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.     

Data Envelopment Analysis with Reverse Inputs and Outputs

Data envelopment analysis (DEA) assumes that inputs and outputs are measured on scales in which larger numerical values correspond to greater consumption of inputs and greater production of outputs. We present a class of DEA problems in which one or more of the inputs or outputs are naturally measured on scales in which higher numerical values represent lower input consumption or lower output production. We refer to such quantities as reverse inputs and reverse outputs. We propose to incorporate reverse inputs and outputs into a DEA model by returning to the basic principles that lead to the DEA model formulation. We compare our method to reverse scoring, the most commonly used approach, and demonstrate the relative advantages of our proposed technique. We use this concept to analyze all 30 Major League Baseball (MLB) organizations during the 1999 regular season to determine their on-field and front office relative efficiencies. Our on-field DEA model employs one output and two symmetrically defined inputs, one to measure offense and one to measure defense. The defensive measure is such that larger values correspond to worse defensive performance, rather than better, and hence is a reverse input. The front office model uses one input. Its outputs, one of which is a reverse output, are the inputs to the on-field model. We discuss the organizational implications of our results.     

Improving discrimination in data envelopment analysis: some practical suggestions

In some contexts data envelopment analysis (DEA) gives poor discrimination on the performance of units. While this may reflect genuine uniformity of performance between units, it may also reflect lack of sufficient observations or other factors limiting discrimination on performance between units. In this paper, we present an overview of the main approaches that can be used to improve the discrimination of DEA. This includes simple methods such as the aggregation of inputs or outputs, the use of longitudinal data, more advanced methods such as the use of weight restrictions, production trade-offs and unobserved units, and a relatively new method based on the use of selective proportionality between the inputs and outputs.     

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.     

Accounting for Environmental Effects and Statistical Noise in Data Envelopment Analysis

In this paper we propose a new technique for incorporating environmental effects and statistical noise into a producer performance evaluation based on data envelopment analysis (DEA). The technique involves a three-stage analysis. In the first stage, DEA is applied to outputs and inputs only, to obtain initial measures of producer performance. In the second stage, stochastic frontier analysis (SFA) is used to regress first stage performance measures against a set of environmental variables. This provides, for each input or output (depending on the orientation of the first stage DEA model), a three-way decomposition of the variation in performance into a part attributable to environmental effects, a part attributable to managerial inefficiency, and a part attributable to statistical noise. In the third stage, either inputs or outputs (again depending on the orientation of the first stage DEA model) are adjusted to account for the impact of the environmental effects and the statistical noise uncovered in the second stage, and DEA is used to re-evaluate producer performance. Throughout the analysis emphasis is placed on slacks, rather than on radial efficiency scores, as appropriate measures of producer performance. An application to nursing homes is provided to illustrate the power of the three-stage methodology.     

Environmental performance evaluation: A state-level DEA analysis

In recent years, the continuous development of every country's economic activities has generated undesirable impacts on the environment. Common problems are high water and energy consumption rates, jointly with harmful pollution levels. This situation has gained the research community's interest in exploring and analyzing the extent to which initiatives to reduce such environmental problems have succeeded. Therefore, it is relevant to have measures that encompass information on the results obtained by such initiatives. Using the data envelopment analysis (DEA) methodology, it is possible to measure the efficiency of an entity under evaluation, such as an industry, state, or country. DEA also allows one to compare the performance measures of entities operating in similar circumstances and identify which entities are performing best, given the inputs they use and the outputs they produce. This study evaluates different states in Mexico in terms of their environmental performance and provides a perspective on how environmental initiatives can contribute to protecting and preserving the environment. By addressing this problem, best-performers and practices are identified, and valuable insights are gained regarding how each state carries out such initiatives.     

基于超效率DEA的企业自主创新项目投资方案决策

本文依据企业自主创新项目具有多投入、多产出的特点,构建了以参与人数、总投资和能耗为投入指标、年产量为产出指标的企业自主创新项目投资方案评价指标体系;基于超效率DEA方法建立了企业自主创新项目投资方案评价模型,并通过某自主创新项目8种投资方案进行了实例研究,结果验证了该方法不仅能够判断出最终最优方案,而且能够提出进一步的目标改进措施。与传统DEA方法相比,基于超效率DEA的企业自主创新项目投资方案评价模型更具应用优势。     

Measuring efficiency under fixed proportion technologies

Data Envelopment Analysis (DEA) applications frequently involve nonsubstitutable inputs and nonsubstitutable outputs (that is, fixed proportion technologies). However, DEA theory requires substitutability. In this paper, we illustrate the consequences of nonsubstitutability on DEA efficiency estimates, and we develop new efficiency indicators that are similar to those of conventional DEA models except that they require nonsubstitutability. Then, using simulated and real-world datasets that encompass fixed proportion technologies, we compare DEA efficiency estimates with those of the new indicators. The examples demonstrate that DEA efficiency estimates are biased when inputs and outputs are nonsubstitutable. The degree of bias varies considerably among Decision Making Units, resulting in substantial differences in efficiency rankings between DEA and the new measures. And, over 90% of the units that DEA identifies as efficient are, in truth, not efficient. We conclude that when inputs and outputs are not substituted for either technological or other reasons, conventional DEA models should be replaced with models that account for nonsubstitutability.     

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.     

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.     

Using Simulation and Data Envelopment Analysis to Compare Assembly Line Balancing Solutions

This paper presents a technique for comparing the results of different assembly line balancing strategies by using Data Envelopment Analysis (DEA). Initially, several heuristics--which can be thought of as assembly line balancing strategies--were used to solve seven line-balancing problems. The resulting line balance solutions provided two pieces of information that were of particular interest: the number of workers needed and the amount of equipment needed. These two items were considered inputs for DEA. The different line balance solutions were then used as layouts for simulated production runs. From the simulation experiments, several output performance measures were obtained which were of particular interest and were used as outputs for DEA. The analysis shows that DEA is effective in suggesting which line balancing heuristics are most promising.     

A review of DEA methods to identify and measure congestion

Congestion is an economic phenomenon of overinvestment that occurs when excessive inputs decrease the maximally possible outputs. Although decision-makers are unlikely to decrease outputs by increasing inputs, congestion is widespread in reality. Identifying and measuring congestion can help decision-makers detect the problem of overinvestment. This paper reviews the development of the concept of congestion in the framework of data envelopment analysis (DEA), which is a widely accepted method for identifying and measuring congestion. In this paper, six main congestion identification and measurement methods are analysed through several numerical examples. We investigate the ideas of these methods, the contributions compared with the previous methods, and the existing shortcomings. Based on our analysis, we conclude that existing congestion identification and measurement methods are still inadequate. Three problems are anticipated for further study: maintaining the consistency between congestion and overinvestment, considering joint weak disposability assumption between desirable outputs and undesirable outputs, and quantifying the degree of congestion.     

A novel method for computing single output for DEA with application in hospital efficiency

There are two main methods for measuring the efficiency of decision-making units (DMUs): data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Each of these methods has advantages and disadvantages. DEA is more popular in the literature due to its simplicity, as it does not require any pre-assumption and can be used for measuring the efficiency of DMUs with multiple inputs and multiple outputs, whereas SFA is a parametric approach that is applicable to multiple inputs and a single output. Since many applied studies feature multiple output variables, SFA cannot be used in such cases. In this research, a unique method to transform multiple outputs to a virtual single output is proposed. We are thus able to obtain efficiency scores from calculated virtual single output by the proposed method that are close (or even the same depending on targeted parameters at the expense of computation time and resources) to the efficiency scores obtained from multiple outputs of DEA. This will enable us to use SFA with a virtual single output. The proposed method is validated using a simulation study, and its usefulness is demonstrated with real application by using a hospital dataset from Turkey.     

Online banking performance evaluation using data envelopment analysis and axiomatic fuzzy set clustering

This paper presents a hybrid model to conducting performance measurements for Internet banking by using data envelopment analysis (DEA) and axiomatic fuzzy set (AFS) clustering. For each bank, DEA is applied to select a best combination by computing an aggregated efficiency score based on outputs, such as web metrics and revenue; and inputs, such as equipment, operation cost and employees. Then AFS clustering method is used to classify the best combination into different groups and provide the definitely semantic interpretations for the evaluation results. Identification of operational fitness and business orientation of each firm, in this way, will yield insights into understanding the weaknesses and strengths of banks, which are considering moving into Internet banking.     

基于DEA的安徽省可持续发展技术创新评价

阐述了DEA方法及区域可持续发展的技术创新的定义与内涵,提出了以区域技术创新为投入,以整个区域包括经济、社会、资源、环境四个方面的复合系统为产出的决策单元(DMU)概念,建立了旨在区别同为有效的DMU的相对效率指数DEA方法。运用该方法,对安徽省近六年来可持续发展的技术创新进行了评价比较。     

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.     

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.     

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.     

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.     

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.