A network DEA assessment of team efficiency in the NBA

In this paper, a Network DEA approach to assess the efficiency of NBA teams is proposed and compared with a black-box (i.e. single-process) DEA approach. Both approaches use a Slack-Based Measure of efficiency (SBM) to evaluate the potential reduction of inputs consumed (team budget) and outputs produced (games won by the team). The study considers the distribution of the budget between first-team players and the rest of the payroll. The proposed network DEA approach consists of five stages, which evaluate the performance of first-team and bench-team players, the offensive and defensive systems and the ability for transforming the points made by itself and by the opponents into wins. It has been applied to the 30 NBA teams for the regular season 2009–2010. The results show that network DEA has more discriminating power and provides more insight than the conventional DEA approach.     

Condorcet efficiency and constant scoring rules

Exact closed form relations are obtained for the Condorcet efficiencies of the four constant scoring rules on three element rankings when all profiles of rankings are assumed to be equally likely to occur. The Condorcet efficiencies of the two stage constant rules are shown to be substantially greater than those of single stage constant rules. The single stage scoring rule that picks the element that is ranked first most often is shown to have a much greater efficiency than the single stage scoring rule that selects the element that has the fewest last place rankings.     

Network DEA: Additive efficiency decomposition

In conventional DEA analysis, DMUs are generally treated as a black-box in the sense that internal structures are ignored, and the performance of a DMU is assumed to be a function of a set of chosen inputs and outputs. A significant body of work has been directed at problem settings where the DMU is characterized by a multistage process; supply chains and many manufacturing processes take this form. Recent DEA literature on serial processes has tended to concentrate on closed systems, that is, where the outputs from one stage become the inputs to the next stage, and where no other inputs enter the process at any intermediate stage. The current paper examines the more general problem of an open multistage process. Here, some outputs from a given stage may leave the system while others become inputs to the next stage. As well, new inputs can enter at any stage. We then extend the methodology to examine general network structures. We represent the overall efficiency of such a structure as an additive weighted average of the efficiencies of the individual components or stages that make up that structure. The model therefore allows one to evaluate not only the overall performance of the network, but as well represent how that performance decomposes into measures for the individual components of the network. We illustrate the model using two data sets.     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

Additive efficiency decomposition in two-stage DEA

Kao and Hwang (2008) [Kao, C., Hwang, S.-N., 2008. Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European Journal of Operational Research 185 (1), 418–429] develop a data envelopment analysis (DEA) approach for measuring efficiency of decision processes which can be divided into two stages. The first stage uses inputs to generate outputs which become the inputs to the second stage. The first stage outputs are referred to as intermediate measures. The second stage then uses these intermediate measures to produce outputs. Kao and Huang represent the efficiency of the overall process as the product of the efficiencies of the two stages. A major limitation of this model is its applicability to only constant returns to scale (CRS) situations. The current paper develops an additive efficiency decomposition approach wherein the overall efficiency is expressed as a (weighted) sum of the efficiencies of the individual stages. This approach can be applied under both CRS and variable returns to scale (VRS) assumptions. The case of Taiwanese non-life insurance companies is revisited using this newly developed approach.     

综合评价方法在NBA赛程分析中的应用

随着认知领域的不断扩大,人们所面临的评价对象日益复杂,综合评价问题得到广泛应用.针对高职类学生知识结构特点,主要介绍层次分析法及模糊综合评价法在建模培训中的应用.在实践中,通过抓住确定影响因素指标体系及确定各指标权重这两个关键环节,把握各种具体的综合评价方法的主体思想.针对08年全国大学生数学建模竞赛D题(NBA赛程分析与评价),介绍赛程评价方法及赛程安排的0-1规划模型.     

Greek football clubs’ efficiency before and after Euro 2004 Victory: a bootstrap approach

This paper examines the technical efficiency of Greek football clubs, taking into account the period before the Euro 2004 victory and the period thereafter. The first stage of analysis is based on a bootstrapped data envelopment analysis approach so as to determine Greek clubs’ efficiency scores during these two distinct time periods. The second stage of analysis investigates possible factors that may have affected the efficiency scores during the examined periods. Our findings reveal that Greek football clubs exhibit surprisingly lower efficiency scores after Euro victory. In effect and explained in the context of the Resource Based Theory, there appears to be no classification of types of football clubs into various divisions, viz. laggards, followers and champions. Finally, it is also found that clubs’ financial health appears to be a crucial factor for their performance in both periods.     

关于科研事业单位知识型团队绩效评价的实证分析——基于胜任力模型

我国科研事业单位普遍面临绩效考核困境,不能满足知识经济背景下知识型团队的管理要求。胜任力模型可以有效地对知识型团队成员进行选拔、配置与管理,是团队取得高绩效的关键。本研究采用问卷调查结合行为事件访谈的方法,筛选科研事业单位知识型团队的胜任力特征,并采用主成分分析方法,从7个维度构建了知识型团队胜任力模型。在此基础上,采用层次分析法,对团队业绩、胜任力、行为指标进行两两比较,确认其相对重要性,进一步构建了绩效评价体系。结果发现,在科研事业单位知识型团队中,成员个人能力的提升、团队信息共享和效率以及团队管理者的能力是最重要的团队胜任力特征,而外部支持和人际关系相对次要。胜任力指标在绩效评价体系中占有重要的地位。而团队行为对团队绩效的影响也不可忽视。     

Asymptotic efficiency of the two-stage estimation method for copula-based models

For multivariate copula-based models for which maximum likelihood is computationally difficult, a two-stage estimation procedure has been proposed previously; the first stage involves maximum likelihood from univariate margins, and the second stage involves maximum likelihood of the dependence parameters with the univariate parameters held fixed from the first stage. Using the theory of inference functions, a partitioned matrix in a form amenable to analysis is obtained for the asymptotic covariance matrix of the two-stage estimator. The asymptotic relative efficiency of the two-stage estimation procedure compared with maximum likelihood estimation is studied. Analysis of the limiting cases of the independence copula and Fréchet upper bound help to determine common patterns in the efficiency as the dependence in the model increases. For the Fréchet upper bound, the two-stage estimation procedure can sometimes be equivalent to maximum likelihood estimation for the univariate parameters. Numerical results are shown for some models, including multivariate ordinal probit and bivariate extreme value distributions, to indicate the typical level of asymptotic efficiency for discrete and continuous data.     

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.     

Operational and economic efficiency analysis of public hospitals in Greece

The continuous growth of hospital costs has driven governments in many countries to seek ways to improve their efficiency. In Greece, this has consistently been a major issue for almost two decades, as efficiency assessment and monitoring systems are lacking. In response to this need, the evaluation of the National Health System hospitals’ efficiency level is a precondition for planning, implementing and monitoring any promising reform. In this paper, a non-parametric modeling approach is employed to assess and analyze the efficiency of 87 Greek public hospitals over the period 2005–2009, using data envelopment analysis. The operational and economic aspects of the hospitals’ operation are considered on the basis of their service/case mix and cost structure. We also investigate the efficiency trends over time with the Malmquist index and a second stage regression analysis is performed to explain the operational and economic efficiency results in terms of the hospitals’ operating characteristics and the environment in which they operate.     

Weight assurance region in two-stage additive efficiency decomposition DEA model: an application to school data

In this paper we use the additive efficiency decomposition approach in two-stage data envelopment analysis. Initially, we evaluate the variable returns to scale version and face a structural difficulty of the model. In an extreme case, weights ξ₁ or ξ₂, which represent the relative importance of the performance of the first and second stages, respectively, become zero for a number of decision making units (DMUs). As a result, individual stage efficiencies for these DMUs are undefined. We propose a weight assurance region model to restrict ξ₁ and ξ₂, which ensures that both weights are always positive, and therefore individual stage efficiency is always defined. Furthermore, the proposed model is appropriate for policy making in the presence of a priori information about the relative importance of each stage in the overall process. We employ the new model to evaluate the efficiency of secondary education in 65 countries and construct an overall ‘school efficiency’ index. In the first stage we measure the ‘learning environment efficiency’ and in the second we measure the ‘student’s performance efficiency’.     

On the decisiveness of a game in a tournament

In sport tournaments in which teams are matched two at a time, it is useful for a variety of reasons to be able to quantify how important a particular game is. The need for such quantitative information has been addressed in the literature by several more or less simple measures of game importance. In this paper, we point out some of the drawbacks of those measures and we propose a different approach, which rather targets how decisive a game is with respect to the final victory. We give a definition of this idea of game decisiveness in terms of the uncertainty about the eventual winner prevailing in the tournament at the time of the game. As this uncertainty is strongly related to the notion of entropy of a probability distribution, our decisiveness measure is based on entropy-related concepts. We study the suggested decisiveness measure on two real tournaments, the 1988 NBA Championship Series and the UEFA 2012 European Football Championship (Euro 2012), and we show how well it agrees with what intuition suggests. Finally, we also use our decisiveness measure to objectively analyse the recent UEFA decision to expand the European Football Championship from 16 to 24 nations in the future, in terms of the overall attractiveness of the competition.     

Semi-radial technical efficiency measurement

Semi-radial efficiency measurement combines technical efficiency, as captured by the classical Farrell measure, with an economically meaningful mix efficiency component. The semi-radial evaluation we propose proceeds in two steps. First, we build on the price interpretation of the generally accepted Koopmans efficiency notion to characterize appropriate benchmarks. Next, we present both a quantity-based distance measure and its dual (price-based) equivalent to evaluate the mix efficiency factor. The type of measures we propose may, e.g., be used to provide a price rationale for the Zieschang technical efficiency evaluation procedure.     

Unveiling endogeneity between competition and efficiency in Chinese banks: a two-stage network DEA and regression analysis

Although there is a growing number of research articles investigating the performance in the banking industry, research on Chinese banking efficiency is rather focused on discussing rankings to the detriment of unveiling its productive structure in light of banking competition. This issue is of utmost importance considering the relevant transformations in the Chinese economy over the last decades. This is a development of a two-stage network production process (production and intermediation approaches in banking, respectively) to evaluate the efficiency level of Chinese commercial banks. In the second stage regression analysis, an integrated Multi-Layer Perceptron/Hidden Markov model is used for the first time to unveil endogeneity among banking competition, contextual variables, and efficiency levels of the production and intermediation approaches in banking. The competitive condition in the Chinese banking industry is measured by Panar–Rosse H-statistic and Lerner index under the Ordinary Least Square regression. Findings reveal that productive efficiency appears to be positively impacted by competition and market power. Second, credit risk analysis in older local banks, which focus the province level, would possibly be the fact that jeopardizes the productive efficiency levels of the entire banking industry in China. Thirdly, it is found that a perfect banking competition structure at the province level and a reduced market power of local banks are drivers of a sound banking system. Finally, our findings suggest that concentration of credit in a few banks leads to an increase in bank productivity.

     

Aggregation of scale efficiency

In this article we generalize the aggregation theory in efficiency and productivity analysis by deriving solutions to the problem of aggregation of individual scale efficiency measures, primal and dual, into aggregate primal and dual scale efficiency measures of a group (e.g., industry). The new aggregation result is coherent with aggregation framework and solutions that were earlier derived for other related efficiency measures and can be used in practice for estimation of scale efficiency of an industry or other groups of firms within it.     

The relationship between the efficiency of orthopedic wards and the socio-economic status of their patients

The purpose of this paper is to study the effect of the socio-economic status of patients on the efficiency of orthopedic wards in acute hospitals in Israel (20 hospitals), from the viewpoint of the regulator—Israel Ministry of Health. At the first stage, data envelopment analysis is used with two inputs, and three outputs, where one output is undesirable—“number of deaths”—which also reflects the quality of the health services. At the second stage, various nonparametric tests are utilized to test the relationship between the socio-economic status of patients and the efficiency. As by-product DEA provides benchmark analysis, which indicates the peers of each inefficient ward, and the I/O improvements are needed for achieving efficiency. Two versions of DEA were used: the output oriented version (variable returns to scale), and the non-oriented version (Additive). Further analysis provides comparison of the results with other simple efficiency measures. We also compare between the efficiency from the regulator viewpoint and the hospitals’ viewpoint.     

Cross-country comparison of the efficiency of the European forest sector and second stage DEA approach

In this paper the relative efficiency of the forest sector of 28 EU/EFTA countries during the period 2010–2015 is assessed using Data Envelopment Analysis (DEA). Three non-discretionary inputs (persons employed, forest available for wood supply and initial growing stock) are considered. The outputs are roundwood production, gross value added and final growing stock. The proposed DEA model not only computes efficiency scores but also improvement targets. The countries with the lowest efficiency scores during the period under study are Greece, Bulgaria and Italy. In the second stage, a fractional regression model is fitted and the factors that have an influence on the estimated efficiency are identified. The factors that have an influence are GDP and belonging to the NORTH Europe and CENTRAL-WEST Europe regions. Quantitative estimates of the partial effects of these factors are provided. The results can contribute in providing guidance towards the best practice in roundwood production.

     

Technical efficiency and economies of scale in state owned enterprises: The Hellenic telecommunications organisation

In this paper we propose methodologies for assessing the relative efficiency of state owned enterprises that operate under monopolistic conditions. Irrespective of the ownership structure (private or public) monopolistic operation is often given unclear/conflicting operating objectives by their principals or regulators and thus efficiency should be assessed using alternative objectives such as cost, production and revenue. On the methodological side the paper employs parametric functional forms using ordinary least squares and goal programming methods of estimation. A secondary estimation stage was also pursued with the input/output variables of the models being corrected for technical inefficiency. The methodology was applied to examine the technical efficiency and economies of scale of the Hellenic telecommunications organisation over the period 1971–1993.