significantly reduces the required computational burden for solving the formulated model. The obtained results clarify the sharper discrimination power of our model compared to the other methods in the literature.

Measuring Spatio-temporal Efficiency: An R Implementation for Time-Evolving Units

Classical data envelopment analysis models have been applied to extract efficiency when time series data are used. However, these models do not always yield realistic results, especially when the purpose of the study is to identify the peers of the decision making unit (DMU) under investigation. This is due to the fact that apart from the spatial distance of DMUs, which is the basis on which efficiency is extracted, the distance in time between DMUs is also important in identifying the most suitable peer that could serve as a benchmark for the DMU under investigation. Based on these two dimensions, i.e. the spatial and the temporal, the concept of spatio-temporal efficiency is introduced and a mixed integer linear programming model is proposed to obtain its value. This model yields a unique past peer for benchmarking purposes based on both dimensions. The implementation has been performed in the R language, where the user can provide, through a graphical interface, the data (inputs and outputs for successive versions of a DMU) for which the spatio-temporal efficiency is measured. Applications to the real world and particularly from the discipline of software engineering are provided to show the applicability of the model to temporally arranged data. Profiling results of the code in the R language are also provided showing the effectiveness of the implementation.

Stepwise pricing in evaluating revenue efficiency in Data Envelopment Analysis: A case study in power plants

Data envelopment analysis (DEA) technique is widely applied for performance assessment of decision making units (DMUs). The revenue efficiency (RE) evaluation is one of the controversial subject matters that can be performed through DEA context. The amount of productions and its prices are crucial factors in the RE. The classical DEA models consider the prices to be fixed and known which are not the case in real world. Also, the classical DEA models considers linear pricing in revenue assessment. However, most of real world problems deal with nonlinear prices. This paper evaluates the RE given the piecewise linear theory in non-competitive situations. In doing so, a stepwise pricing function is introduced which lets the prices to be changed in relation to the amount of the production. As an innovative idea, a more accurate mathematical modeling for the RE is proposed. We define a dynamic weights’ function in maximum revenue optimization model which no longer considers fixed prices. A case study validates our proposed model.

A Revised Inverse Data Envelopment Analysis Model Based on Radial Models

In recent years, there has been an increasing interest in applying inverse data envelopment analysis (DEA) to a wide range of disciplines, and most applications have adopted radial-based inverse DEA models. However, results given by existing radial based inverse DEA models can be unreliable as they neglect slacks while evaluating decision-making units’ (DMUs) overall efficiency level, whereas classic radial DEA models measure the efficiency level through not only radial efficiency index but also slacks. This paper points out these disadvantages with a counterexample, where current inverse DEA models give results that outputs shall increase when inputs decrease. We show that these unreasonable results are the consequence of existing inverse DEA models’ failure in preserving DMU’s efficiency level. To rectify this problem, we propose a revised model for the situation where the investigated DMU has no slacks. Compared to existing radial inverse DEA models, our revised model can preserve radial efficiency index as well as eliminating all slacks, thus fulfilling the requirement of efficiency level invariant. Numerical examples are provided to illustrate the validity and limitations of the revised model.

MEASUREMENT OF EFFICIENCY OF DIDACTIC ACTIVITIES OF PUBLIC UNIVERSITIES OF TECHNOLOGY IN POLAND: DIRECTIONAL DISTANCE FUNCTION WITH UNDESIRABLE OUTPUT APPROACH

Purpose – The conducted research aimed at estimating the technical efficiency of didactic activity in the group of universities of technology in Poland using the non-parametric Data Envelopment Analysis (DEA) method. Research methodology – The measurement was based on the model of directional distance function with undesirable output under variable return-to-scale and output-oriented (DDF BadOutput-V-O). Findings – The research allowed to group universities in 2010 and 2015 into three categories, i.e. efficient universities and universities above and below the average efficiency. It has been shown that it is justified to use alternative models of efficiency measurement covering different perspectives. The application of the model from a financial and employment perspective showed significant differences in performance levels in some cases. Research limitations – This study only looks at universities of technology, so the future study should be extended to other universities and compare efficiency of higher education with the level of study effectiveness (dropout rate education, graduation rates). Practical implications – The use of the DDF model with undesirable output allowed to obtain results closer to the actual conditions of teaching in public universities than in the case of using classic DEA models, wich only take the desired output into accoount. Originality/Value – The originality of the work lies in the use of a more general and flexible DDF approach than the classical DEA models, which made it possible to estimate the efficiency of universities taking into account the desirable (positive) and undesirable (negative) output.

Assessing sustainability of suppliers: A novel stochastic-fuzzy DEA model

Appropriate supplier selection due to its direct impact on profitability and maintaining the competitive status of an organization is one of the vital decisions for each company. Data envelopment analysis (DEA) is a proper tool for measuring the sustainability of suppliers. Classic DEA models suppose that inputs and outputs are deterministic; consequently, the relative efficiencies of suppliers are also deterministic. However, in real-life applications, all inputs and outputs are not deterministic. Some could be stochastic and/or fuzzy. This study consists of four types of supplier selection models in supply chains and provides a decision making scheme for selecting appropriate model for supplier selection under deterministic, stochastic and fuzzy conditions. The proposed stochastic-fuzzy DEA model (SFDEA) can be solved as crisp program for each α∈01 using α-cut method. This is the first study to a present a flexible approach for evaluating supplier’s sustainability in supply chain management. A case study is presented for validating the proposed model.

Ranking sustainable suppliers using congestion approach of data envelopment analysis

Abstract Selecting sustainable suppliers is one of the important tasks of decision makers to survive in today's competitive businesses. One of the uses of data envelopment analysis (DEA) is to provide improvement solutions (benchmarks) for inefficient decision making units (DMUs). In classical DEA models, improvement solutions are merely proposed by one of the triple approaches including input-oriented, output-oriented, and hybrid approaches. However, based on the congestion approach of the “theory of economies of scale”, in some cases, the benchmarks derived from the triple approaches are not sufficiently precise. In “theory of economies of scale”, sometimes with an increase in inputs we see more increment in outputs (Wei and Yan, 2004). This means that the triple approaches do not consider all contributing factors of inefficiencies of DMUs. In other words, the triple approaches overlook the shortage of congested inputs as an inefficiency reason of DMUs. Focusing solely on triple approaches cannot always be correct given that sometimes inefficiency reason for some DMUs is due to a shortage of inputs. The objective of this paper, accordingly, is to consider congestion approach (congested inputs) in evaluations of DMUs. To do so, we propose a novel DEA model to show that an increase in congested inputs may lead to higher outputs/efficiency. By so doing, the reliability of improvement solutions are increased. Here, a DEA model is developed to assess the sustainability of suppliers. Also, the congestion of DMUs is detected in pairwise comparisons. A case study is presented to demonstrate the applicability of the presented model.

Optimising virtual networks over time by using Windows Multiplicative DEA model

Recently, the prediction of the most efficient configuration of a vast set of devices used for mounting an optimised cloud computing services and virtual networks environments have attracted growing attention. This paper proposes a paradigm shift in modelling transmission control protocol (TCP) behaviour over time in virtual networks by using data envelopment analysis (DEA) models. Firstly, it proves that self-similarity with long-range dependency is presented differently in every network device. This study implements a novel fractal dimension concept on virtual networks for prediction, where this key index informs if the transport layer forwards services with smooth or jagged behaviour over time. Another substantial contribution is proving that virtual network devices have a distinct fractal memory, TCP bandwidth performance, and fractal dimension over time, presenting themselves as important factor for forecasting of spatiotemporal data. Thus, a continuous stepwise fractal performance evaluation framework methodology is developed as an expert system for virtual network assessment and performs a fractal analysis as a knowledge representation. In addition, due to the limitations of classical DEA models, the windows multiplicative data envelopment analysis (WMDEA) model is used to dynamically assess the fractal time series from virtual network hypervisors. For knowledge acquisition, 50 different virtual network hypervisors were appraised as decision-making units (DMU). Finally, this expert system also acts as a math hypervisor capable of determining the correct fractal pattern to follow when delivering TCP services in an optimised virtual network.