DEA efficiency in agriculture: Measurement unit issues

The selection of inputs and outputs in DEA models represents a vibrant methodological topic. At the same time; however, the problem of the impact of different measurement units of selected inputs is understated in empirical literature. Using the example of Czech farms, we show that the DEA method does not provide consistent score estimates, neither a stable ranking for different popular measurements of labour and capital factors of production. For this reason, studies based on DEA efficiency results for differently measured inputs should be compared only with great caution.     

Centralized Resource Allocation Using Data Envelopment Analysis

While conventional DEA models set targets separately for each DMU, in this paper we consider that there is a centralized decision maker (DM) who “owns” or supervises all the operating units. In such intraorganizational scenario the DM has an interest in maximizing the efficiency of individual units at the same time that total input consumption is minimized or total output production is maximized. Two new DEA models are presented for such resource allocation. One type of model seeks radial reductions of the total consumption of every input while the other type seeks separate reductions for each input according to a preference structure. In both cases, total output production is guaranteed not to decrease. The two key features of the proposed models are their simplicity and the fact that both of them project all DMUs onto the efficient frontier. The dual formulation shows that optimizing total input consumption and output production is equivalent to finding weights that maximize the relative efficiency of a virtual DMU with average inputs and outputs. A graphical interpretation as well as numerical results of the proposed models are presented.     

A new methodology to measure efficiencies of inputs (outputs) of decision making units in Data Envelopment Analysis with application to agriculture

This paper aims at developing a new methodology to measure and decompose global DMU efficiency into efficiency of inputs (or outputs). The basic idea rests on the fact that global DMU's efficiency score might be misleading when managers proceed to reallocate their inputs or redefine their outputs. Literature provides a basic measure for global DMU's efficiency score. A revised model was developed for measuring efficiencies of global DMUs and their inputs (or outputs) efficiency components, based on a hypothesis of virtual DMUs. The present paper suggests a method for measuring global DMU efficiency simultaneously with its efficiencies of inputs components, that we call Input decomposition DEA model (ID-DEA), and its efficiencies of outputs components, that we call output decomposition DEA model (OD-DEA). These twin models differ from Supper efficiency model (SE-DEA) and Common Set Weights model (CSW-DEA). The twin models (ID-DEA, OD-DEA) were applied to agricultural farms, and the results gave different efficiency scores of inputs (or outputs), and at the same time, global DMU's efficiency score was given by the Charnes, Cooper and Rhodes (Charnes et al., 1978) [1], CCR78 model. The rationale of our new hypothesis and model is the fact that managers don't have the same information level about all inputs and outputs that constraint them to manage resources by the (global) efficiency scores. Then each input/output has a different reality depending on the manager's decision in relationship to information available at the time of decision. This paper decomposes global DMU's efficiency into input (or output) components' efficiencies. Each component will have its score instead of a global DMU score. These findings would improve management decision making about reallocating inputs and redefining outputs. Concerning policy implications of the DEA twin models, they help policy makers to assess, ameliorate and reorient their strategies and execute programs towards enhancing the best practices and minimising losses.     

Marginal Rates and Elasticities of Substitution with Additive Models in DEA

Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, but is not restricted to, the case in which all slacks must be zero for full attainment of efficiency—as in standard versions of additive models.     

Short and long-run cost efficiency in Indian public bus companies using Data Envelopment Analysis

State Transport Undertakings (STUs) are key players in providing mass road transport in India. Given that they operate under high levels of government imposed regulatory constraints, it is imperative to study their efficiency levels. Given that capital is a relatively scarce resource in developing countries like India, it is important to obtain efficiency in the short-run where some inputs are fixed as well as over the long run, where all inputs are variable. The technique used for capturing efficiency is Data Envelopment Analysis (DEA). A key possible limitation of DEA models based on physical inputs and outputs is that for an inefficient firm, reduction in some or all inputs may be recommended. It may often be desirable for an inefficient firm to increase some less expensive inputs while reducing the use of relatively expensive ones. Hence, when market price data is available, it is advisable to use the cost variant of DEA. Also, it is possible to determine variable cost efficiency in the short run when some inputs cannot be varied. Such inputs are referred to as “quasi-fixed” inputs. In this paper, we examine short and long term efficiencies of select bus companies in India known as State Transport Undertakings (STUs) over a period of 10 years. Fleet strength has been used as the quasi-fixed input. It is possible to ascertain, through a comparison of shadow price of the quasi-fixed input, vis-à-vis its market price, as to whether the quantity of this input is sub-optimally small or large. It is found that by adopting efficiency enhancing practices, STUs can cumulatively reduce their operating costs to the extent of 9123.35 million dollars. Also the tendency to minimize costs is found to be declining over time. In the short run some STUs are found to operate with a sub optimally low fleet size.     

Sensitivity Analysis of an Efficient DMU in DEA Model with Variable Returns to Scale (VRS)

In this paper we consider the Variable Returns to Scale (VRS) Data Envelopment Analysis (DEA) model. In a DEA model each Decision Making Unit (DMU) is classified either as efficient or inefficient. Changes in inputs or outputs of any DMU can alter its classification, i.e. an efficient DMU can become inefficient and vice versa. The goal of this paper is to assess changes in inputs and outputs of an extreme efficient DMU that will not alter its efficiency status, thus obtaining the region of efficiency for that DMU. Namely, a DMU will remain efficient if and only if after applying changes this DMU stays in that region. The representation of this region is done using an iterative procedure. In the first step an extended DEA model, whereby a DMU under evaluation is excluded from the reference set, is used. In the iterative part of the procedure, by using the obtained optimal simplex tableau we apply parametric programming, thus moving from one facet to the adjacent one. At the end of the procedure we obtain the complete region of efficiency for a DMU under consideration.     

Using DEA to evaluate the state of society as measured by multiple social indicators

This paper presents an approach for discussing the state of society, which is measured by multiple social indicators, using data envelopment analysis (DEA). Replacing inputs and outputs in DEA with negative and positive social indicators respectively, we analyze the desirability of living in the 47 prefectures of Japan. This is also a proposal for the potential use of DEA in multi-dimensional evaluation analysis other than the standard DEA efficiency analysis. The results using eight social indicators identify 26 DEA desirable prefectures out of the 47 and present other useful knowledge and information. It is concluded that DEA, which can avoid uniform evaluation by an a priori weighting system, provides availability as a comprehensive evaluation tool different from traditional ones.     

Public-private partnerships and scale efficiency in Brazilian ports: Evidence from two-stage DEA analysis

This paper assesses the impacts of public-private partnerships on major Brazilian public ports. It is proposed that these kinds of arrangements with private terminal operators could help achieving higher levels of scale efficiency by enhancing coordination processes, providing more adequate information technologies, and higher connectivity with other transportation modes. Methodology relies on factor extraction of inputs/outputs as a first step to compute DEA efficiency estimates, followed by truncated bootstrapped regression analysis to test different contextual variables. Results indicate a strong positive impact of public-private partnerships on port scale efficiency, corroborating their impacts in relation to the most productive scale size.     

One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient,root-<Emphasis Type="Italic">n</Emphasis> consistent StoNEZD method

Understanding the effects of operational conditions and practices on productive efficiency can provide valuable economic and managerial insights. The conventional approach is to use a two-stage method where the efficiency estimates are regressed on contextual variables representing the operational conditions. The main problem of the two-stage approach is that it ignores the correlations between inputs and contextual variables. To address this shortcoming, we build on the recently developed regression interpretation of data envelopment analysis (DEA) to develop a new one-stage semi-nonparametric estimator that combines the nonparametric DEA-style frontier with a regression model of the contextual variables. The new method is referred to as stochastic semi-nonparametric envelopment of z variables data (StoNEZD). The StoNEZD estimator for the contextual variables is shown to be statistically consistent under less restrictive assumptions than those required by the two-stage DEA estimator. Further, the StoNEZD estimator is shown to be unbiased, asymptotically efficient, asymptotically normally distributed, and converge at the standard parametric rate of order n ^−1/2. Therefore, the conventional methods of statistical testing and confidence intervals apply for asymptotic inference. Finite sample performance of the proposed estimators is examined through Monte Carlo simulations.     

An analysis of operations efficiency in large-scale distribution systems

This research applies Data Envelopment Analysis (DEA) methodology to evaluate the efficiency of units within a large-scale network of petroleum distribution facilities in the USA. Multiple inputs and outputs are incorporated into a broad set of DEA models, yielding a comprehensive approach to evaluating supply chain efficiency. This study empirically separates three recognized, important and yet different causes of performance shortfalls which have been generally difficult for managers to identify. They are: (1) managerial effectiveness; (2) scale of operations and potential for a given market area (and efficiency of resource allocation given the scale); and (3) understanding the resource heterogeneity via programmatic differences in efficiency. Overall, the efficiency differences identified raised insightful questions regarding top management’s selection of the appropriate form and type of inputs and outputs, as well as questions regarding the DEA model form selected.     

基于DEA模型的我国轻工业经营效率研究

运用DEA模型对我国31个省区市轻工业的经营效率进行了实证研究和分析,结果表明,大部分省份轻工业的经营效率是非DEA有效的,尤其是沿海发达地区的轻工业大省。针对此现象进行了深入分析,并提出了相应的对策。     

Measuring efficiency in the presence of head-to-head competition

We develop a new DEA model that measures organizational efficiency in the presence of head-to-head competition. Our model differs from existing DEA models that ignore competition (or any other form of interaction) among the organizations under analysis. The model assumes that organizations deploy inputs for the explicit purpose of increasing its own outputs while reducing the outputs of its competitors. We apply this model to the 2002, 2004, and 2006 political campaigns in New York State for the US. House of Representatives in which candidates spent money to increase the number of votes that they received and decrease the number of votes that their opponents received. We show that campaign inefficiency can alter the outcome of an election. Specifically, a loser would have won in six of the 57 races had he or she been efficient. We also show that incumbents are more likely to spend inefficiently than are challengers. Overall, inefficiency accounts for less than 5% of campaign funding but a loss of about 9% in votes received. We find evidence that campaign efficiency has increased since the passage of the Bipartisan Campaign Reform Act of 2002, known widely as the McCain-Feingold Act.     

Stochastic DEA Models With Different Types of Input-Output Disturbances

This paper presents stochasticmodels in data envelopment analysis (DEA) for the possibilityof variations in inputs and outputs. Efficiency measure of adecision making unit (DMU) is defined via joint probabilisticcomparisons of inputs and outputs with other DMUs and can becharacterized by solving a chance constrained programming problem.By utilizing the theory of chance constrained programming, deterministicequivalents are obtained for both situations of multivariatesymmetric random disturbances and a single random factor in theproduction relationships. The linear deterministic equivalentand its dual form are obtained via the goal programming theoryunder the assumption of the single random factor. An analysisof stochastic variable returns to scale is developed using theidea of stochastic supporting hyperplanes. The relationshipsof our stochastic DEA models with some conventional DEA modelsare also discussed.     

Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA

Pareto-Koopmans efficiency in Data Envelopment Analysis (DEA) is extended to stochastic inputs and outputs via probabilistic input-output vector comparisons in a given empirical production (possibility) set. In contrast to other approaches which have used Chance Constrained Programming formulations in DEA, the emphasis here is on joint chance constraints. An assumption of arbitrary but known probability distributions leads to the P-Model of chance constrained programming. A necessary condition for a DMU to be stochastically efficient and a sufficient condition for a DMU to be non-stochastically efficient are provided. Deterministic equivalents using the zero order decision rules of chance constrained programming and multivariate normal distributions take the form of an extended version of the additive model of DEA. Contacts are also maintained with all of the other presently available deterministic DEA models in the form of easily identified extensions which can be used to formalize the treatment of efficiency when stochastic elements are present.     

基于DEA的备件ABC分类模型

提出了一种基于DEA的维修备件ABC分类方法。该方法根据DEA中确定指标是输入（出）的原理，将备件的多个属性指标分成输入指标和输出指标，使得模型效率值大小能直接表示备件的重要程度，并根据相应的效率值对备件进行ABC分类。该方法不仅克服了传统ABC分类法存在的指标单一的缺陷，也解决了多指标之间数值量纲的不一致所产生的问题。该方法用于设备维修备件的分类，能科学有效地找出维修备件管理中的关键备件，提高备件分类的有效性和备件管理的针对性。     

Qualitative data envelopment analysis by affinity set: a survey of subjective opinions for NPOs

Measuring the performance of Non-Profit Organizations (NPOs) is a complicated issue: data envelopment analysis (DEA) is a popular quantitative tool in the past literature. However, the subjective opinions of NPOs could disturb their actual performance, and this problem is seldom considered. In this study, we use the qualitative DEA as a tool to find the emphasized inputs and outputs for these NPOs. Most DEA models are established by the basis of quantitative data, they are difficult to describe the qualitative performance of NPOs. This paper proposes a new perspective for computing the efficiency of a Decision Making Unit based on qualitative data by affinity Set. The DEA model for qualitative data could be traced back to the work of Cook et al. early in 1993. Our contribution prevents the identical efficiency scores from the model of Cook et al., and a combinatorial optimization technique is used to solve the new problem. Finally, we found most NPOs would like to get more resources from outside; but interestingly, they don’t like to be officially monitored. Therefore, we should use the quantitative DEA on NPOs very carefully.     

Advances in physician profiling: the use of DEA

Insurers, health plans, and individual physicians in the United States are facing increasing pressures to reduce costs while maintaining quality. In this study, motivated by our work with a large managed care organization, we use readily available data from its claims database with data envelopment analysis (DEA) to examine physician practices within this organization. Currently the organization evaluates primary care physicians using a profile of 16 disparate ratios involving cost, utilization, and quality. We employed these same factors along with indicators of severity to develop a single, comprehensive measure of physician efficiency through DEA. DEA enabled us to identify a reference set of “best practice” physicians tailored to each inefficient physician. This paper presents a discussion of the selection of model inputs and outputs, the development of the DEA model using a “stepwise” approach, and a sensitivity analysis using superefficiency scores. The stepwise and superefficiency analyses required little extra computation and yielded useful insights into the reasons as to why certain physicians were found to be efficient. This paper demonstrates that DEA has advantages for physician profiling and usefully augments the current ratio-based reports.     

A structure for classifying and characterizing efficiency and inefficiency in Data Envelopment Analysis

DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions and, in addition, sources and amounts of inefficiency are estimated for each input and each output for every DMU. Earlier theory is extended so that DEA can deal with zero inputs and outputs and zero virtual multipliers (shadow prices). This is accomplished by partitioning DMUs into six classes via primal and dual representation theorems by means of which restrictions to positive observed values for all inputs and outputs are eliminated along with positivity conditions imposed on the variables which are usually accomplished by recourse to nonarchimedian concepts. Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (zero waste) efficient.The refereeing process of this paper was handled through R. Banker. This paper was prepared as part of the research supported by National Science Foundation grant SES-8722504 and by the IC² Institute of The University of Texas and was initially submitted in May 1985.     

Restricting Multiple-Output Multiple-Input DEA Models by Disaggregating the Output–Input Vector

One of the strengths of DEA in the measurement of technical efficiency is that it readily accommodates multiple-output multiple-input production technologies. In doing so, it assumes that each of the inputs is used jointly in the production of each output. In some applied studies, this can be undesirable. We propose a new disaggregated formulation that allows a specific output to be made independent of a specific input, while maintaining the joint production relationship for the other outputs and inputs. We demonstrate the approach by applying it to measure the technical efficiency of national rail systems in 20 countries between 1990 and 1998.JEL Classification: C6, D24, N7     

Reverse efficiency measures for environmental assessment in data envelopment analysis

Environmental issues are becoming more and more important in our everyday life. Data Envelopment Analysis (DEA) is a tool developed for measuring relative operational efficiency. DEA can also be employed to estimate environmental efficiency where undesirable outputs like greenhouse gases exist. The classical DEA method identifies best practices among a given empirical data set. In many situations, however, it is advantageous to determine the worst practices and perform efficiency evaluation by comparing DMUs with the full-inefficient frontier. This strategy requires that the conventional production possibility set is defined from a reverse perspective. In this paper, presence of both desirable and undesirable outputs is assumed and a methodological framework for performing an unbiased efficiency analysis is proposed. The reverse production possibility set is defined and new models are presented regarding the full-inefficient frontier. The operational, environmental and overall reverse efficiencies are studied. The important notion of weak disposability is discussed and the effects of this assumption on the proposed models are investigated. The capability of the proposed method is examined using data from a real-world application about paper production.