DEA models for resource reallocation and production input/output estimation

This paper discusses the “inverse” data envelopment analysis (DEA) problem with preference cone constraints. An inverse DEA model can be used for a decision making unit (DMU) to estimate its input/output levels when some or all of its input/output entities are revised, given its current DEA efficiency level. The extension of introducing additional preference cones to the previously developed inverse DEA model allows the decision makers to incorporate their preferences or important policies over inputs/outputs into the production analysis and resource allocation process. We provide the properties of the inverse DEA problem through a discussion of its related multi-objective and weighted sum single-objective programming problems. Numerical examples are presented to illustrate the application procedure of our extended inverse DEA model. In particular, we demonstrate how to apply the model to the case of a local home electrical appliance group company for its resource reallocation decisions.     

Technological externalities and environmental policy

The directional distance function defined in a DEA type non-parametric framework provides a highly flexible structure for modelling producer behaviour in the presence of polluting emissions and environmental regulations. This article presents five models describing different “command and control” type policy measures as an economic one about nitrogen pollution of agricultural origin. These measures concern the management of the mandatory constraint on the spreading of organic manure and the investment in manure treatment facilities. The study also simulates the use of an economic instrument by enforcing the individual manure constraint at an aggregated level. Using individual and aggregated DEA models, this paper provides insights into the impact of individual and collective management of environmental policy instruments.     

Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods

The aim of the paper is to present and substantiate a technique to visualize DEA modelling results without any loss of mathematical rigour. The proposed family of parametric optimization methods allows one to construct an intersection of the multidimensional frontier with a two-dimensional plane determined by any pair of given directions. This approach reduces the efficiency analysis of production units to the investigation of well-known functions in economics. We also propose constructive methods to calculate marginal rates of substitution, marginal rates of transformation and so on.     

The relationship between the efficiency of orthopedic wards and the socio-economic status of their patients

The purpose of this paper is to study the effect of the socio-economic status of patients on the efficiency of orthopedic wards in acute hospitals in Israel (20 hospitals), from the viewpoint of the regulator—Israel Ministry of Health. At the first stage, data envelopment analysis is used with two inputs, and three outputs, where one output is undesirable—“number of deaths”—which also reflects the quality of the health services. At the second stage, various nonparametric tests are utilized to test the relationship between the socio-economic status of patients and the efficiency. As by-product DEA provides benchmark analysis, which indicates the peers of each inefficient ward, and the I/O improvements are needed for achieving efficiency. Two versions of DEA were used: the output oriented version (variable returns to scale), and the non-oriented version (Additive). Further analysis provides comparison of the results with other simple efficiency measures. We also compare between the efficiency from the regulator viewpoint and the hospitals’ viewpoint.     

The relevance of DEA benchmarking information and the Least-Distance Measure

Efficiency analysis is performed not only to estimate the current level of efficiency, but also to provide information on how to remove inefficiency, that is, to obtain benchmarking information. Data Envelopment Analysis (DEA) was developed in order to satisfy both objectives and the strength of its benchmarking analysis gives DEA a unique advantage over other methodologies of efficiency analysis. This study proposes the use of the Least-Distance Measure in order to obtain the shortest projection from the evaluated Decision Making Unit (DMU) to the strongly efficient production frontier, thus allowing an inefficient DMU to find the easiest way to improve its efficiency. In addition to producing reasonable benchmarking information, the proposed model provides efficiency values which satisfy the general requirements that every well-defined efficiency measure should meet.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

Productivity and customer satisfaction in Swedish pharmacies: A DEA network model

This paper presents a Data Envelopment Analysis (DEA) network model that allows inclusion of customer satisfaction in efficiency and productivity measures. The network consists of a production node and a consumption node and offers flexibility in modelling the production and consumption process where a firm-specific allocation of input resources to production and customer oriented activities is allowed. The proposed model is applied on a sample of Swedish pharmacies with organizational objectives that necessitates a monitoring of efficiency and productivity as well as customer satisfaction. Estimation results from the network model and a direct productivity model (without customer satisfaction) are compared and indicate that the technical efficiency is lower under the network model. The productivity results indicate productivity progress under both models, albeit with a slower rate of change under the network model.     

Two-dimensional efficiency decomposition to measure the demand effect in productivity analysis

This paper proposes a two-dimensional efficiency decomposition (2DED) of profitability for a production system to account for the demand effect observed in productivity analysis. The first dimension identifies four components of efficiency: capacity design, demand generation, operations, and demand consumption, using Network Data Envelopment Analysis (Network DEA). The second dimension decomposes the efficiency measures and integrates them into a profitability efficiency framework. Thus, each component’s profitability change can be analyzed based on technical efficiency change, scale efficiency change and allocative efficiency change. An empirical study based on data from 2006 to 2008 for the US airline industry finds that the regress of productivity is mainly caused by a demand fluctuation in 2007-2008 rather than technical regression in production capabilities.     

Sensitivity analysis of inefficient units in data envelopment analysis

One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data.This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score.     

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.     

Measuring dynamic efficiency: Theories and an integrated methodology

Almost all dynamic production systems are subject to lagged productive effects, which are an often-ignored latent source of interference in the efficiency measuring process. Existing data envelopment analysis (DEA) approaches rely on a static production environment. They can easily lead to biased evaluation results due to the erroneous assumption. To tackle this issue, this paper develops a dynamic DEA model that allows intertemporal effects in efficiency measuring. Specifically, the dynamic DEA model incorporates dynamic factors via a linear parametric formulation. Our model can be applied in place of static DEA models to a wide range of applications, such as analyzing longitudinal firm performance and productivity changes. As for the empirical efficiencies, we demonstrate how the lag parameters in the dynamic model can be estimated by the panel vector autoregressive model (PVAR). We use our methodology to evaluate advertising efficiencies of several major automobile and pharmaceutical firms in North America. The result shows that using static DEA in dynamic production can lead to both rank reversals and changes in efficiency scores.     

Maintaining the Regular Ultra Passum Law in data envelopment analysis

The variable returns to scale data envelopment analysis (DEA) model is developed with a maintained hypothesis of convexity in input–output space. This hypothesis is not consistent with standard microeconomic production theory that posits an S-shape for the production frontier, i.e. for production technologies that obey the Regular Ultra Passum Law. Consequently, measures of technical efficiency assuming convexity are biased downward. In this paper, we provide a more general DEA model that allows the S-shape.     

Statistical inference for DEA estimators of directional distances

In productivity and efficiency analysis, the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set. The most familiar non-parametric methods use Farrell–Debreu, Shephard, or hyperbolic radial measures. These approaches require that inputs and outputs be non-negative, which can be problematic when using financial data. Recently, Chambers et al. (1998) have introduced directional distance functions which can be viewed as additive (rather than multiplicative) measures efficiency. Directional distance functions are not restricted to non-negative input and output quantities; in addition, the traditional input and output-oriented measures are nested as special cases of directional distance functions. Consequently, directional distances provide greater flexibility. However, until now, only free disposal hull (FDH) estimators of directional distances (and their conditional and robust extensions) have known statistical properties (Simar and Vanhems, 2012). This paper develops the statistical properties of directional d estimators, which are especially useful when the production set is assumed convex. We first establish that the directional Data Envelopment Analysis (DEA) estimators share the known properties of the traditional radial DEA estimators. We then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance, estimation of confidence intervals, and bias correction. The methods are illustrated in some empirical examples.     

Data Envelopment Analysis Applied to Electricity Distribution Districts

In this paper Data Envelopment Analysis (DEA) is used to evaluate efficiency measures for the 45 distribution districts of the Greek Public Power Corporation (PPC). Results are derived under different sets of assumptions and are compared with simple productivity indices used by PPC and with efficiency measures produced by econometric methods. DEA scores appear to be more reliable than simple productivity indices. Comparison of the different cases explains the reason for the low efficiencies, which can be due to the management of controllable inputs, the design of the supply system or other environmental factors.     

Determining new possible weight values in PROMETHEE: a procedure based on data envelopment analysis

Operational research (OR) offers efficient tools to support managers in strategic decision-making processes. Data envelopment analysis (DEA) and multiple criteria decision aid (MCDA) are two important research areas in OR. These two domains are both based on the evaluation of “objects” according to multiple “points of views”. Within the MCDA framework, choosing appropriate weights for the different criteria often arises as a problem itself for decision makers. As a consequence, researchers have developed original methodologies to help them during this elicitation phase. In this work, we aim to investigate how DEA can be used to propose weights in the context of the PROMETHEE II method. More precisely, we suggest an extension of the so-called “decision maker brain” used in the GAIA plane (also known as PROMETHEE VI) based on DEA. The underlying idea is based on the computation of weights in PROMETHEE (GAIA brain) which are compatible with the DEA analysis. We end this paper with a numerical example.     

Costs and efficiency of higher education institutions in England: a DEA analysis

As student numbers in higher education in the UK have expanded during recent years, it has become increasingly important to understand its cost structure. This study applies Data Envelopment Analysis (DEA) to higher education institutions in England to assess their cost structure, efficiency and productivity. The paper complements an earlier study that used parametric methods to analyse the same panel data. Interestingly, DEA provides estimates of subject-specific unit costs that are in the same ballpark as those provided by the parametric methods. The paper then extends the previous analysis and finds that further student number increases of the order of 20–27% are feasible through exploiting operating and scale efficiency gains and also adjusting student mix. Finally the paper uses a Malmquist index approach to assess productivity change in the UK higher education. The results reveal that for a majority of institutions productivity has actually decreased during the study period.     

Measuring the efficiency of forest districts with multiple working circles

Data envelopment analysis (DEA) is a methodology extensively applied to measuring the relative efficiency of decision making units with multiple inputs and multiple outputs. Herein, a DEA model is developed to measure the efficiency of forest districts which are divided into a number of subdistricts called working circles (WCs). The idea is to construct district production frontiers from the WCs of individual districts. Superimposing the district production frontiers of different districts one derives the forest production frontier. The closeness of a district production frontier to the forest production frontier indicates this district's efficiency. As an illustration, the developed model measures the eight districts, with a total of thirty-four WCs, of the national forests of the Republic of China on Taiwan. The results provide the top management with an idea of how far each district can be expected to improve its performance when compared with other districts.     

Improving data envelopment analysis by the use of production trade-offs

Production technologies in data envelopment analysis (DEA) are described in terms of inputs and outputs. Production trade-offs represent simultaneous changes to the inputs and outputs that are possible in the technology under consideration. Recently, a method for their incorporation in DEA models has been developed. It was shown that the use of production trade-offs not only improves the discrimination of DEA models but also preserves the traditional meaning of efficiency as a radial improvement factor for inputs and outputs. This new paper follows the above development and provides an example of its use in the assessment of efficiency of university departments. The paper avoids excessive technical detail which can be found in the previous publication and instead focuses on the implementation of this new technique.     

Dual models of interval DEA and its extension to interval data

The purpose of this paper is to develop a new DEA with an interval efficiency. An original DEA model is to evaluate each DMU optimistically. There is another model called “Inverted DEA” to evaluate each DMU pessimistically. But, there are no relations essentially between DEA and inverted DEA. Thus, we formulate a DEA model with an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints. Thus, two end points can construct an interval efficiency. With the same idea, we deal with the interval inefficiency model which is inverse to interval efficiency. Finally, we extend the proposed DEA model to interval data and fuzzy data.     

Efficiency analysis in multi-period systems: an application to performance evaluation in Czech higher education

Data envelopment analysis (DEA) is a non-parametric method for efficiency and performance analysis of decision making units. The paper deals with production systems where decision making units are described by their inputs and outputs in several consecutive periods. The paper presents (Park and Park in Eur J Oper Res 193(2):567–580, 2009) multi-period DEA model that is oriented on the “best” period of the unit under evaluation only. This aim of this paper is to overcome the disadvantage of this model and formulate new models of this class that allow evaluation the efficiency of decision making units within the whole production chain. The presented efficiency and super-efficiency multi-period DEA models are illustrated on a case study. The study consists in analysis of research and teaching performance of 19 Czech economic faculties in four years period from 2009 until 2012. The model considers two inputs (number of academic employees and labour costs) and two outputs for teaching efficiency (number of students and number of graduated). Research efficiency is expressed using the number of publications in various important categories and the number of so called RIV points that describe the quality of publications.