Data Envelopment Analysis Frontier Research Articles

Mixed input and output orientations of Data Envelopment Analysis with Linear Fractional Programming and Least Distance Measures

Data Envelopment Analysis (DEA) is an optimization technique to evaluate the efficiency of Decision- Making Units (DMU’s) together with multiple inputs and multiple outputs on the strength of weighted input and output ratios, where as Linear fractional programming is used to obtain DEA frontier. The efficiency scores of DMU obtained through either input orientation or output orientation DEA model will provide only local optimum solution. However, the mixed orientation of input and output variables will provide the global optimal solution for getting the efficient DMUs in DEA. This study has proposed the relationships of a mixed orientation of input and output variables using fractional linear programming along with Least-Distance Measure (LDM). Both constant returns to scale (CRS) and variable returns to scale (VRS) are considered for the comparative study.

Future planning for benchmarking and ranking sustainable suppliers using goal programming and robust double frontiers DEA

Decision-making for selecting sustainable suppliers has become an intricate duty. To rank sustainable suppliers and select benchmarks this paper proposes an efficiency improvement plan. Two levels of improvement plans including goals and benchmarks are presented for the suppliers. To this end, the first-level goals are obtained using goal programming (GP) and data envelopment analysis (DEA). Since inputs and outputs of the first-level goals might be imprecise, robust Charnes-Cooper-Rhodes (CCR) model is run. As a result, the benchmarks of the second-level are obtained. Then, a robust CCR inefficiency model is applied for ranking the suppliers. In fact, such a ranking capability is made by creating double-frontiers including CCR efficiency and inefficiency frontiers. Accordingly, the suppliers are ranked using the first-level goals. In the new ranking, uncertainty of the goals is considered by running robust optimization technique. The proposed approach provides technical and planning capabilities which are demonstrated by a case study.

Graph productivity change measure using the least distance to the pareto-efficient frontier in data envelopment analysis

This paper proposes a new method to measure productivity change of decision making units in the full input-output space. The new approach is based on the calculation of the least distance to the Pareto-efficient frontier and hence provides the closest targets for evaluated decision making units to reach the strongly efficient frontier with least effort. Another advantage of the new methodology is that it always leads to feasible solutions. The productivity change in the new approach is operationalized as a Luenberger-type indicator in the Data Envelopment Analysis framework and it is decomposed into efficiency change and technical change. The paper empirically illustrates the new method using recent data on the Spanish quality wine sector.

The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects

Determining the least distance to the efficient frontier for estimating technical inefficiency, with the consequent determination of closest targets, has been one of the relevant issues in recent Data Envelopment Analysis literature. This new paradigm contrasts with traditional approaches, which yield furthest targets. In this respect, some techniques have been proposed in order to implement the new paradigm. A group of these techniques is based on identifying all the efficient faces of the polyhedral production possibility set and, therefore, is associated with the resolution of a NP-hard problem. In contrast, a second group proposes different models and particular algorithms to solve the problem avoiding the explicit identification of all these faces. These techniques have been applied more or less successfully. Nonetheless, the new paradigm is still unsatisfactory and incomplete to a certain extent. One of these challenges is that related to measuring technical inefficiency in the context of oriented models, i.e., models that aim at changing inputs or outputs but not both. In this paper, we show that existing specific techniques for determining the least distance without identifying explicitly the frontier structure for graph measures, which change inputs and outputs at the same time, do not work for oriented models. Consequently, a new methodology for satisfactorily implementing these situations is proposed. Finally, the new approach is empirically checked by using a recent PISA database consisting of 902 schools.

The carbon dioxide marginal abatement cost calculation of Chinese provinces based on stochastic frontier analysis

The Chinese government made a commitment to achieve a 40–45 % reduction in carbon emissions per unit of gross domestic product (GDP) by 2020 compared with 2005. Most provinces followed the national commitment due to unified task of 40–45 % reduction in carbon emissions. However, different industrial structures, energy consumption structures and natural resources endowment of each province vary the emission abatement costs. Each province should take the carbon dioxide abatement cost into consideration for the carbon dioxide reduction target. Data envelopment analysis (DEA) and linear programming (LP) methods were used to measure the marginal abatement cost in previous studies. In this paper, we built a quadratic parametric directional distance function (DDF) to measure the carbon dioxide marginal abatement cost of Chinese provinces. To overcome the flaw of ignoring random errors in previous research, this paper compared results of stochastic frontier analysis (SFA) method and DEA method. Because DEA method only considers the inefficiency and SFA method can distinguish the random error from inefficiency, the result of the average carbon dioxide marginal abatement cost of each province calculated by SFA was 55 % lower than DEA method. As the random error may be introduced by chosen function form, Spearman test and paired sample T test were used to test the correlation of two methods’ MAC results. The results show that the ranking order MAC results sequence of SFA method and DEA method is highly correlated. But the MAC value of SFA and DEA methods has significant difference. As half of the error comes from the random error, the MAC results calculated by SFA method are more precise than DEA method. So SFA method is more appropriate than DEA in this paper. This result reinforces the feasibility of the Chinese government carbon dioxide emission reduction target. However, this study proved that the carbon dioxide emissions and marginal abatement cost varied from province to province. Furthermore, there was no distinct correlation between carbon dioxide emissions and the marginal abatement cost. On the contrary, the marginal abatement cost was related to the industrial structures, energy consumption structures and natural resources endowment of each province. Therefore, two policy suggestions are proposed as CO2 emission reduction principle: First, central government should establish CO2 emission reduction targets based on MAC and local economic affordability. Second, resource endowments and embodied carbon transfer should be considered.

From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scale

The characterization of a technology, from an economic point of view, often uses the first derivatives of either the transformation or the production function. In a parametric setting, these quantities are readily available as they can be easily deduced from the first derivatives of the specified function. In the standard framework of data envelopment analysis (DEA) models these quantities are not so easily obtained. The difficulty resides in the fact that marginal changes of inputs and outputs might affect the position of the frontier itself while the calculation of first derivatives for economic purposes assumes that the frontier is held constant. We develop here a procedure to recover first derivatives of transformation functions in DEA models and we show how we can evacuate the problem of the (marginal) shift of the frontier. We show how the knowledge of the first derivatives of the frontier estimated by DEA can be used to deduce and compute marginal products, marginal rates of substitution, and returns to scale for each decision making unit (DMU) in the sample.

Using multi-level frontiers in DEA models to grade countries/territories

Several investigations to and approaches for categorizing academic journals/institutions/countries into different grades have been published in the past. To the best of our knowledge, most existing grading methods use either a weighted sum of quantitative indicators (including the case of one properly defined quantitative indicator) or quantified peer review results. Performance measurement is an important issue of concern for science and technology (S&T) management. In this paper we address this issue, leading to multi-level frontiers resulting from data envelopment analysis (DEA) models to grade selected countries/territories. We use research funding and researchers as input indicators, and take papers, citations and patents as output indicators. Our research results show that using DEA frontiers we can unite countries/territories by different grades. These grades reflect the corresponding countries’ levels of performance with respect to multiple inputs and outputs. Furthermore, we use papers, citations and patents as single output (with research funding and researchers as inputs), respectively, to show country/territory grade changes. In order to increase the insight in this approach, we also incorporate a simple value judgment (that the number of citations is more important than the number of papers) as prior information into the DEA models to study the resulting changes of these Countries/Territories’ performance grades.

A generalized equilibrium efficient frontier data envelopment analysis approach for evaluating DMUs with fixed-sum outputs

The recently published equilibrium efficient frontier data envelopment analysis (EEFDEA) approach (Yang et al., 2014) represents a step forward in evaluating decision-making units (DMUs) with fixed-sum outputs when compared to prior approaches such as FSODEA (fixed-sum outputs DEA) approach (Yang et al., 2011) and ZSG-DEA (zero sum gains DEA) approach (Lins et al., 2003) and so on. Based on the EEFDEA approach, in this paper, we proposed a generalized equilibrium efficient frontier data envelopment analysis approach (GEEFDEA) which improves and strengthens the EEFDEA approach. Compared to EEFDEA approach, this approach makes several improvements in evaluation, namely that (1) it is not necessary to determine the evaluation order in advance, which overcomes the limitation that different evaluation orders will lead to different results; (2) the equilibrium efficient frontier can be achieved in only one step no matter how many DMUs they are, which greatly simplifies the procedure to reach the equilibrium efficient frontier especially when the number of DMUs is large; and (3) the constraint that signs of outputs’ adjustment of each DMU must be same (all non-positive or all non-negative) in prior approaches has been relaxed. In this sense, the result obtained by the proposed approach is more consistent with the demand of practical applications. Finally, the proposed approach combined with assurance regions (AR) is applied to the data set of 2012 London Olympic Games.

Efficiency of Higher Technical Educational Institutions in India

There has been a significant growth in the number of higher technical educational institutions (HTEIs) in India during the past six decades. To evaluate the competency of the Indian HTEIs, in terms of number of students produced, quality of students’ training etc., it is necessary to assess the economic efficiency of these institutions. This paper examines the technical efficiency (TE) of eight important HTEIs in India, namely, seven Indian Institutes of Technology (IITs) and Indian Institute of Science (IISc), by applying Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA) to balanced panel data during 2001-05. The study uses the input-oriented and output-oriented stochastic distance function models, as well as constant returns to scale DEA approach to measure the TE of the above institutions. The paper demonstrates that TE varies across the above HTEIs and highlights the need for strengthening the know-how (concerning higher technical education) of the Indian HTEIs, so that they can exploit the full potential of the existing educational inputs.

An empirical study on the influencing factors of transportation carbon efficiency: Evidences from fifteen countries

In this paper, transportation carbon efficiency is redefined, and its inputs and outputs are obtained from a literature review. Carbon, capital and labor are selected as the inputs, and passenger turnover volume and freight turnover volume are defined as the outputs. A new model, a virtual frontier DEA (virtual frontier Data Envelopment Analysis), is applied to evaluate transportation carbon efficiencies, and cases from 15 countries during the period of 2003–2010 are analyzed to verify the results. Next, a Tobit regression model is applied to identify the important influencing factors of transportation carbon efficiency. The results indicate that compared to the technology factor and management factor, the influencing degree of a structure factor is relatively small.

Using Genetic Algorithms for Maximizing Technical Efficiency in Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a non-parametric technique for estimating the technical efficiency of a set of Decision Making Units (DMUs) from a database consisting of inputs and outputs. This paper studies DEA models based on maximizing technical efficiency, which aim to determine the least distance from the evaluated DMU to the production frontier. Usually, these models have been solved through unsatisfactory methods used for combinatorial NP-hard problems. Here, the problem is approached by metaheuristic techniques and the solutions are compared with those of the methodology based on the determination of all the facets of the frontier in DEA. The use of metaheuristics provides solutions close to the optimum with low execution time.

Financial performance evaluation of present petrochemical companies in stock exchange by data envelopment analysis

Evaluating companies' performance and comparing them have enjoyed stakeholders' attention. Also, since analysing financial ratios is not capable of finding the most desirable performance and determining inefficient units, it is possible to employ data envelopment analysis (DEA) for using several financial criteria in order to determine evaluation rate of financial performance. The present study tries to shed light upon DEA through a financial approach to judge the performance of present petrochemical companies in stock exchange that submitted their financial records to stock exchange organisations between 2006-2011. After calculating financial ratios and entering data in an input-based BCC model, in DEA Frontier 2007 software, the efficiency of each company in end of each year will be measured and next, geometric mean of efficiency for related year will be gauged. Finally, results reveal that Farabi Petrochemical Company is financially the most efficient and Jam Petrochemical Company is financially the most inefficient.

An equilibrium efficiency frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

Based on the minimal reduction strategy, Yang et al. (2011) developed a fixed-sum output data envelopment analysis (FSODEA) approach to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs. However, in terms of such a strategy, all DMUs compete over fixed-sum outputs with “no memory” that will result in differing efficient frontiers’ evaluations. To address the problem, in this study, we propose an equilibrium efficiency frontier data envelopment analysis (EEFDEA) approach, by which all DMUs with fixed-sum outputs can be evaluated based on a common platform (or equilibrium efficient frontier). The proposed approach can be divided into two stages. Stage 1 constructs a common evaluation platform via two strategies: an extended minimal adjustment strategy and an equilibrium competition strategy. The former ensures that original efficient DMUs are still efficient, guaranteeing the existence of a common evaluation platform. The latter makes all DMUs achieve a common equilibrium efficient frontier. Then, based on the common equilibrium efficient frontier, Stage 2 evaluates all DMUs with their original inputs and outputs. Finally, we illustrate the proposed approach by using two numerical examples.

The evaluation of transportation energy efficiency: An application of three-stage virtual frontier DEA

In this paper, transportation energy efficiency is newly defined and its inputs and outputs are obtained through literature review. Labor input, capital input and energy input are selected as the inputs, passenger turnover volume and freight turnover volume are defined as the outputs. A new model—three-stage virtual frontier DEA (three-stage virtual frontier Data Envelopment Analysis) is proposed to evaluate transportation energy efficiencies. The case of thirty Chinese PARs (provincial administrative regions) from 2003 to 2012 is applied to verify its rationality. In the three-stage virtual frontier DEA, the reference DMU (decision-making unit) set and the evaluated DMU set are two different sets so that it can distinguish the DEA efficient DMUs. And in the evaluating process, the reference DMU set remains unchanged to assure its results more reasonable than Super DEA model. The results show that transport structure and management measures have important impacts on transportation energy efficiency.

Data dimensionality reduction for hospital efficiency measurement

A comparison was made for the correlation and application scope of the statistical methods commonly used by hospitals for their efficiency measurement.Hospital data processed with PCA (principal component analysis)for dimension reduction were used in a correlation analysis for the results of ratio analysis (RA),stochastic frontier analysis(SFA)and data envelopment analysis(DEA).The authors hold that the RA can expediently display the order of hospital efficiency,the SFA demands a stricter premise yet presents more stable results,while the DEA boasts greater relative advantages and thus suitable for processing hospital efficiency measurement tasks of multi-input and multi-output indexes. Key words: Hospital efficiency; Measurement; Data dimensionality reduction; Statistical methods; Application

Closest targets and strong monotonicity on the strongly efficient frontier in DEA

The determination of closest efficient targets has attracted increasing interest of researchers in recent Data Envelopment Analysis (DEA) literature. Several methods have been introduced in this respect. However, only a few attempts exist that analyze the implications of using closest targets on the technical inefficiency measurement. In particular, least distance measures based on Hölder norms satisfy neither weak nor strong monotonicity on the strongly efficient frontier. In this paper, we study Hölder distance functions and show why strong monotonicity fails. Along this line, we provide a solution for output-oriented models that allows assuring strong monotonicity on the strongly efficient frontier. Our approach may also be extended to the most general case, i.e. non-oriented models, under some conditions of regularity.

Data envelopment analysis: Prior to choosing a model

In this paper, we address several issues related to the use of data envelopment analysis (DEA). These issues include model orientation, input and output selection/definition, the use of mixed and raw data, and the number of inputs and outputs to use versus the number of decision making units (DMUs). We believe that within the DEA community, researchers, practitioners, and reviewers may have concerns and, in many cases, incorrect views about these issues. Some of the concerns stem from what is perceived as being the purpose of the DEA exercise. While the DEA frontier can rightly be viewed as a production frontier, it must be remembered that ultimately DEA is a method for performance evaluation and benchmarking against best-practice. DEA can be viewed as a tool for multiple-criteria evaluation problems where DMUs are alternatives and each DMU is represented by its performance in multiple criteria which are coined/classified as DEA inputs and outputs. The purpose of this paper is to offer some clarification and direction on these matters.

Do efficiency scores depend on input mix? A statistical test and empirical illustration

In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.

Efficiency and productivity of banking sector

PurposeThe purpose of this paper is to discuss a comprehensive literature survey of studies focusing on the efficiency and productivity of the banking sector using parametric and non‐parametric frontier techniques.Design/methodology/approachCritically reviewing 106 studies published across the world from 1994 to 2011, a conceptual framework is developed for the studies assessing the efficiency and productivity of the banking industry using non‐parametric DEA frontier approach.FindingsBoth the frontier approaches, parametric and non‐parametric, are gaining an edge over the traditional financial performance measures. In the non‐parametric approach, data envelopment analysis (DEA) is widely applied to measure a bank's efficiency and productivity. Studies conducted in developed countries such as the USA, the UK and Europe are now emerging with the new concepts of banking efficiency.Research limitations/implicationsThese findings are based only on the critical review of 106 studies. This study suggests the direction for future research and identifies the gap in existing literature with the development of a conceptual model.Originality/valueThis study is original in nature and included literature published in recent issues of 2011.

Expansion of the cross-efficiency evaluation by using the equations forming the efficient frontier in DEA

In this paper, we propose an algorithm to calculate cross-efficiency scores which used the equations forming the efficient frontier in data envelopment analysis (DEA). In many standard DEA models, each decision-making unit (DMU) is evaluated by using the advantageous weight for itself. Then, many DMUs are evaluated as efficient, and those efficient DMUs are not ranked by the models. The cross-efficiency evaluation is a method to rank DMUs by using the advantageous weights for all DMUs. Previously, the cross-efficiency scores based on different ideas are calculated by solving multiple linear or nonlinear programming problems. However, it is often hard to solve such a nonlinear programming problem. Therefore, by analysing the efficient frontier, we construct an algorithm to calculate alternative cross-efficiency scores.