Models for measuring and benchmarking olympics achievements

As demonstrated in several recent studies, data envelopment analysis (DEA) is a useful tool for evaluating and comparing the performance of nations competing in the Olympic Games. Assurance regions (ARs) have been used to further refine the DEA results. These AR DEA models assume that ARs apply uniformly across all nations. Such models can have shortcomings in the sense that different nations may impose different ARs, as nations may value gold, silver, and bronze medals differently. This paper extends previous DEA studies by incorporating multiple sets of nation-specific ARs into the DEA. By doing so, we establish fair models for measuring and benchmarking the performance of nations at six summer Olympic Games.     

Two-stage DEA models with undesirable input-intermediate-outputs

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks.     

Estimation of portfolio efficiency via DEA

Traditional DEA models and nonlinear (diversification) DEA models are often used in performance evaluation of portfolios. However, the diversification models are usually very complicated to compute except the very basic models. And the classic DEA models still need to be further justified and tested, since it is not clear whether they are over-linearised according to the diversification models. The existing studies on performance evaluation via the classic DEA models generally focus on the selection of inputs and outputs. In this work, we investigate theoretical foundation of DEA models for portfolios from a perspective of sampling portfolio. We show the classic DEA provides an effective and practical way to approximate the portfolio efficiency (PE). We further verify this approach through different portfolio models with various frictions and bounds on the market. Through the comprehensive simulations carried out in this study, we show that with adequate data sets, the classic DEA models can effectively sample portfolios to take into account sufficient diversification, and thus can be used as an effective tool in computing the PE for their performance assessments. This study can be viewed as a justification of the classic DEA performance assessments and the way to introduce other efficiency notions (like allocation efficiency, scale efficiency, etc) into assessment of portfolios.     

Optimising correlated QCHs in robust design using principal components analysis and DEA techniques

Taguchi method is found efficient for optimising process performance with a single quality characteristic (QCH) of a product or process. In practice, however, customers are concerned about multiple QCHs, which are usually correlated. This research proposes and implements an approach using principal components analysis (PCA) and two data envelopment analysis (DEA) models, including CCR and super efficiency, for optimising multiple correlated QCHs in robust design. The PCA is first utilised to obtain multiple uncorrelated linear combinations of principal components, which are the same number of QCHs and hence avoid the loss of information by ignoring some principal components. Then, these components are utilised in two DEA models to decide optimal factor levels. Three real case studies are provided for illustration; in all of which the proposed approach is found more efficient than some other techniques in literature, including engineering judgement, PCA, PCA and grey analysis, and utility concept. In conclusion, the proposed approach shall provide a great assistance to process/product engineers for obtaining robust design with multiple correlated QCHs.     

基于多种DEA模型和Gini准则的效率评价方法——兼对我国高校运营绩效的评价

针对多种数据包络分析（Data Envelopment Analysis,简称DEA）模型会产生不同绩效评价结果的问题,提出基于Gini准则科学地融合各DEA模型结果的方法。首先基于Gini准则定义信息纯度以衡量各DEA模型结果的确定性并赋予权重,然后通过加权融合最终得出客观唯一的综合效率。此外,根据评价者的偏好信息或先验知识,进一步提出交互式多DEA模型-Gini准则方法。以前学者仅从单一角度出发选择DEA模型评价高校的运营绩效,考虑到从不同角度出发的多种DEA模型可以给出高校更加全面客观的运营绩效评价,利用以上方法对2011年国内25所理工类高校的运营绩效进行了实证分析,结果验证了以上方法可以合理有效的衡量各高校的运营绩效表现,对于高校运营绩效的评价研究具有实际指导意义。     

Incorporating cost and environmental factors in quality function deployment using data envelopment analysis

Quality function deployment (QFD) is an important tool available to organizations for efficient product design and development. Traditionally, QFD rates the design requirements (DRs) with respect to customer needs, and aggregates the ratings to get relative importance scores of DRs. An increasing number of studies stress on the need to incorporate additional factors, such as cost and environmental impact, while calculating the relative importance of DRs. However, there is a paucity of methodologies for deriving the relative importance of DRs when several additional factors are considered. In this paper, data envelopment analysis (DEA) is suggested for the purpose. It is proved that the relative importance values computed by DEA coincide with traditional QFD calculations when only the ratings of DRs with respect to customer needs are considered, and when only one additional factor, namely cost, is considered. DEA provides a general framework facilitating QFD computations when more factors need to be considered. The calculations are explained using a step-by-step procedure and illustrations. The proposed QFD–DEA methodology is applied to the design of security fasteners for a Chinese company. Though traditional QFD calculations consider the ratings as cardinal numbers, DEA has the flexibility to treat the ratings as qualitative variables. This aspect is illustrated in a separate section.     

部分中间产出作为最终产品的两阶段合作效率

网络DEA模型研究多个进程和多个子系统的复杂系统的效率度量.针对中间产出无法为第2阶段完全消耗的情形,传统DEA模型对系统效率的评价偏高,已有网络DEA模型则对系统效率的评价偏低.本文提出部分中间产出作为最终产品,进入流通渠道的两阶段效率模型,用来测度两阶段生产过程的真实效率.采用乘积形式描述两阶段合作的特征,给出不同...     

Efficiency measurement for hierarchical network systems

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for systems with a hierarchical structure. It is shown that the hierarchical structure is equivalent to a parallel structure, with the components being the units at the bottom of the hierarchy. Due to the characteristics of a parallel system, the efficiency of a hierarchical system is thus a weighted average of those of the units at the bottom of the hierarchy. A hypothetic example shows that the proposed model is able to distinguish the order of the efficient DMUs evaluated by the conventional DEA model. Moreover, it provides the efficiencies of the functions of the DMU, which enables managers to identify areas of weakness, and thus better focus efforts to improve overall performance.     

只有输出的广义样本区间DEA模型

在应用多个绩效指标综合评价决策单元有效性时，决策者常常把这些决策单元与另外预先指定的标准（样本单元）进行比较。由于客观事物的复杂性和不确定性导致样本单元和决策单元的指标信息有时必须用区间数的形式给出。针对区间数指标信息的综合评价问题，本文通过分解的方法讨论样本单元和决策单元指标信息为区间数时用广义DEA模型评价决策单元有效性的方法，并相应地构建了只有输出的广义区间DEA模型。同时，对模型的含义、求解以及性质等进行了分析。之后，探讨了该方法在决策单元有效性分类和排序中的应用。最后，通过实例表明该方法的可行性和有效性。     

A network DEA quantity and quality-orientated production model: An application to Australian university research services

The motivation for this analysis is the recently developed Excellence in Research for Australia (ERA) program developed to assess the quality of research in Australia. The objective is to develop an appropriate empirical model that better represents the underlying production of higher education research. In general, past studies on university research performance have used standard DEA models with some quantifiable research outputs. However, these suffer from the twin maladies of an inappropriate production specification and a lack of consideration of the quality of output. By including the qualitative attributes of peer-reviewed journals, we develop a procedure that captures both quality and quantity, and apply it using a network DEA model. Our main finding is that standard DEA models tend to overstate the research efficiency of most Australian universities.     

The implementation of management science in higher education administration

Literature surveys during the 1970s found that many more management science models had been developed for higher education administration than had actually been implemented. This paper uses a survey of 146 recent articles to assess the current state of implementation in that area. The percentage of articles reported to have been implemented is presented for each administrative level, from departmental administration up to the federal level. Purposes for which the models were designed and the management science techniques used are also discussed as they relate to the record of successful implementation. The results are both surprising and informative. For example, although the largest number of models have been developed foruse at the presidential or vice presidential level of an institution, the highest percentage of successful implementations have occurred at the departmental administration level. There have been very few implementations at the state or federal levels. While scheduling was the one purpose for which the fewest number of models were developed, those models also had the highest rate of implementation. The most commonly used technique was mathematical programming, but it also had an extremely low percentage of ongoing implementations. The results indicate areas that need further work while also pinpointing areas that have probably been modelled too much.     

Incorporating quality into data envelopment analysis of nursing home performance: A case study

When using data envelopment analysis (DEA) as a benchmarking technique for nursing homes, it is essential to include measures of the quality of care. We survey applications where quality has been incorporated into DEA models and consider the concerns that arise when the results show that quality measures have been effectively ignored. Three modeling techniques are identified that address these concerns. Each of these techniques requires some input from management as to the proper emphasis to be placed on the quality aspect of performance. We report the results of a case study in which we apply these techniques to a DEA model of nursing home performance. We examine in depth not only the resulting efficiency scores, but also the benchmark sets and the weights given to the input and output measures. We find that two of the techniques are effective in insuring that DEA results discriminate between high and low quality performance.     

MEASUREMENT OF MULTIPLE SITES IN SERVICE FIRMS WITH DATA ENVELOPMENT ANALYSIS

Data envelopment analysis (dea) has become an increasingly popular method to measure performance for service firms with multiple sites. DEA is superior to many traditional methods for firms that have multiple goals. The promise of DEA is that the complex, multi-objective problem of performance measurement can be reduced to a single number. Unfortunately, the practice of DEA often belies the promise. Misconceptions concerning the purpose and implementation of DEA can cause DEA applications to be less than successful. Here, the technique is explained, and a guide to the implementation of DEA is proposed, utilizing DEA studies of retail bank branches.     

存在非期望输入输出的多阶段系统效率评价模型

现有多阶段DEA模型的研究普遍假设所有输入、输出均为期望指标, 对存在非期望指标的情况研究较少, 尚无对最初投入和中间产出带有非期望指标的研究。为此, 本文首先提出了输入、输出类型的判定方法, 并将其应用于存在非期望输入、输出的两阶段系统。进一步针对存在非期望指标的两阶段生产系统中同种输入、输出, 尤其中间产出类型判定一致与不一致的情况, 构建了相应的生产可能集以及两阶段DEA模型, 最后利用本文方法和模型对我国上市银行效率进行了评价。     

Two-level DEA approaches in research evaluation

It is well known that the discrimination power of data envelopment analysis (DEA) models will be much weakened if too many input or output indicators are used. It is a dilemma if decision makers wish to select comprehensive indicators, which often have some hierarchical structures, to present a relatively holistic evaluation using DEA. In this paper we show that it is possible to develop DEA models that utilize hierarchical structures of input–output data so that they are able to handle quite large numbers of inputs and outputs. We present two approaches in a pilot evaluation of 15 institutes for basic research in the Chinese Academy of Sciences using the DEA models.     

存在保证域的模糊非径向偏好DEA模型——基于中科院24个研究所的实证分析

数据包络分析（DEA）是一种非参数化的方法,用于评价具有类似输入和输出的决策单元的效率。传统的非径向DEA模型假设输入和输出数据均为准确值,且对权重变量不加以限制,本文构建了存在保证域的模糊非径向偏好DEA模型,并给出了一种基于模糊数截集的模型求解方法,有效地解决了输入和输出全部或部分为模糊数的决策单元评价问题。最后给出了一个中科院研究所效率评价的实例说明了方法的有效性。     

数据包络分析中变量分类研究评述

数据包络分析的研究历史与研究者对于变量特性的认知历史是紧密联系在一起的。在数据包络分析的早期研究中,所有的投入或者产出变量都被视为可数量化、可自由处置、单角色的等。研究者逐渐认识到有些变量是不可数量化的、非自由处置的、双角色的,因此,不同目的的DEA模型被提出并加以研究。本文对数据包络分析中有关变量分类的研究进行系统性评述。     

DEA博弈模型的分析与发展

数据包络分析(Data Envelopment Analysis,DEA)与博弈论之间关系密切.传统DEA模型忽略了决策单元(Decision Making Units,DMUs)之间的竞合关系,对权重的限制过于宽松,难以合理评价DMU效率值.为此,将博弈论方法引入至DEA模型,开展DEA的博弈研究,既是对DEA理论的重大发展,也将极大拓宽博弈论的应用研究.本文分三个阶段对现有的DEA博弈研究进行述评:(1)DEA的博弈论解释;(2)DEA Game模型及其应用;(3)DEA效率博弈;在深入分析重点模型基础上,总结其发展脉络,促进DEA理论与实践的发展.     

Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture

In this paper we consider the use of data envelopment analysis (DEA) for the assessment of efficiency of units whose output profiles exhibit specialisation. An example of this is found in agriculture where a large number of different crops may be produced in a particular region, but only a few farms actually produce each particular crop. Because of the large number of outputs, the use of conventional DEA models in such applications results in a poor efficiency discrimination. We overcome this problem by specifying production trade-offs between different outputs, relying on the methodology of Podinovski (J Oper Res Soc 2004;55:1311–22). The main idea of our approach is to relate various outputs to the production of the main output. We illustrate this methodology by an application of DEA involving agricultural farms in different regions of Turkey. An integral part of this application is the elicitation of expert judgements in order to formulate the required production trade-offs. Their use in DEA models results in a significant improvement of the efficiency discrimination. The proposed methodology should also be of interest to other applications of DEA where units may exhibit specialization, such as applications involving hospitals or bank branches.     

DEA game cross-efficiency approach to Olympic rankings

A number of studies have used data envelopment analysis (DEA) to evaluate the performance of the countries in Olympic games. While competition exists among the countries in Olympic games/rankings, all these DEA studies do not model competition among peer decision making units (DMUs) or countries. These DEA studies find a set of weights/multipliers that keep the efficiency scores of all DMUs at or below unity. Although cross efficiency goes a further step by providing an efficiency measure in terms of the best multiplier bundle for the unit and all the other DMUs, it is not always unique. This paper presents a new and modified DEA game cross-efficiency model where each DMU is viewed as a competitor via non-cooperative game. For each competing DMU, a multiplier bundle is determined that optimizes the efficiency score for that DMU, with the additional constraint that the resulting score should be at or above that DMU 's estimated best performance. The problem, of course, arises that we will not know this best performance score for the DMU under evaluation until the best performances of all other DMUs are known. To combat this “chicken and egg” phenomenon, an iterative approach leading to the Nash equilibrium is presented. The current paper provides a modified variable returns to scale (VRS) model that yields non-negative cross-efficiency scores. The approach is applied to the last six Summer Olympic Games. Our results may indicate that our game cross-efficiency model implicitly incorporates the relative importance of gold, silver and bronze medals without the need for specifying the exact assurance regions.