Lower Bound Restrictions on Intensities in Data Envelopment Analysis

We propose an extension to the basic DEA models that guarantees that if an intensity is positive then it must be at least as large as a pre-defined lower bound. This requirement adds an integer programming constraint known within Operations Research as a Fixed-Charge (FC) type of constraint. Accordingly, we term the new model DEA_FC. The proposed model lies between the DEA models that allow units to be scaled arbitrarily low, and the Free Disposal Hull model that allows no scaling. We analyze 18 datasets from the literature to demonstrate that sufficiently low intensities—those for which the scaled Decision-Making Unit (DMU) has inputs and outputs that lie below the minimum values observed—are pervasive, and that the new model ensures fairer comparisons without sacrificing the required discriminating power. We explain why the low-intensity phenomenon exists. In sharp contrast to standard DEA models we demonstrate via examples that an inefficient DMU may play a pivotal role in determining the technology. We also propose a goal programming model that determines how deviations from the lower bounds affect efficiency, which we term the trade-off between the deviation gap and the efficiency gap.     

The Use of Data Envelopment Analysis with Probabilistic Assurance Regions for Measuring Hospital Efficiency

This paper uses Data Envelopment Analysis (DEA) for an estimation of the cost efficiency of 70 Danish hospitals. The analysis relates to a cost function based on 483 outputs in combination with a set of probabilistic assurance regions defined by the cost distributions for each output. It is demonstrated that the probabilistic assurance region approach allows for (i) a frontier estimation in the full output space, i.e., no fixed aggregation is required, and (ii) a controlling of the variation in heterogeneity of the output clusters, in casu Diagnosis Related Groups. The likelihood of the estimated efficiency score for a given hospital can be measured based on the sensitivity of the score w.r.t. the probability levels used in the specification of confidence intervals for the probabilistic assurance regions.     

A new method for measuring congestion in data envelopment analysis

In data envelopment analysis (DEA), there are two principal methods for identifying and measuring congestion: Those of Färe et al. [Färe R, Grosskopf S. When can slacks be used to identify congestion. An answer to W. W. Cooper, L. Seiford, J. Zhu. Socio-Economic Planning Sciences 2001;35:1–10] and Cooper et al. [Cooper WW, Deng H, Huang ZM, Li SX. A one-model approach to congestion in data envelopment analysis. Socio-Economic Planning Sciences 2002;36:231–8]. In the present paper, we focus on the latter work in proposing a new method that requires considerably less computation. Then, by proving a selected theorem, we show that our proposed methodology is indeed equivalent to that of Cooper et al.     

The Fixed Weighting Nature of A Cross-Evaluation Model

Cross-evaluation has been touted as a powerful extension of Data Envelopment Analysis that provides, not only a unique ordering among the Decision Making Units (DMUs), but also eliminates unrealistic weighting schemes without requiring the elicitation of weight restrictions from application area experts. The goal of this paper is to prove, in the single-input, multiple-output case, cross-evaluation implicitly uses a single fixed set of weights. We demonstrate how this unseen fixed set of weights may still be unrealistic.     

Economic interpretations of DEA

Research on productive efficiency at the firm level has developed as an important and active strand of research the last decades, both within operations research, management science and economics. Two apparently different definitions of efficiency are examined, but it is shown that when both estimation methods are based on solving linear programming problems the definitions of efficiency are identical. The purpose of the paper is to give the basic ideas of efficiency analyses using DEA as a tool for researchers not so familiar with efficiency analysis and DEA. The concept of shadow prices is given special attention.     

Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. This paper extends this methodology in two substantive ways. First, a method is developed that determines the least-norm projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the observable frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs (or convex combinations of such) and thus, the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical example is used to illustrate the importance of these two methodological extensions.     

A Mathematical Programming Approach for Measuring Technical Efficiency in a Fuzzy Environment

A three stage approach is proposed to measure technical efficiency in a fuzzy environment. This approach uses the traditional data envelopment analysis framework and then merges concepts developed in fuzzy parametric programming (Carlsson and Korhonen, 1986). In the first stage, vague input and output variables are expressed in terms of their risk-free and impossible bounds and a membership function. This membership function represents the degree to which a production scenario is plausible. In the second stage, conventional efficiency measurement models (Banker, Charnes and Cooper, 1984; Deprins, Simar and Tulkens, 1984) are re-formulated in terms of the risk-free and impossible bounds and the membership function for each of the fuzzy input and output variables. In the third stage, technical efficiency scores are computed for different values of the membership function so as to identify uniquely sensitive decision making units. The approach is illustrated in the context of a preprint and packaging manufacturing line which inserts commercial pamphlets into newspapers.     

Benchmarking Warehousing and Distribution Operations: An Input-Output Approach

We developan input-output model of a warehouse system to assess operationalefficiency. Our model simultaneously accounts for all of thecritical resources (labor, space, storage and handling equipment)and the different workload requirements (broken case, full caseand pallet picking, storage and order accumulation) of a warehouse.We collected extensive data on 57 warehouse and distributionfacilities from a variety of industries, including auto parts,dental and office supplies, electronics, fine papers, hardware,health care, industrial packaging, mail order apparel, officemachines, photographic supplies, and wholesale drugs, and usedthe model to assess and compare their efficiencies. We offer3 conclusions based on a statistical analysis of the operatingefficiencies obtained from several models: Smaller warehouses tend to be more efficient than larger warehouses.Warehouses using lower levels of automation tend to be moreefficient. This association is more pronounced in small firms.Unionization is not negatively associated with efficiencyand in fact may actually contribute to higher efficiency.     

On the Use of Value Efficiency Analysis and Some Further Developments

The purpose of this paper is to discuss the use of Value Efficiency Analysis (VEA) in efficiency evaluation when preference information is taken into account. Value efficiency analysis is an approach, which applies the ideas developed for Multiple Objective Linear Programming (MOLP) to Data Envelopment Analysis (DEA). Preference information is given through the desirable structure of input- and output-values. The same values can be used for all units under evaluation or the values can be specific for each unit. A decision-maker can specify the input- and output-values subjectively without any support or (s)he can use a multiple criteria support system to assist him/her to find those values on the efficient frontier. The underlying assumption is that the most preferred values maximize the decision-maker's implicitly known value function in a production possibility set or a subset. The purpose of value efficiency analysis is to estimate a need to increase outputs and/or decrease inputs for reaching the indifference contour of the value function at the optimum. In this paper, we briefly review the main ideas in value efficiency analysis and discuss practical aspects related to the use of value efficiency analysis. We also consider some extensions.     

Extending Productivity Research Frontiers: DEA Resource of Datasets and Errata

Website databases provide the opportunity to fundamentally change the way research and knowledge are advanced and disseminated. This paper describes a website, http://www.etm.pdx.edu/dea/dataset/, focused on Data Envelopment Analysis and DEA researchers.     

On the Role of Weight Restrictions in Data Envelopment Analysis

This paper examines the role that weight restrictions play in Data Envelopment Analysis (DEA). It is argued that the decision to include a factor (input or output) in a DEA model represents an implicit judgement that the factor has a non-trivial weight. It therefore seems perverse to allow DEA to assign a trivial weight to that factor in assessing the efficiency of a unit. There is therefore a strong case for imposing restrictions on factor weights. However, many existing methods of weight restriction are in practice unwieldy. This paper proposes an alternative approach we term contingent weight restriction which is both practical and intellectually consistent with the DEA philosophy. The paper explores the implications of alternative methods of weight restriction using simulated data from a well known production process.     

Testing Independence in Models of Productive Efficiency

Bootstrap methods for inference in nonparametric models of productive efficiency can be simplified, reducing computational burden, when the independence condition implicitly assumed in Simar and Wilson (1998) holds. This paper surveys nonparametric tests of independence that might be useful in this context.     

基于DEA方法的银行网点服务绩效评价研究

随着我国银行业的发展,商业银行的绩效评价问题成为银行与专家学者共同关注的焦点。在回顾国内外研究成果的基础上,提出了银行绩效评价的DEA模型。并通过数据采集,进行了相关的实证分析。     

Multiple Objective Approach as an Alternative to Radial Projection in DEA

Radial projection is a standard technique applied in data envelopment analysis (DEA) to calculate efficiency scores for input and/or output variables. In this paper, we have studied the appropriateness of radial projection for target setting. We have created a situation where the decision making units (DMUs) are free to choose their own target values on the efficient frontier and then compared the results to those of radial projection. In practice, target values are primarily used for future goal attainment; hence, not only preferences but also, and on the whole, change in time frame, affect the choice of target values. Based on that, we conducted an empirical experiment with an aim to study how the DMUs choose their most preferred target values on the efficient frontier. The subjects, who all were students of the Helsinki School of Economics, were given the freedom to explore their personalized efficient frontiers by using a multiple objective linear programming (MOLP) approach. To study various and relevant scenarios, the personalized efficient frontiers for all students were constructed in such a way that the current position of each student in relation to the frontier made him/her inefficient, efficient, or super-efficient. The results show that the use of radial projection for target setting is too restrictive.     

Slack-adjusted efficiency measures and ranking of efficient units

In non-parametric methods many units are calculated as efficient. The article suggests a method for ranking efficient units, not by their efficiency, but by importance as benchmarks for the inefficient units, in contrast to earlier suggestions in the literature which rank units high if they are specialized. However, the total potentials for improvement frequently remain unrevealed by calculating radial efficiency measures of the Farrell type only. The article therefore first develops efficiency measures that explicitly extend the radial measures to include slacks. The new measures are applied to a typical multidimensional small-sample data set for Norwegian employment offices.     

Technical Efficiency of the Brazilian Municipalities: Correcting Nonparametric Frontier Measurements for Outliers

In this paper we estimate the DEA technical efficiency for 4796 Brazilian municipalities, by applying a recently proposed “Jackstrap” method, which combines Bootstrap and Jackknife resampling techniques, to reduce the effect of outliers and possible errors in the data set. We perform calculations to identify and eliminate high leverage municipalities, using different variants of Data Envelopment Analysis (DEA), as well as Free Disposal Hull (FDH). Corroborating previous results, efficiency results for the Brazilian municipalities show a clear relationship between the size of the municipality and its efficiency scores. Indeed, under both DEA variants, smaller cities tend to be less efficient than larger ones hence indicating that the quality of the frontier adjustment improves significantly as the size of the municipality increases. We present arguments that may explain to some extent these findings, such as economies of scale and the excess spending due to revenue from royalties. However, such effects require further, more careful examination.     

数据包络分析在企业盈利能力评价中的应用

本文是基于数据包络分析(DEA)模型对房地产上市公司盈利能力的分析。并从综合效率,规模效率,技术效率,规模报酬四个方面对房地产进行综合评价。     

区域技术创新体系评价模型研究

本文首先探讨了区域创新体系的结构特征，在此基础上从区域技术创新体系的基点、构架、动力三个方面建立了区域技术创新体系的评价指标体系，按照投入产出的关系将这些指标分为输入指标和输出指标，从而运用DEA的方法对大连、沈阳和哈尔滨三个城市进行了评价，得出了制度和法律建设在区域技术创新体系的建设中有着举足轻重的作用。     

On the calculation of the scale elasticity in DEA models

An issue in the multiple-output case within the literature on piecewise linear frontier production functions has been how to determine the nature of the scale properties. It is shown that knowledge of scale efficiency does not permit calculation of scale elasticity or vice versa. For inefficient units there is a relationship between input-saving and output-increasing efficiency measures through the average value of the scale elasticity between the two different reference points on the frontier. A direct approach to determine the scale properties is to calculate the scale elasticity from the dual problem to the calculation of Farrell efficiency measures.