Data Envelopment Analysis: From Foundations to Modern Advancements

Combining ranking scales and selecting variables in the DEA context: The case of industrial branches

This chapter presents work on the use of an artificial intelligence technique to cluster stratified samples of container terminals derived from Data Envelopment Analysis (DEA). This technique is Kohonen’s self-organizing map (SOM; (Kohonen, 1995)). Data envelopment analysis measures the relative efficiency of comparable entities called Decision Making Units (DMUs) essentially performing the same task using similar multiple inputs to produce similar multiple outputs ((Charnes et al., 1978)). The purpose of DEA is to empirically estimate the so-called efficient frontier based on the set of available DMUs. DEA provides the user with information about the efficient and inefficient units, as well as the efficiency scores and reference sets for inefficient units. The results of the DEA analysis, especially the efficiency scores, are used in practical applications as performance indicators. There are many problems associated with applying the DEA in some applications. One problem is that the improvement projection for inefficient units in DEA analysis is concrete relative to its efficiency score. This means, in DEA, relative performance of any DMU can be contrasted only to the efficient DMUs that register unit efficiency score. There is no influence on the performance of efficient DMUs by presence or absence of inefficient DMUs. Therefore, the classical DEA does not actually provide a direct means to rank DMUs based on their relative degrees of efficiency or inefficiency ((Sharma & Yu, 2010)). The second problem is that the DEA models assume that all DMUs are homogenous and identical in their operations ((Seiford, 1994)). Since various applications have heterogeneous DMUs and there is a high request to evaluate these applications under the DEA due to its acceptance as a performance measurement in different kind of business, we have to modify the DEA to work with these applications. If the heterogeneous DMUs are assessed by DEA without any modifications, the DEA yields a biased performance scores and inaccurate analyses. For example, the resources (land, equipment, and labor) of container terminals varies across the world, which requires to be evaluated in term of its common input characterstics. An essential requirement in analyzing these container terminals is to build a fair referencing system for each container terminal to manage and provide a solid plan that improves all inefficient terminals and supports all efficient terminals. This system can not be assessed under the standard DEA due to the non-homogenous nature of these container terminals in terms of their operations, different standards of equipments, infrastructure, and variety in quay length and area size. These factors will yield unfair benchmarking evaluation 5

DEA (Data Envelopment Analysis) is a nonparametric approach that has been used to estimate fuzzy portfolio efficiency. In this paper, we propose an approach under the fuzzy theory framework that can both improve the DEA frontier and suggest a replicable benchmark for investors. We first construct an improved DEA model using the proposed approach and then investigate the relationships among the evaluation model based on a portfolio frontier, the traditional DEA model and the improved DEA model. We show the convergence of the improved DEA model under the fuzzy framework. The simulation indicates that the improved DEA frontier is closer to the portfolio frontier than to the traditional DEA frontier. More importantly, we incorporate the diversification DEA model and improved DEA model to analyze the performance of China’s open-end fund. The empirical results indicate that the improved DEA model not only provides a quicker way to assess the investment funds compared to the diversification DEA model but also makes up for the shortcoming of the traditional DEA model, which overestimates the fuzzy portfolio efficiency.

Objectives: To provide a critical appraisal of the methods, results and policy value of two frontier methods for hospital efficiency measurement: data envelopment analysis (DEA) and stochastic frontier analysis (SFA). To compare the policy value of DEA- and SFA-based measures against more commonly used indicators of hospital performance. Methods: Comparative analysis of DEA and SFA in estimating the relative efficiency of public hospitals in Victoria. Possible sources of measured inefficiency are investigated via the Battese and Coelli (1995) effects model in the case of SFA-based efficiency scores and via second-stage regressions in the case of DEA-based efficiency measures. The content and consistency of DEA- and SFA-based targets and measures are then compared against simple cost/output ratios. Results: Moderate correspondence between DEA- and SFA-based efficiency scores with measured inefficiency at least partially attributable to between-hospital differences in casemix, stay-mix, quality of care, teaching/research activity and location. More or less the same set of hospital characteristics turned out to be important in explaining between-hospital variation in both DEA- and SFA-based measures of hospital efficiency. In short, results provided some reassurance that DEA and SFA are measuring closely related constructs, along similar dimensions. Perhaps surprisingly, there is at least as much common ground between simple cost/output ratios and SFA-based measures of hospital efficiency, as there is between DEA- and SFA-based alternatives. Conclusions: Frontier-based measures of hospital performance are broadly consistent with simpler, more commonly available performance measures. However, consistency and precision are not the only considerations in selecting policy-ready performance measures and deliberations as to the policy-value of frontier- and ratio-based options should take account of both precision and content.

Methodological comparison between DEA (data envelopment analysis) and DEA–DA (discriminant analysis) from the perspective of bankruptcy assessment

Data envelopment analysis (DEA) has become the dominant approach to efficiency measurement in health care and in many other sectors of the economy (Hollingsworth 2003). While the parametric approach is guided by economic theory, DEA is a data-driven approach. The location (and the shape) of the efficiency frontier is determined by the data, using the simple notion that an organisation that employs less input than another to produce the same amount of output can be considered more efficient. Those observations with the highest ratios of output to input are considered efficient, and the efficiency frontier is constructed by joining these observations up in the input-output space. The frontier thus comprises a series of linear segments connecting one efficient observation to another. The construction of the frontier is based on ‘best observed practice’ and is therefore only an approximation to the true, unobserved efficiency frontier.

Purpose: The objective of this article is to investigate the technical efficiency of Poland's district court system from 2002 to 2021, employing a constrained variant of Data Envelopment Analysis (DEA) on appropriately processed time series data. Design/methodology/approach: Different DEA models were employed to estimate the technical efficiency of this system, beginning with classical CCR DEA and super-efficiency DEA. After identifying crucial shortcomings in the outcomes produced by these two methods, a novel procedure based on constrained DEA was proposed to address and overcome these limitations in the context of evaluating judicial efficiency using DEA. Findings: Applying super-efficiency DEA to a small sample does not yield sound or fully interpretable outcomes regarding the estimated scores of individual DMUs, despite seemingly increasing the variability of these scores. It is only when adequate restrictions are imposed on both the input and output weights—price and virtual alike—that one can obtain results free from the significant imperfections commonly associated with the classical DEA method in the context of judicial efficiency. Research limitations/implications: Ignoring the inherent shortcomings of classical or super efficiency DEA can lead to significant distortions in the estimated ratings assigned to individual DMUs. Practical implications: Policy recommendations derived from traditional unconstrained DEA, intended to enhance the actual efficiency of specific DMUs, might ultimately be misleading. Originality/value: The research contributes to the existing body of knowledge on judicial efficiency in at least two significant ways. First, unlike previous studies, it focuses on a single DMU (the first-instance court system) over a long 20-year period, allowing conclusions drawn from this investigation to be interpreted within the context of systemic macro-level efficiency over time. Secondly, and more importantly, the article highlights the inherent weaknesses of classical DEA, which cast reasonable doubt on the quality and interpretability of the results obtained using this method. To address these issues, the article introduces—for the first time in the field of judicial efficiency research—a procedure specifically designed to overcome these limitations. Keywords: efficiency, DEA, weight constraints, judiciary. Category of the paper: Research article.

The standard Data Envelopment Analysis (DEA) method requires that the values for all inputs and outputs are known exactly. When some inputs and output are imprecise data, such as interval or bounded data, ordinal data, and ratio bounded data, the resulting DEA model becomes a non-linear programming problem. Such a DEA model is called imprecise DEA (IDEA) in the literature. There are two approaches in dealing with such imprecise inputs and outputs. One approach uses scale transformations and variable alternations to convert the non-linear IDEA model into a linear program. The other identifies a set of exact data from the imprecise inputs and outputs and then uses the standard linear DEA model. This chapter focuses on the latter IDEA approach that uses the standard DEA model. This chapter shows that different results are obtained depending on whether the imprecise data are introduced directly into the multiplier or envelopment DEA model. Because the presence of imprecise data invalidates the linear duality between the multiplier and envelopment DEA models. The multiplier IDEA (MIDEA), developed based upon the multiplier DEA model, presents the best efficiency scenario whereas the envelopment IDEA (EIDEA), developed based upon the envelopment DEA model, presents the worst efficiency scenario. Weight restrictions are often redundant if they are added into MIDEA. Alternative optimal solutions on the imprecise data can be determined using the recent sensitivity analysis approach. The approaches are illustrated with both numerical and real world data sets.

In view of the defect that network DEA (data envelopment analysis) can not reflect the network structure when it comes to dynamic evaluation, we proposed a two-stage evaluation method of dynamic network DEA. Time parameter was introduced to network DEA and dynamic network DEA model was established. In order to evaluate the efficiency of dynamic network DEA in several time spans, we built a two-stage evaluation method. In the first stage, dynamic network DEA efficiency matrix was formulated. In the second one, a new input-output DEA unit was set up to evaluate the synthetical efficiency of dynamic network DEA. The two-stage method can manifest the real dynamic property in network DEA, as well as consider the network structure which involves intermediate products by dynamic measure. A numerical example indicated that the two-stage evaluation method can solve dynamic network DEA problem efficiently, it can also provide improved information between inefficient DMU and optimum values by slacks. The new measure can be a good tool of systems analysis.

Data envelopment analysis (DEA) is a method for measuring efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU using a set of most favourable weights. As a result, traditional DEA models can be considered methods for the analysis of the best relative efficiency or analysis of the optimistic efficiency. DEA efficient DMUs obtained from conventional DEA models create an efficient production frontier. Traditional DEA can be used to identify units with good performance in the most desirable scenarios. There is a similar approach that evaluates the performance indicators of each DMU using a set of most unfavourable weights. Accordingly, such models can be considered models for analysing the worst relative efficiency or pessimistic efficiency. This approach uses the inefficient production frontier for determining the worst relative efficiency that can be assigned to each DMU. DMUs lying on the inefficient production frontier are referred to as DEA inefficient while those neither on the efficient frontier nor on the inefficient frontier are declared DEA inefficient. It can be argued that both relative efficiencies should be considered simultaneously and any approach with only one of them would be biased. This paper proposed the integration of both efficiencies as an interval so that the overall performance score would belong to this interval. It was shown that efficiency interval provided more information than either of the two efficiencies, which was illustrated using two numerical examples.

This paper proposes that data envelopment analysis (DEA) should be viewed as a method (or tool) for data-oriented analytics in performance evaluation and benchmarking. While computational algorithms have been developed to deal with large volumes of data (decision making units, inputs, and outputs) under the conventional DEA, valuable information hidden in big data that are represented by network structures should be extracted by DEA. These network structures, e.g., transportation and logistics systems, encompass a broader range of inter-linked metrics that cannot be modelled by conventional DEA. It is proposed that network DEA is related to the value dimension of big data. It is shown that network DEA is different from standard DEA, although it bears the name of DEA and some similarity with conventional DEA. Network DEA is big data enabled analytics (big DEA) when multiple (performance) metrics or attributes are linked through network structures. These network structures are too large or complex to be dealt with by conventional DEA. Unlike conventional DEA that are solved via linear programming, general network DEA corresponds to nonconvex optimization problems. This represents opportunities for developing techniques for solving non-linear network DEA models. Areas such as transportation and logistics system as well as supply chains have a great potential to use network DEA in big data modeling.

The healthcare industry is one application for data envelopment analysis (DEA) that can have significant benefits for standardizing health service delivery. This narrative review focuses on the application of DEA in emergency departments (EDs) and the management of emergency conditions such as acute ischemic stroke and acute myocardial infarction (AMI). This includes benchmarking the proportion of patients that receive treatment for these emergency conditions. The most frequent primary areas of study motivating work in DEA, EDs and management of emergency conditions including acute management of stroke are sorted into five distinct clusters in this study: (1) using basic DEA models for efficiency analysis in EDs, i.e., applying variable return to scale (VRS), or constant return to scale (CRS) to ED operations; (2) combining advanced and basic DEA approaches in EDs, i.e., applying super-efficiency with basic DEA or advanced DEA approaches such as additive model (ADD) and slack-based measurement (SBM) to clarify the dynamic aspects of ED efficiency throughout the duration of a first-aid program for AMI or heart attack; (3) applying DEA time series models in EDs like the early use of thrombolysis and percutaneous coronary intervention (PCI) in AMI treatment, and endovascular thrombectomy (EVT) in acute ischemic stroke treatment, i.e., using window analysis and Malmquist productivity index (MPI) to benchmark the performance of EDs over time; (4) integrating other approaches with DEA in EDs, i.e., combining simulations, machine learning (ML), multi-criteria decision analysis (MCDM) by DEA to reduce patient waiting times, and futile transfers; and (5) applying various DEA models for the management of acute ischemic stroke, i.e., using DEA to increase the number of eligible acute ischemic stroke patients receiving EVT and other medical ischemic stroke treatment in the form of thrombolysis (alteplase and now Tenecteplase). We thoroughly assess the methodological basis of the papers, offering detailed explanations regarding the applied models, selected inputs and outputs, and all relevant methodologies. In conclusion, we explore several ways to enhance DEA's status, transforming it from a mere technical application into a strong methodology that can be utilized by healthcare managers and decision-makers.

Data envelopment analysis (DEA) is a non-parametric technique to measure the efficiency of productive units as they transform inputs into outputs. A productive unit has, in DEA terms, an all-encompassing definition. It may as well refer to a factory whose products were made from raw materials and labor or to a school that, from prior knowledge and lessons time, produces more knowledge. All these units are usually named decision making units (DMU). So, DEA is a technique enabling the calculation of a single performance measure to evaluate a system. Although some DEA techniques that cater for decision makers’ preferences or specialists’ opinions do exist, they do not allow for interactivity. Inversely, interactivity is one of the strongest points of many of the multi-criteria decision aid (MCDA) approaches, among which those involved with multi-objective linear programming (MOLP) are found. It has been found for several years that those methods and DEA have several points in common. So, many works have taken advantage of those common points to gain insight from a point of view as the other is being used. The idea of using MOLP, in a DEA context, appears with the Pareto efficiency concept that both approaches share. However, owing to the limitations of computational tools, interactivity is not always fully exploited. In this article we shall show how one, the more promising model in our opinion that uses both DEA and MOLP (Li & Reeves, 1999), can be better exploited with the use of TRIMAP (Climaco & Antunes, 1987, 1989). This computational technique, owing in part to its graphic interface, will allow the MCDEA method potentialities to be better used. MOLP and DEA share several concepts. To avoid naming confusion, the word weights will be used for the weighing coefficients of the objective functions in the multi-objective problem. For the input and output coefficients the word multiplier shall be used. Still in this context, the word efficient shall be used only in a DEA context and, for the MOLP problems, the optimal Pareto solutions will be called non-dominated solutions.

The field of data envelopment analysis (DEA) has evolved rapidly since its introduction to decision-making science 40 years ago. DEA has since attracted the attention of many researchers because of its unique characteristic to measure the efficiency of multiple-input and multiple-output decision-making units (DMUs) without assigning prior weight to the input and output, unlike most available decision analysis tools. The body of research has resulted in a huge amount of literature and diverse DEA models with very many different approaches. DEA classifies all units under assessment into two groups: efficient with a 100% efficiency score and inefficient with a less than 100% efficiency score. This ability is considered both a strength and a weakness of the standard DEA model because, although it allows DEA to evaluate the efficiency of any dataset, it lacks the power to rank all DMUs, by giving full efficiency scores to many efficient units. This issue has attracted many researchers to investigate the weak discrimination power of classical DEA models, resulting in a subfield of research that focuses on DEA ranking. This thesis focuses on the development of the conventional DEA model, and an attempt has been made to study models that are considered as improved models, or approaches that bring a better ranking field, that may bring more accurate evaluation than the original DEA. After studying DEA ranking models, the thesis presents various models under the optimistic and pessimistic DEA ranking approaches. The first and fundamental contribution are the optimistic and pessimistic free disposal hull (FDH) models. In this study, authentic optimistic and pessimistic DEA models without convexity are developed from both input and output orientation. Further into the research investigation, extended models have been proposed, by combining the conventional and FDH ranking models with other different approaches in the literature. Chapter 4 of this thesis presents three extended FDH models: an FDH slack-based model, an FDH superefficiency model, and a dual frontier without infeasibility super-efficiency FDH model. Chapter 5 shows the development of extended models when virtual DMUs are considered. Improved virtual DMU models and improved FDH virtual DMU models are proposed in order to develop the DEA ranking ability from both optimistic and pessimistic approaches. The final model is an optimistic and pessimistic forecasting approach using regression analysis. The forecasting model can be used by decision makers to determine the resources needed for future planning to build an efficient new unit with reference to the current DMU set.

Data envelopment analysis (DEA) has gained great popularity in environmental performance measurement because it can provide a synthetic, standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. This paper applies the DEA approaches to evaluate the CO2 emission performance and measure its satisfaction degree of 40 countries and regions from 2008 to 2009. We use the input variables of capital, energy consumption and population and the output variables of gross domestic product (GDP) and the amount of fossil-fuel CO2 emissions. Past studies about the application of DEA to environmental performance measurement have not considered uncontrollable factors. In this paper, we present the DEA formulas with controllable and uncontrollable factors to measure environment performance and its satisfaction degree. We first define and construct the environmental production technologies with desirable and undesirable outputs. The degree of environment satisfaction performance based on the DEA approach can be computed by solving a series of data envelopment analysis formulas. A case study of 40 countries and regions applying the DEA approach is also presented.