Traditional Data Envelopment Analysis Models Research Articles

Choquet-Integral-Based Data Envelopment Analysis with Stochastic Multicriteria Acceptability Analysis

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiencies of decision-making units (DMUs) by using a set of inputs and a set of outputs. However, traditional DEA models always assume that the inputs or outputs are independent of each other, which is unrealistic in practical problems. To reflect the interactions between inputs or outputs, the Choquet integral is employed in DEA models. The traditional DEA models are usually used to find some specific input and output weights of DMUs to optimize the efficiency score of DMUs, but the corresponding input and output weights for the optimal efficiency score of a DMU may not be distributed symmetrically, that is to say, the space of weights may be different for different DMUs. Instead of finding the self-efficiency score and the cross-efficiency score of a DMU in traditional DEA models based on some specific input and output weights, stochastic multicriteria acceptability analysis is used to explore the input or output evaluation space and weight space to calculate the Choquet-integral-based acceptability indices of DMUs. The proposed method considers the interactions between inputs or outputs, which can make more DMUs efficient and can also measure the acceptability of a DMU to become an efficient one by exploring the supporting information space. Examples are given to illustrate the proposed method.

Homogeneity and Best Practice Analyses in Hospital Performance Management: An Analytical Framework

Performance modeling of hospitals using data envelopment analysis (DEA) has received steadily increasing attention in the literature. As part of the traditional DEA framework, hospitals are generally assumed to be functionally similar and therefore homogenous. Accordingly, any identified inefficiency is supposedly due to the inefficient use of inputs to produce outputs. However, the disparities in DEA efficiency scores may be a result of the inherent heterogeneity of hospitals. Additionally, traditional DEA models lack predictive capabilities despite having been frequently used as a benchmarking tool in the literature. To address these concerns, this study proposes a framework for analyzing hospital performance by combining two complementary modeling approaches. Specifically, we employ a self-organizing map artificial neural network (SOM-ANN) to conduct a cluster analysis and a multilayer perceptron ANN (MLP-ANN) to perform a heterogeneity analysis and a best practice analysis. The applicability of the integrated framework is empirically shown by an implementation to a large dataset containing more than 1,100 hospitals in Germany. The framework enables a decision-maker not only to predict the best performance but also to explore whether the differences in relative efficiency scores are ascribable to the heterogeneity of hospitals.

Efficiency of secondary schools in Ecuador: A value based DEA approach

This paper proposes a novel Value-Based Data Envelopment Analysis model which specifically tackles non-discretionary data to assess the performance of 159 secondary schools from Ecuador by employing data from the Programme for International Student Assessment for Development. When contrasted with traditional Data Envelopment Analysis models, the Value-Based Data Envelopment Analysis model has several innovative characteristics that can be particularly convenient not only for including the preferences (generally not incorporated) of the decision-makers, but because it easily handles negative or null data. In addition, this methodology also employs a procedure that allows performing the robustness assessment (rarely employed in similar studies) of the results obtained. The factors considered to perform the efficiency assessment of each school include indexes, which reflect the quality of both basic school infrastructures and instructional resources, the economic, social, and cultural level index of students, the student-teacher ratio, and test scores in maths, reading and science. Our findings suggest that the average efficient school has mean scores across all competencies below the average of Latin American and Caribbean countries. Besides, inefficient schools need to make a greater effort to improve results in maths when compared to reading and science competencies. Finally, it can be concluded that inefficient schools can improve students’ achievements by about 11%–12%, with almost the same instructional resources and with a ratio of students per teacher 23% higher but requiring an enhancement of the basic school infrastructure by about 7%.

Modely analýzy obalu dat s fixním součtem výstupů

raditional data envelopment analysis (DEA) models do not consider any relations with respect to the sum of values of outputs. In many real applications, the sum of outputs is predetermined and cannot be changed. In this paper, main models considering fixed-sum outputs are formulated and discussed their properties. They usually proceed in two steps. The first step consists in deriving a new efficient frontier, usually called equilibrium efficient frontier. This frontier is computed in such a way that the values offixed-sum outputs for all units are modified to reach maximum efficiency of all units. In the second step, the efficiency score of the original units is derived with respect to the new frontier. This characteristic allows complete ranking of the units. The results of the model are illustrated on the evaluation of efficiency ofcountries attending Winter Olympic Games 2022. They are compared with traditional DEA models.

Network DEA based on DEA-ratio

Data envelopment analysis (DEA) is a technique to measure the performance of decision-making units (DMUs). Conventional DEA treats DMUs as black boxes and the internal structure of DMUs is ignored. Two-stage DEA models are special case network DEA models that explore the internal structures of DMUs. Most often, one output cannot be produced by certain input data and/or the data may be expressed as ratio output/input. In these cases, traditional two-stage DEA models can no longer be used. To deal with these situations, we applied DEA-Ratio (DEA-R) to evaluate two-stage DMUs instead of traditional DEA. To this end, we developed two novel DEA-R models, namely, range directional DEA-R (RDD-R) and (weighted) Tchebycheff norm DEA-R (TND-R). The validity and reliability of our proposed approaches are shown by some examples. The Taiwanese non-life insurance companies are revisited using these proposed approaches and the results from the proposed methods are compared with those from some other methods.

Evaluation of the Efficiency of European Health Systems Using Fuzzy Data Envelopment Analysis.

Many studies that assess efficiency in health systems are based on output mean values. That approach ignores the representativeness of the average statistic, which can become a serious problem in estimation. To solve this question, this research contributes in three different ways: the first aim is to evaluate the technical efficiency in the management of European health systems considering a set of DEA (Data Envelopment Analysis) and FDEA (Fuzzy Data Envelopment Analysis) models. A second goal is to assess the bias in the estimation of efficiency when applying the conventional DEA. The third objective is the evaluation of the statistical relationship between the bias in the efficiency estimation and the macroeconomic variables (income inequality and economic freedom). The main results show positive correlations between DEA and FDEA scores. Notwithstanding traditional DEA models overestimate efficiency scores. Furthermore, the size of the bias is positively related to income inequality and negative with economic freedom in the countries evaluated.

A DANP-Based NDEA-MOP Approach to Evaluating the Patent Commercialization Performance of Industry–Academic Collaborations

The industry–academic collaboration (IAC) in developed and developing countries enables these economies to gain momentum in continuous innovation and, thus, economic growth. Patent commercialization is one major channel of knowledge flow in IAC. However, very few studies consider the flow of knowledge between industrial firms and universities. Moreover, ways that the patent commercialization performance of IACs can be evaluated are rarely discussed. Therefore, defining an analytic framework to evaluate the performance of IAC from the aspect of patent commercialization is critical. Traditionally, data envelopment analysis (DEA) models have widely been adopted in performance evaluation. However, traditional DEA models cannot accurately evaluate the performance of IACs with complex university–industry interconnections, the internal linkages, or linking activities of knowledge-flow within the decision-making units (DMUs), i.e., the IACs. In order to solve the abovementioned problems, this study defines a multiple objective programming (MOP)-based network DEA (NDEA), with weighting derived from the decision-making trial and evaluation laboratory (DEMATEL)-based analytic network process (ANP), or the DANP. The proposed analytic framework can evaluate the efficiency of decision-making units (DMUs) with a network structure (e.g., supply chains, strategic alliances, etc.) based on the weights that have been derived, based on experts’ opinions. An empirical study based on the performance of the patent commercialization of Taiwanese IACs was used to demonstrate the feasibility of the proposed framework. The results of the empirical research can serve as a basis for improving the performance of IAC.

A box-uncertainty in DEA: A robust performance measurement framework

The problem of assessment of Decision Making Units (DMUs) by using Data Envelopment Analysis (DEA) may not be straightforward due to the data uncertainty. Several studies have been developed to incorporate uncertainty into input/output values in the DEA literature. On the other hand, while traditional DEA models focus more on crisp data, there exist many applications in which data is reported in form of intervals. This paper considers the box-uncertainty in data which means that each input/output value is selected from a symmetric box. This specific type of uncertainty has been addressed as Interval DEA approaches. Our proposed model deals with efficiency evaluation of DMUs with imprecise data in a robust optimization. We assume that inputs and outputs are reported in the form of intervals and propose the robust counterpart problem for the envelopment form of the DEA model. Further, we also develop two ranking methods which have more benefits compared to some existing approaches. An illustrative example is provided to show how the proposed approaches work. An application on hospital efficiency in East Virginia is used to show the usefulness of the proposed approaches.

Two-stage DEA models with fairness concern: Modelling and computational aspects

In a two-stage series system with two sub-stages connected, fairness concern between two sub-stages is critical. In order to evaluate system performance fairly and objectively, data envelopment analysis (DEA) has been widely applied for evaluating multi-input and multi-output two-stage series systems. Traditional two-stage evaluation DEA models ignore the behavioral factors between two sub-stages. This paper studies how one behavioral factor, fairness concern, impacts decision making unit (DMU) by proposing new utility-based two-stage DEA models to analyse the non-cooperative and cooperative modes. Two simple algorithms are proposed to solve our nonlinear models and one simple algorithm is proposed to determine the parameters of fairness concern. Further, theorems are proposed to better understand the impacts of fairness concern on DMUs. Finally, a numerical example and an application of fairness concern between sub-stages in non-life insurance companies are given to illustrate the proposed approach and to compare it in different scenarios, respectively. The results from two examples show that acknowledging fairness concern in two-stage system is imperative to achieve its best performance.

Sustainability and Resilience Revisited: Impact of Information Technology Disruptions on Empirical Retail Logistics Efficiency

The increasing use of information technology (IT) in supply chain management and logistics is connected to corporate advantages and enhanced competitiveness provided by enterprise resource planning systems and warehouse management systems. One downside of advancing digitalization is an increasing dependence on IT systems and the negative effects of technology disruption impacts on firm performance, measured by logistics efficiency, e.g., with data envelopment analysis (DEA). While the traditional DEA model cannot deconstruct production processes to find the underlying causes of inefficiencies, network DEA (NDEA) can provide insights into resource allocation at the individual stages of operations. We apply an NDEA approach to measure the impact of IT disruptions on the efficiency of operational processes in retail logistics. We compare efficiency levels during IT disruptions, as well as ripple effects throughout subsequent days. In the first stage, we evaluate the efficiency of order picking in retail logistics. After handing over the transport units to the outgoing goods department of a warehouse, we assess the subsequent process of truck loading as a second stage. The obtained results underline the analytical power of NDEA models and demonstrate that the proposed model can evaluate IT disruptions in supply chains better than traditional approaches. Insights show that efficiency reductions after IT disruptions occur at different levels and for diverse reasons, and successful preparation and contingency management can support improvements.

Eco-efficiency evaluation in wastewater treatment plants considering greenhouse gas emissions through the data envelopment analysis-tolerance model

The eco-efficiency evaluation in wastewater treatment plants (WWTPs) is used to know and improve the environmental and economic efficiency of these processes, systems, products, and services. The eco-efficiency evaluations in WWTP contemplate the inputs to be minimized, the desirable results to be maximized, and the undesired results to be minimized. Data envelopment analysis (DEA) is a widely used method to evaluate the eco-efficiency of WWTPs; integrating several approaches in a single index, traditional DEA models do not take into account the uncertainty in the data. This study evaluates the eco-efficiency of a sample of Catalan WWTPs, considering the uncertainty of the data (DEA tolerance model), and it is for the first time that together with CO2, other greenhouse gas (GHG) such as CH4 and N2O are considered as part of the process outputs. GHG emissions were quantified using methods reported in the literature. Seven hundred twenty-nine eco-efficiency scores were estimated for each WWTP instead of a single score like conventional DEA models, analyzing optimistic and pessimistic scenarios. The WWTPs were classified according to the estimated eco-efficiency scores, accounting for the uncertainty in each of the scenarios, and demonstrating the changes in the performance of the WWTPs in the different scenarios. Only two WWTPs were eco-efficient in all the scenarios evaluated. This approach provides essential information to improve efficiency and innovation in the wastewater sector.

R&D innovation efficiency of Chinese high-tech industries: Three-stage network approach with fairness consideration

Recently, innovation evaluation has played an increasingly important role in the development of high-tech industry and the enhancement of international competitiveness. Data envelopment analysis (DEA) has been viewed as an effective data-driven method in evaluating the performance of decision-making units (DMUs). However, the traditional DEA models treat the DMUs as “black box.” As an extension of traditional DEA, a three-stage network evaluation transforming from a “black box” to a “gray box” structure has appeared. Unfortunately, the problem of intermediate elements has reduced the usefulness of the extended method. Although some gaming approaches have been introduced in the DEA model to reduce internal conflicts, the issue of fairness in the three stages, which have a significant impact on the behavior of the decision-makers, has still not been considered. To fill this gap, Neumann-Morgenstern cardinal utility is adopted to express the basic utility of a certain stage by considering itself efficiency and additional fairness utility from the other’s efficiency. Afterward, several non-cooperative DEA models have been developed by considering the efficiency of the leader stage and fairness disutility from other stages. Finally, a numerical example is presented and an empirical application is given to verify the proposed method.

Efficiency Measurement of Cloud Service Providers Using Network Data Envelopment Analysis

An increasing number of organizations and businesses around the world use cloud computing services to improve their performance in the competitive marketplace. However, one of the biggest challenges in using cloud computing services is performance measurement and the selection of the best cloud service providers (CSPs) based on quality of service (QoS) requirements <xref ref-type="bibr" rid="ref13" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[13]</xref> . To address this shortcoming in this article we propose a network data envelopment analysis (DEA) method in measuring the efficiency of CSPs. When network dimensions are taken into consideration, a more comprehensive analysis is enabled where divisional efficiency is reflected in overall efficiency estimates. This helps managers and decision makers in organizations to make accurate decisions in selecting cloud services. In the current study, the non-oriented network slacks-based measure (SBM) model and conventional SBM model with the assumptions of constant returns to scale (CRS) and variable returns to scale (VRS) are applied to measure the performance of 18 CSPs. The obtained results show the superiority of the network DEA model and they also demonstrate that the proposed model can evaluate and rank CSPs much better than compared to traditional DEA models.

Data envelopment analysis using the binary-data

PurposeThe purpose of this paper is to propose the data envelopment analysis (DEA) model that can be used as binary-valued data. Often the basic DEA models were developed by assuming that all of the data are non-negative. However, there are situations where all data are binary. As an example, the information on many diseases in health care is binary data. The existence of binary data in traditional DEA models may change the behavior of the production possibility set (PPS). This study defines a binary summation operator, expresses the modified principles and introduces the extracted PPS of axioms. Furthermore, this study proposes a binary integer programming of DEA (BIP-DEA) for assessing the efficiency scores to use as an alternate tool in prediction.Design/methodology/approachIn this study, the extracted PPS of modified axioms and the BIP-DEA model for assessing the efficiency score is proposed.FindingsThe binary integer model was proposed to eliminate the challenges of the binary-value data in DEA.Originality/valueThe importance of the proposed model for many fields including the health-care industry is that it can predict the occurrence or non-occurrence of the events, using binary data. This model has been applied to evaluate the most important risk factors for stroke disease and mechanical disorders. The targets set by this model can help to diagnose earlier the disease and increase the patients’ chances of recovery.

A data envelopment analysis model for performance evaluation and ranking of DMUs with alternative scenarios

Data envelopment analysis (DEA) is a general tool for measuring the relative efficiency ofhomogeneous decision-making units (DMUs). DEA models usually deal with crisp data and do not consider the conditions in which the inputs and outputs are uncertain. Many researchers have focused their research on these types of conditions, in which they assumed fuzzy data, interval data, and probabilistic data, as well as other expressions of uncertainty in the dataset. Various models, such as mean value and variance, robust DEA, multiple criteria decision-making (MCDM) models, and several other models, have been proposed. This paper deals withinstances in which uncertainty in the dataset is expressed by several alternative scenarios. The first presented model for problems with several alternative scenarios in their inputs and outputs is derived directly from the definition of the relative efficiency formula similar as those in traditional DEA models. This model is not linear and cannot be linearized. Due to this, we modify this model and derive a new model that is linear and can be solved easily. The proposed models have none of the common drawbacks attending other methods commonly applied to this set of issues. They are always feasible; moreover, they are able to generate a complete ranking of all DMUs using a computationally efficient procedure. Bothmodels are illustrated using a numerical example with 10 DMUs and three scenarios for input and output values, and their results are compared and discussed.

The circular economy transformation in industrial parks: Theoretical reframing of the resource and environment matrix

Checking the circular economy (CE) efficiency of industrial parks and exploring the potential reasons involved have not been systematically investigated. Recent researches lacked a unified and up-to-date framework toward CE in industrial parks emerging in high-quality development stage. It is therefore critical to build a new dimension and quantify the CE efficiency of industrial parks under the new historical period, so that appropriate policies can be formulated. This paper measures the CE efficiency of circular transformation by developing an original DEARA (Data Envelopment-Regression Analysis) model, and highlighting its advantages over the traditional DEA (Data Envelopment Analysis) model. To do this, an evaluation model is constructed that combines eight key indicators for environment, resources, economics and driving factors. The first batch of circular transformation pilot parks in China were selected for empirical analysis. The results show that the CE efficiency of sample parks has high variability from 0.112 to 1.030 in 2011. The efficiency matrix reveals a positive correlation between resources and environmental performance, with the driving factors for circular transformation being mainly GDP and leading industries. Compared with national indicators, the circular transformation of park levels is more effective in improving CE efficiency than the national average level of circular development, among which the experiences of the Beijing and Tianjin development zones are worthy of being exported to other industrial parks. Ultimately, this paper intends to contribute to policy instruments for developing viable and efficient industrial parks.

A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units that convert multiple inputs into multiple outputs. Traditional DEA models measure technical (radial) efficiencies by assuming the input and output status of each performance measure is known, and the data associated with the performance measures are non-negative. These assumptions are restrictive and limit the applications of DEA to real-world problems. We propose a new extended non-radial directional distance model, which is a variant of the weighted additive model, to cope with negative data. We then extend our model and use flexible measures, which play the role of both inputs and outputs, to cope with the unknown status of the performance measures. We also present a case study in the automotive industry to exhibit the efficacy of the models proposed in this study.

Methodological Approach for Providing a Suitable Model for Financial Ranking of Educational Hospitals by using of Cross-Performance Procedures (Case Work, Hospitals of Ahvaz Jundishapur University of Medical Sciences)

Background: Hospitals are multi-specialist social security organizations that account for a significant portion of the health system’s budget. Given the economic conditions and the importance of hospitals in the field of social health, it seems important and necessary to pay attention to financial performance and compare them with each other. Objectives: The purpose of this study was to provide a model for evaluating the performance and financial ranking of Ahvaz Jundishapur University of Medical Sciences’ Hospitals during 2018. Methods: This cross-sectional study was conducted at Ahvaz hospitals. Twenty-two hospitals were chosen according to random stratified sampling. First, the financial performance indicators of hospital performance evaluations are identified using the previous study method. Then, the financial performance evaluation indicators of hospitals are finalized by interviews with managers and experts of Ahvaz Medical Sciences’ Hospitals. To rank the hospitals, a cross-performance approach was used. Cross-performance is an acceptable approach in data envelopment analysis that provides a complete ranking of decision-making units (DMUs). In addition, a new secondary goal is presented in cross-performance. In this paper, an algorithm based on cross-performance is presented, and we will provide a model for ranking hospitals. Data were entered and analyzed using Statistical Package for Social Sciences (SPSS) and t-student and ANOVA tests. Results: The results show that although the traditional data envelopment analysis model is not able to rank uniquely from hospitals, the introduced pattern offers a unique ranking of hospitals. According to the results of this study, Imam Khomeini Hospital of Ramhormoz has the first rank, and Baqaei Hospital has the rank (22nd) in this ranking. Conclusions: The findings of this study represent the Hospital of financial position at the other hospitals and can be used in the hospital with good rankings in the service level of self-awareness as a template.

Cross-efficiency evaluation in data envelopment analysis based on the perspective of fairness utility

Data envelopment analysis (DEA) has been widely applied as an effective data-driven tool in evaluating the efficiency of decision making units (DMUs). However, traditional DEA models evaluate DMU efficiencies in a self-evaluation mode. As an extension of traditional DEA, cross-efficiency evaluation links one DMU’s performance with others and has the appeal that scores arise from peer evaluation. Unfortunately, the problem of non-unique optimal weights has reduced the usefulness of this extended method. Although, some current secondary goal approaches have reduced the non-uniqueness of optimal weights, they are mostly based on the perspectives of improving or worsening the evaluated DMU’s or other DMUs’ position or efficiency, which fails to consider DMU’s fairness mentality that plays an important role in guiding human interaction in behavioral economics. To fill this gap, we propose the concept of a fairness utility to construct our secondary goal model. Specifically, the secondary goal is to maximize the minimum fairness of the other DMUs when keeping the evaluated DMU’s optimal efficiency. Two algorithms are proposed. One is used to solve the nonlinear fairness utility model. The other is used to guarantee the unique optimal weights. Finally, a numerical example is presented, and an empirical application is given to verify the proposed method.

Integration Methodology of Spare Parts Supply Network Optimization and Decision-making

In order to optimize the spare parts supply network, a multi-objective optimization model is established with the objectives of the shortest supply time, the lowest risk, and the minimum supply cost. A decomposition-based multi-objective evolutionary algorithm with differential evolution strategy is introduced to solve the multi-objective model. A series of non-dominated solutions, that is, representing the optimal spare parts supply schemes are obtained. In order to comprehensively measure the performance of these solutions, suitable quantitative metrics are selected, and the secondary goal-based cross-efficiency Data Envelopment Analysis (DEA) model has been used to evaluate the efficiency of the obtained optimal schemes. The improved DEA model overcomes the problems that the efficient units cannot be sorted and the optimal weight is not unique in traditional DEA model. Finally, the self-evaluation efficiency and cross-evaluation efficiency of each scheme are obtained, and the optimal supply scheme is found based on their cross-evaluation efficiency.