离散蝙蝠算法在三阶段装配流水线调度问题的应用

针对数据包络分析(DEA)交叉效率方法大多是面向结果采用平均方式集结交叉效率,没有考虑评价过程中属性效用数据及其变动的特性,导致大量决策信息丢失、相对效率评价值与被评价决策单元的指标值关联性不够等问题,以交叉效率评价过程为导向,引入群决策理论,研究属性偏好及其属性效用变化特征,运用熵权法分析属性效用稳定性,发现评价中存在属性效用的熵及其熵权的唯一性性质,从而将各决策单元(DMU)的自评权重(个体偏好)集结为一个DEA评价系统的群权重(DEA系统偏好或群偏好),建立仅有一组公共权重的群决策他评交叉效率评价方法.该方法面向过程,依据他评交叉属性效用稳定性区分其在评价中的作用,用群决策他评交叉综合群效用替代交叉效率平均作为相对效率评价值,变结果导向的交叉效率集结为过程导向的权重偏好集结,实现将相对效率评价值与群权重和属性指标值直接关联.改进后的方法简洁直观,同时方便寻求改善相对效率的途径.最后,通过算例分析验证了所提出方法的可行性与有效性.     

基于改进数据包络分析的高速列车开行方案的动态评价

针对数据包络分析(DEA)方法不能反映评价指标间权重的差异性以及不能对有效决策单元排序和调整的缺点,提出一种改进的DEA方法.首先, 运用层次分析法确定各指标的权重并建立偏好锥模型;然后, 运用交叉效率对所有决策单元进行排序并根据上座率和理想决策单元对部分决策单元进行调整; 最后,运用该方法对京沪高速列车开行方案进行评价.研究发现6条运行线中有4条是DEA有效的,需要对2条非有效和1条有效运行线进行调整.实验结果表明,改进的DEA方法能够为高速旅客列车开行方案的动态调整提供理论依据.     

基于熵权和超效率DEA模型的装备立项评估排序

针对交叉效率不唯一而导致的决策单元(DMU)无法排序, 以及在集结各DMU 交叉效率时等权重的处理问题, 运用数据包络分析(DEA)方法, 构建基于超效率的交叉效率矩阵, 应用信息熵确定各DMU的客观权重。并以此计算各DMU的交叉效率值, 进而可有效对各DMU进行排序, 通过对比算例分析, 说明该方法可行。最后将该方法应用于装备立项评估排序, 结果表明, 能够较好地解决装备立项的评估排序和择优问题。     

基于模糊期望值的模糊DEA 交叉效率评价方法

基于模糊DEA的交叉效率评价方法研究是一个崭新的研究课题,有着广阔的应用前景。结合基于模糊期望值的模糊 DEA 模型和交叉效率原理,提出一种新的交叉效率的评价方法。该方法首先求出基于模糊期望值的最优效率值权重,然后由这组模糊最优权重求解他评效率并构造交叉效率矩阵,最后根据求出的模糊期望交叉效率值对各DMU进行排序。     

基于经验数据评价的非参数系统分析方法

针对以往权重确定型评价方法中存在权重确定困难、忽视指标个性差异等弱点,以及传统数据包络分析方法难于评价非效率问题,给出了一种基于样本评价决策单元整体绩效的非参数方法,构造了相应的数学模型,并对模型的含义、模型性质以及模型的求解方法进行了分析.同时探讨了该方法在决策单元的有效性度量与排序、决策单元的无效原因分析中的应用.最后,应用该方法分析了中国西部地区工业企业经济效益状况.     

基于后悔理论及EDAS法的概率语言多属性群决策方法

针对属性权重未知的群体决策问题,提出基于离平均方案（平均解）距离的评价方法（EDAS）及考虑决策者后悔规避心理行为的概率语言术语集（PLTS）多属性群决策方法。首先,根据PLTS的相关性质定义概率语言术语集信息熵及交叉熵并建立属性权重模型;然后,将群体满意度公式拓展到概率语言术语集环境下,并用于后悔理论中效用值的计算;随后,基于概率语言术语集的属性权重确定模型及群体满意度公式,将后悔理论与EDAS法相结合提出新的多属性决策方法,并对各备选方案进行选择排序;最后,以实例网络舆情突发事件的选择排序为实例对所提出的方法进行验证,并通过对比分析来证明所提方法的有效性。     

基于后悔理论及EDAS法的概率语言多属性群决策方法

针对属性权重未知的群体决策问题，提出基于离平均方案（平均解）距离的评价方法（EDAS）及考虑决策者后悔规避心理行为的概率语言术语集（PLTS）多属性群决策方法。首先，根据PLTS的相关性质定义概率语言术语集信息熵及交叉熵并建立属性权重模型；然后，将群体满意度公式拓展到概率语言术语集环境下，并用于后悔理论中效用值的计算；随后，基于概率语言术语集的属性权重确定模型及群体满意度公式，将后悔理论与EDAS法相结合提出新的多属性决策方法，并对各备选方案进行选择排序；最后，以实例网络舆情突发事件的选择排序为实例对所提出的方法进行验证，并通过对比分析来证明所提方法的有效性。     

一种权重未知的多属性多阶段决策方法

针对属性权重与时间权重未知且属性值为区间数的一类决策问题,提出一种新的多属性多阶段决策方法.该方法首先无量纲化处理属性值,并运用灰色关联方法确定各阶段属性值的权重;然后综合考虑属性测度值与正、负理想效果值的接近性和时间权重本身的不确定性,运用极大熵原理建立多目标优化模型,并利用拉格朗日乘子法求解获得时间权重表达式,从而确定对象的综合评价值;最后通过实例验证了该方法的合理性与有效性.     

基于基尼系数-交叉效率的多属性决策方法

在数据包络分析(DEA)方法的基础上,提出一种基于基尼系数-交叉效率的多属性决策方法,用于解决具有多个投入、产出指标的多属性决策问题.首先,借鉴基尼系数的优化准则构建基尼系数-交叉评价策略模型,从而得到相对唯一的DEA交叉效率矩阵;然后,应用基尼准则计算各个效率值所包含的信息纯度,并借之实现交叉效率矩阵的集结;最后,根据集结结果对决策单元进行排序和择优.所提决策方法不仅能够克服传统DEA交叉效率方法的交叉评价策略选择难的问题,而且能够保证决策过程的客观性和公平性.同时,所提方法还对交叉评价所得的决策信息进行提纯,为科学合理地进行决策提供更多的有效信息.通过对中国各地区的医疗资源配置效率进行实证,验证了所提出方法的有效性和实用性.     

基于多元Copula函数的冗余系统可靠性模型研究

在传统k/n表决冗余系统的基础上考虑了系统中部件单元的权重输出形成权重表决系统，该系统中的部件单元寿命变量间具有相依性。运用统计学领域中的多元Copula函数理论刻画各部件单元之间的相关性，基于容斥原理推导出多种部件类型的权重表决系统可靠性模型。结合具体算例，选定典型的Copula函数以及部件独立状态计算系统可靠度，并分析了部件间相关程度对系统可靠度的实际影响，为考虑部件间相依关系的冗余系统可靠度计算提供了参考。     

A cross-efficiency fuzzy Data Envelopment Analysis technique for performance evaluation of Decision Making Units under uncertainty

The paper presents a novel cross-efficiency fuzzy Data Envelopment Analysis (DEA) technique for evaluating different elements (Decision Making Units or DMUs) under uncertainty. In order to evaluate the performance of several DMUs while dealing with uncertain input and output data, the presented technique employs triangular fuzzy numbers. A fuzzy triangular efficiency is associated to each DMU through a cross evaluation obtained by a compromise between suitably chosen objectives. Results are then defuzzified to provide a ranking of the DMUs. The proposed method is applied to the performance evaluation of healthcare systems in a region of Southern Italy. The DMU data uncertainty derives from ongoing reforms and the reported assessment is conducted firstly in order to evaluate and rank the efficiency of the considered healthcare systems, and subsequently to assess the evolution of the performance of one of the most affected among these DMUs by the reform plans. The case study demonstrates the model ease of application, its discriminative power among DMUs when compared to a more classical fuzzy DEA approach, and the usefulness in planning and validating targeted reforms in the case of healthcare systems.     

Minimax and maximin formulations of cross-efficiency in DEA

In the conventional cross-efficiency formulation, the efficiency score of a DMU under evaluation is maximized as the primary goal while the average cross-efficiency of peer DMUs is minimized (or maximized) as the secondary goal. The proposed models replace the secondary goal with the minimization (or maximization) of the best (or worst) cross-efficiency of peer DMUs. We demonstrate the appropriateness of the proposed formulations of cross-efficiency for certain efficiency evaluation contexts, and show how they help enhance the usefulness of cross-efficiency evaluation in DEA using a randomly generated sample data set. For a solution method for the proposed models of cross-efficiency, we develop a bisection algorithm whose computational complexity is polynomial.     

Expansion of the cross-efficiency evaluation by using the equations forming the efficient frontier in DEA

In this paper, we propose an algorithm to calculate cross-efficiency scores which used the equations forming the efficient frontier in data envelopment analysis (DEA). In many standard DEA models, each decision-making unit (DMU) is evaluated by using the advantageous weight for itself. Then, many DMUs are evaluated as efficient, and those efficient DMUs are not ranked by the models. The cross-efficiency evaluation is a method to rank DMUs by using the advantageous weights for all DMUs. Previously, the cross-efficiency scores based on different ideas are calculated by solving multiple linear or nonlinear programming problems. However, it is often hard to solve such a nonlinear programming problem. Therefore, by analysing the efficient frontier, we construct an algorithm to calculate alternative cross-efficiency scores.     

A new DEA‐based method for fully ranking all decision‐making units

Abstract: Decision makers always lay great emphasis on performance evaluation upon a group of peer business units to pick out the best performer. Standard data envelopment analysis models can evaluate the relative efficiency of decision‐making units (DMUs) and distinguish efficient ones from inefficient ones. However, when there are more than one efficient DMU, it is impossible to rank all of them solely according to standard efficiency scores. In this paper, a new method for fully ranking all DMUs is proposed, which is based on the combination of each efficient DMU's influence on all the other DMUs and the standard efficiency scores. This method is effective in helping decision makers differentiate all units' performance thoroughly and select the best performer.     

Evaluation method based on ranking in data envelopment analysis

Data envelopment analysis (DEA) has been developed as a method to evaluate efficiency of Decision Making Unit (DMU). In order to analyze DMU in detail, each DEA model is formulated as a mathematical programming problem utilizing the values of inputs and outputs of all DMUs as coefficients. Each DMU is evaluated by a different weight. Then, the efficiency score of each DMU is determined by using an advantageous weight for itself. In general, the efficiency score is obtained by selecting the most advantage weight. In some real cases, seeking the best ranking is sometimes more important than maximizing the efficiency score.In this paper, we propose a model called rank-based measure (RBM) to evaluate DMU from a different standpoint. We suggest a method to obtain a weight which gives the best ranking, and calculates a weight between maximizing the efficiency score and keeping the best ranking. In order to calculate an efficiency score and the best ranking, we repeatedly solve linear programming problems. Moreover, we apply RBM model to the cross efficiency evaluation. Furthermore, a numerical experiment is shown to compare the rankings and scores with traditional evaluations.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

Additive centralized and Stackelberg DEA models for two‐stage system with shared resources

Data envelopment analysis (DEA) is a nonparametric programming method for evaluating the efficiency performance of decision making units (DMUs) with multiple inputs and outputs. The classic DEA model cannot provide accurate efficiency measurement and inefficiency sources of DMUs with complex internal structure. The network DEA approach opens the “black box” of DMU by taking its internal operations into consideration. The complexities of DMU's internal structure involve not only the organization of substages, but also the inputs allocation and the operational relations among the individual stages. This paper proposes a set of additive DEA models to evaluate and decompose the efficiency of a two‐stage system with shared inputs and operating in cooperative and Stackelberg game situations. Under the assumptions of cooperative and noncooperative gaming, the proposed models are able to highlight the effects of strategic elements on the efficiency formation of DMUs by calculating the optimal proportion of the shared inputs allocated to each stage. The case of information technology in the banking industry at the firm level, as discussed by Wang, is revisited using the developed DEA approach.     

Cross-efficiency evaluation method based on the conservative point of view

Traditional cross-efficiency evaluation models have ignored the problem that large differences may exist among cross-efficiencies, which may make decision making units (DMUs) unwilling to accept cross-efficiency evaluation results. Aimed at solving this problem, this paper proposes an altruism cross-efficiency model based on the conservative point of view. Compared with other cross-efficiency evaluation models, the proposed model mainly exhibits the following advantages. First, the proposed model no longer guarantees the DMU's self-evaluation efficiency, allowing the self-evaluation efficiency to adaptively change. Therefore, the peer-evaluation process is flexible and adaptable to the actual situation. Second, the proposed model abandons the traditional max-average secondary objective function and proposes to use a max–min objective function. Thus, the proposed model can maximize the peer-efficiency of the worst performing peer-DMU, achieving the effects of reducing the gaps among cross-efficiencies. Third, the cross-efficiency evaluation model is based on the conservative point of view, which helps the DMU to distinguish potential competitors among peer-DMUs. Lastly, to solve the non-linear model proposed in this paper, the algorithm is designed to describe how to solve the model. The case of a flexible manufacturing system is used to show the appropriateness of the suggested model and algorithm.     

A new network epsilon-based DEA model for supply chain performance evaluation

Supply chain performance evaluation problems are inherently complex problems with multilayered internal linking activities and multiple entities. Data Envelopment Analysis (DEA) has been used to evaluate the relative performance of organizational units called Decision Making Units (DMUs). However, the conventional DEA models cannot take into consideration the complex nature of supply chains with internal linking activities. Network DEA models using radial measures of efficiency are used for supply chain performance evaluation problems. However, these models are not suitable for problems where radial and non-radial inputs and outputs must be considered simultaneously. DEA models using Epsilon-Based Measures (EBMs) of efficiency are proposed for a simultaneous consideration of radial and non-radial inputs and outputs. We extend the EBM model and propose a new Network EBM (NEBM) model. The proposed NEBM model combines the radial and non-radial measures of efficiency into a unified framework for solving network DEA problems. A case study is presented to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed method to a supply chain performance evaluation problem in the semiconductor industry.     

A learning performance evaluation with benchmarking concept for English writing courses

This paper adopts data envelopment analysis (DEA), a robust and reliable evaluation method widely applied in various fields to explore the key indicators contributing to the learning performance of English freshmen writing courses in a university of Taiwan from the academic year 2004 to 2006. The results of DEA model applied in learning performance change our original viewpoint and reveal that some decision-making units (DMUs) with higher actual values of inputs and outputs have lower efficiency because the relative efficiency of each DMU is measured by their distance to the efficiency frontier. DMUs may refer to different facet reference sets according to their actual values located in lower or higher ranges. In the managerial strategy of educational field, the paper can encourage inefficient DMUs to always compare themselves with efficient DMUs in their range and make improvement little by little. The results of DEA model can also give clear indicators and the percentage of which input and output items to improve. The paper also demonstrates that the benchmarking characteristics of the DEA model can automatically segment all the DMUs into different levels based on the indicators fed into the performance evaluation mechanism. The efficient DMUs on the frontier curve can be considered as the boundaries of the classification which are systematically defined by the DEA model according to the statistic distribution.