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.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

Combining two approaches to efficiency assessment

The advent of data envelopment analysis (DEA) enabled the measurement of efficiency to be extended to the case of multiple outputs. Prior to DEA we had the parametric approach based on multiple regression. We highlight some difficulties associated with these two approaches and present a hybrid which overcomes them whilst maintaining the respective advantages of each. This hybrid models the efficient frontier using an algebraic expression; the resulting smooth representation allows all units to be naturally enveloped and hence slacks to be avoided. (Slacks are potential improvements for inefficient units which are not accounted for in the DEA (radial) score, and so have been problematic for DEA.) The approach identifies the DEA-efficient units and fits a smooth model to them using maximum correlation modelling. This new technique extends the method of multiple regression to the case where there are multiple variables on each side of the model equation (eg outputs and inputs). The resulting expression for the frontier permits managers to estimate the effect on their efficiency score of adjustments in one or more input or output levels.     

An application of DEA for comparative analysis and ranking of regions in Serbia with regards to social-economic development

In this paper, we use data envelopment analysis (DEA) to estimate how well regions in Serbia utilize their resources. Based on data for four inputs and four outputs we applied an output-oriented CCR DEA model and it appears that 17 out of 30 regions are efficient. For each inefficient unit, DEA identifies the sources and level of inefficiency for each input and output. An output-oriented set of targets is determined for 13 inefficient regions. In addition, the possibilities of combining DEA and linear discriminant analysis (LDA) in evaluating performance are explored. The efficient regions are ranked using a cross efficiency matrix and an output-oriented version of Andersen–Petersen’s DEA model and the results are analyzed and compared.     

链式网络DEA模型

数据包络分析(DEA)是评价决策单元(DMU)相对有效性的一种工具,现已得到广泛的应用.传统的DEA不考虑系统内部结构,而是将系统作为一个"黑箱"来度量效率.针对多阶段网络结构提出一个新的网络DEA模型—链式网络DEA模型.研究网络决策单元的网络DEA有效性及各个阶段的弱DEA有效性之间的关系,给出了网络DEA有效的充分必要条件.若网络决策单元不是网络DEA有效的,根据模型可以指出系统在哪些阶段是无效的.     

Chapter 12 New uses of DEA and statistical regressions for efficiency evaluation and estimation — with an illustrative application to public secondary schools in Texas

This paper examines new combinations of Data Envelopment Analysis (DEA) and statistical approaches that can be used to evaluate efficiency within a multiple-input multiple-output framework. Using data on five outputs and eight inputs for 638 public secondary schools in Texas, unsatisfactory results are obtained initially from both Ordinary Least Squares (OLS) and Stochastic Frontier (SF) regressions run separately using one output variable at-a-time. Canonical correlation analysis is then used to aggregate the multiple outputs into a single aggregate output, after which separate regressions are estimated for the subsets of schools identified as efficient and inefficient by DEA. Satisfactory results are finally obtained by a joint use of DEA and statistical regressions in the following manner. DEA is first used to identify the subset of DEA-efficient schools. The entire collection of schools is then comprehended in a single regression with dummy variables used to distinguish between DEA-efficient and DEA-inefficient schools. The input coefficients are positive for the efficient schools and negative and statistically significant for the inefficient schools. These results are consistent with what might be expected from economic theory and are informative for educational policy uses. They also extend the treatments of production functions usually found in the econometrics literature to obtain one regression relation that can be used to evaluate both efficient and inefficient behavior.     

A new method for evaluating decision making units in DEA

This paper provides a new structure in data envelopment analysis (DEA) for assessing the performance of decision making units (DMUs). It proposes a technique to estimate the DEA efficient frontier based on the Arash Method in a way different from the statistical inferences. The technique allows decisions in the target regions instead of points to benchmark DMUs without requiring any more information in the case of interval/fuzzy DEA methods. It suggests three efficiency indexes, called the lowest, technical and highest efficiency scores, for each DMU where small errors occur in both input and output components of the Farrell frontier, even if the data are accurate. These efficiency indexes provide a sensitivity index for each DMU and arrange both inefficient and technically efficient DMUs together while simultaneously detecting and benchmarking outliers. Two numerical examples depicted the validity of the proposed method.     

Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.     

Review of ranking methods in the data envelopment analysis context

Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.     

DEA-based production planning considering influencing factors

When planning production in a centralized decision-making environment using data envelopment analysis (DEA), previous researches usually plan for units by selecting best-practice points within the entire production possibility set or adhering to their original abilities so that potentials may not be fully explored. In practice, there often exist factors that influence units’ production abilities. Difficulties may occur when improving inefficient units’ performances or they can only be improved in a limited room. This paper takes these influencing factors into account to avoid new plans beyond units’ abilities or not fully exploring their potentials. Depending on performance variability, two DEA-based production planning approaches are proposed to optimize the total resource utilization assuming demand changes in the next production season can be forecasted. When performances are improvable, units are grouped according to the influencing factors they face. Simple numerical examples and a real world data set are used to illustrate the proposed approaches.     

Fixed cost and resource allocation based on DEA cross-efficiency

In many managerial applications, situations frequently occur when a fixed cost is used in constructing the common platform of an organization, and needs to be shared by all related entities, or decision making units (DMUs). It is of vital importance to allocate such a cost across DMUs where there is competition for resources. Data envelopment analysis (DEA) has been successfully used in cost and resource allocation problems. Whether it is a cost or resource allocation issue, one needs to consider both the competitive and cooperative situation existing among DMUs in addition to maintaining or improving efficiency. The current paper uses the cross-efficiency concept in DEA to approach cost and resource allocation problems. Because DEA cross-efficiency uses the concept of peer appraisal, it is a very reasonable and appropriate mechanism for allocating a shared resource/cost. It is shown that our proposed iterative approach is always feasible, and ensures that all DMUs become efficient after the fixed cost is allocated as an additional input measure. The cross-efficiency DEA-based iterative method is further extended into a resource-allocation setting to achieve maximization in the aggregated output change by distributing available resources. Such allocations for fixed costs and resources are more acceptable to the players involved, because the allocation results are jointly determined by all DMUs rather than a specific one. The proposed approaches are demonstrated using an existing data set that has been applied in similar studies.     

Convexity,quality and efficiency in education

While Data Envelopment Analysis (DEA) has many attractions as a technique for analysing the efficiency of educational organisations, such as schools and universities, care must be taken in its use whenever its assumption of convexity of the prevailing technology and associated production possibility set may not hold. In particular, if the convexity assumption does not hold, DEA may overstate the scope for improvements in technical efficiency through proportional increases in all educational outputs and understate the importance of improvements in allocative efficiency from changing the educational output mix. The paper therefore examines conditions under which the convexity assumption is not guaranteed, particularly when the performance evaluation includes measures related to the assessed quality of the educational outputs. Under such conditions, there is a need to deploy other educational efficiency assessment tools, including an alternative non-parametric output-orientated technique and a more explicit valuation function for educational outputs, in order to estimate the shape of the efficiency frontier and both technical and allocative efficiency.     

Deriving the DEA frontier for two-stage processes

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model provides not only an overall efficiency score for the entire process, but as well yields an efficiency score for each of the individual stages. Due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores, as in the standard DEA approach, does not necessarily yield a frontier projection. The current paper develops an approach for determining the frontier points for inefficient DMUs within the framework of two-stage DEA.     

Calculating scale elasticity in DEA models

In the data envelopment analysis (DEA) efficiency literature, qualitative characterizations of returns to scale (increasing, constant, or decreasing) are most common. In economics it is standard to use the scale elasticity as a quantification of scale properties for a production function representing efficient operations. Our contributions are to review DEA practices, apply the concept of scale elasticity from economic multi-output production theory to DEA piecewise linear frontier production functions, and develop formulas for scale elasticity for radial projections of inefficient observations in the relative interior of fully dimensional facets. The formulas are applied to both constructed and real data and show the differences between scale elasticities for the two valid projections (input and output orientations). Instead of getting qualitative measures of returns to scale only as was done earlier in the DEA literature, we now get a quantitative range of scale elasticity values providing more information to policy-makers.     

Measurement of multiperiod aggregative efficiency

This article proposes a new method for measuring an aggregative efficiency of multiple period production systems. Every organization or firm generates a time series of data that represent its performances in the resource utilization and output production over multiple periods, and often desires an aggregated measure of efficiency for several periods of interest. Data envelopment analysis (DEA) has become an accepted and well-known approach to evaluating efficiency performance in a wide range of cases. However, most of the DEA studies have dealt primarily with ways to gauge the efficiency of production in only a single period so this efficiency reflects the insufficient or partial performance of multiple period productions. The new method is developed through extensions of the concept of Debreu–Farrell technical efficiency and is applied to evaluating the efficiency of cable TV service units with 3-year data.     

Supply chain DEA: production possibility set and performance evaluation model

Performance evaluation is of great importance for effective supply chain management. The foundation of efficiency evaluation is to faithfully identify the corresponding production possibility set. Although a lot of researches have been done on supply chain DEA models, the exact definition for supply chain production possibility set is still in absence. This paper defines two types of supply chain production possibility sets, which are proved to be equivalent to each other. Based upon the production possibility set, a supply chain CRS DEA model is advanced to appraise the overall technical efficiency of supply chains. The major advantage of the model lies on the fact that it can help to find out the most efficient production abilities in supply chains, by replacing or improving inefficient subsystems (supply chain members). The proposed model also directly identifies the benchmarking units for inefficient supply chains to improve their performance. A real case validates the reasonableness and acceptability of this approach.     

Impacts of random noise and specification on estimates of capacity derived from data envelopment analysis

Data envelopment analysis (DEA) is widely used to estimate the efficiency of firms and has also been proposed as a tool to measure technical capacity and capacity utilization (CU). Random variation in output data can lead to downward bias in DEA estimates of efficiency and, consequently, upward bias in estimates of technical capacity. This can be particularly problematic for industries such as agriculture, aquaculture and fisheries where the production process is inherently stochastic due to environmental influences. This research uses Monte Carlo simulations to investigate possible biases in DEA estimates of technically efficient output and capacity output attributable to noisy data and investigates the impact of using a model specification that allows for variable returns to scale (VRS). We demonstrate a simple method of reducing noise induced bias when panel data is available. We find that DEA capacity estimates are highly sensitive to noise and model specification. Analogous conclusions can be drawn regarding DEA estimates of average efficiency.     

Nonparametric analysis of educational costs

Traditional economic analyses of the public sector that assume cost minimization are not consistent with political models of bureaucracy. If costs are not minimized then estimated cost functions will be biased. The purpose of this paper is to provide a flexible nonparametric technique based on Farrell-type efficiency measures to estimate public sector costs. Standard indices need to be modified to fit the special nature of public sector service provision which is characterized by an influence of exogenous variables on cost. A useful by-product is an index of environmental harshness faced by local governments. For illustrative purposes, this technique is applied to a sample of New York State school districts. It is found that nearly 64% of districts are cost inefficient, spending on average $1200 per pupil above the cost minimizing level. In addition, it is estimated that the average school district faces environmental cost of over $1700 per pupil.     

Relative Efficiency Assessments Using Data Envelopment Analysis: An Application to Data on Rates Departments

This paper examines the nature of information obtained from data envelopment analysis (DEA) in comparative studies of the efficiency of decision-making units, and it discusses the interpretation and practical usefulness of such information. The themes developed in the paper are illustrated by an application of DEA to data on the rate-collection function of London Boroughs and Metropolitan District Councils. The paper begins with an overview of DEA, followed by a discussion of some of the practical considerations arising in the application of DEA. It then describes the structuring of the rate-collection function for assessment by DEA, and explores the extent to which units can be classified as relatively efficient or inefficient. In respect of relatively inefficient units, it illustrates the construction of target inputs and outputs so that their relative efficiency may improve. In respect of relatively efficient units, it is argued that their identification is weak in the sense that for some of them their apparent efficiency may be simply a reflection of an uncommon input-output profile. It is shown, nevertheless, that information about relatively efficient units can be used to identify those of them which may prove examples of good operating practice in given aspects of their function. (Readers not familiar with British taxes may wish to note that rates are a tax on property, levied by local authorities.)     

Resource allocation and target setting for parallel production system based on DEA

The paper proposes methodology for resource allocation and target setting based on DEA (data envelopment analysis). It deals with organization can be modeled as consisting of several production units, each of which has parallel production lines. The previous studies in the DEA literature only deal with reallocating/allocating organizational resources to production units and set targets for them. In their researches, the production unit is treated as a black box. In such circumstances, how to arrange the production at production unit level is not clear. This paper serves to generate resource allocation and target setting plan for each production unit by opening the black box. The proposed model exploits production information of production lines in generating production plans. The resulting plan has following characteristics: (1) the performance of each production lines are evaluated under common weights; (2) the weights chose for evaluation keep the efficiency of the entire unit not worse off; (3) the worst behaved production line in the production unit under evaluation are improved as much as possible. Finally, the real data of a production system extracted from extant literature are used to demonstrate the proposed method.