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。     

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.     

基于证据理论-DEA 交叉效率的混合型多属性决策方法

针对含有投入产出指标的混合型多属性决策问题,提出一种基于证据理论和数据包络分析(DEA)交叉效率的决策方法.首先运用DEA对决策系统中投入产出指标进行处理,得到DEA交叉效率矩阵,并运用证据理论集结其交叉效率得分;然后将效率得分作为决策系统指标值,与系统中其他指标进行模糊等级转换,通过证据理论对指标值融合,进而得到决策单元的期望效用,据此对决策单元进行排序;最后通过实例与其他文献方法进行对比分析,以表明所提出方法的可行性和有效性.     

整合多维不确定投入产出关系的效率评价新方法

为还原多维不确定投入产出关系在效率评价理念、理论与评价方法方面存在的创新需求,从评价目标导向、评价要素构成和要素关联不确定三个维度,刻画一般效率评价情景中的要素间不确定关联呈现特征。在此基础上,针对现有方法在提取投入产出指标多维关联、刻画多类型效率涌现路径、促成多元效率内涵横向比较等方面存在的不足,创新性融合ANP方法与DEA方法构建了能够应对复杂情景下多维效率内涵提取、转换与融合需求的新方法。案例应用结果表明,以上所提出的理论及方法有效、可行,对延伸及拓展DEA方法的相对权比较理念实现复杂投入产出关联的跨层次比较,具有一定借鉴价值。     

考虑广告投入影响的再制造闭环供应链优化决策博弈模型研究

针对制造/再制造产品的市场竞争与合作问题, 考虑广告投入对产品消费者效用的增长效应及消费者环境偏好的影响, 在构建制造产品和再制造产品的市场需求函数基础上, 应用博弈方法比较分析合作博弈、纳什均衡博弈、Stackelberg主从博弈三种决策模式下制造/再制造产品的最优定价和广告投入策略, 并针对非合作博弈下的效率损失设计了闭环供应链中制造和再制造过程的利益协调机制。数值算例分析表明, 合作博弈决策下供应链总利润最优、制造和再制造产品市场销售价格最高, 而合作博弈和Stackelberg主从博弈都会以牺牲再制造产品利润为代价获得最优利润, 因此再制造部门会偏好纳什均衡博弈, 采取以自身利益最优为目标的竞争策略, 没有动机成为制造部门的跟随者。     

基于决策单元异质性的群组交叉效率评价方法

交叉效率评价方法是数据包络分析（DEA）的拓展工具,但是现存交叉效率方法是对所有决策单元（DMUs）统一测评,没有考虑决策单元间的异质性问题。提出了一种考虑决策单元异质性的群组交叉效率模型,将具有异质性的群组间效率值进行合理集结的绩效评价方法。运用仁慈型交叉效率模型分析各群组内部的相对效率值;运用改进的熵权法为群组内部各决策单元分配适当权重,得到群组整体的最优权重向量;运用传统交叉效率模型评价与分析群组之间的相对效率值,并以此进行综合排序。为证明该方法具有理论与适用效力,2015年应用于16家中国商业银行的绩效评价,结果表明该方法行之有效。     

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DEA模型的体系作战目标节点价值评价

根据基于信息系统的体系作战的特点,构建了目标节点价值评价指标体系,将评价指标分为成本型和效益型两部分,分别作为DEA评价模型决策单元的输入指标和输出指标,并对多个DEA有效的决策单元运用超效率DEA模型进行了分析和评价,取得了较好的评价效果.     

基于模糊MACBETH和生态位理论的PSS方案评价方法

针对多属性决策方法与生态位理论结合的PSS评价方法权重确定过程中一致性检验繁琐、权重计算过程复杂和未考虑评价语义的模糊性的问题,模糊MACBETH用于确定客户价值的权重和客户体验阶段提供客户价值的重要性系数;该方法不需要复杂的计算过程,利用三角模糊数处理语义的模糊性且依托软件系统自动检验一致性,提高了评价效率和准确度。针对生态位优势仅适用于完全竞争状态的优势计算,将生态位重叠与生态位优势结合,提出的竞争优势公式可以体现方案间竞争程度和生态位优势表示方案间的竞争优势的优点,反映方案间真实的竞争状态。最后以某新能源汽车制造企业PSS方案评价问题为例验证了所提方法的有效性。     

Data Envelopment Analysis Based on Choquet Integral

Data envelopment analysis (DEA) is a widely used technique in decision making. The existing DEA models always assume that the inputs (or outputs) of decision‐making units (DMUs) are independent with each other. However, there exist positive or negative interactions between inputs (or outputs) of DMUs. To reflect such interactions, Choquet integral is applied to DEA. Self‐efficiency models based on Choquet integral are first established, which can obtain more efficiency values than the existing ones. Then, the idea is extended to the cross‐efficiency models, including the game cross‐efficiency models. The optimal analysis of DEA is further investigated based on regret theory. To estimate the ranking intervals of DMUs, several models are also established. It is founded that the models considering the interactions between inputs (or outputs) can obtain wider ranking intervals.     

Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an efficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods.     

An ideal-seeking fuzzy data envelopment analysis framework

Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.     

A bargaining game model for efficiency decomposition in the centralized model of two-stage systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). The centralized model has been widely used to examine the efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Since there may exist some flexibility in decomposing the overall efficiency between the two stages when multiple optimal weights exist, we develop a Nash bargaining game model to obtain a fair efficiency decomposition for the two stages while keeping the overall efficiency unchanged under this circumstance. The minimal achievable efficiencies for the two stages are used as the breakdown point and the unique bargaining decomposition of the overall efficiency is obtained subsequently. The Nash bargaining game model is applied to evaluate the performance of 10 branches of China Construction Bank.     

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.     

A new data envelopment analysis method for ranking decision making units: an application in industrial parks

Relative efficiency of decision‐making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach.     

Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game

This paper firstly revisits the cross efficiency evaluation method which is an extension tool of data envelopment analysis (DEA), then analyzes the potential flaws which happens when the ultimate average cross efficiency scores are used. In this paper, we consider the DMUs as the players in a cooperative game, where the characteristic function values of coalitions are defined to compute the Shapley value of each DMU, and the common weights associate with the imputation of the Shapley values are used to determine the ultimate cross efficiency scores. In the end, an empirical example is illustrated to examine the validity of the proposed method, and we also point out some further research directions in future.     

A full ranking methodology in data envelopment analysis based on a set of dummy decision making units

In this paper, we propose a new methodology for ranking decision making units in data envelopment analysis (DEA). Our approach is a benchmarking method, seeks a common set of weights using a proposed linear programming model and is based on the TOPSIS approach in multiple attribute decision making (MADM). To this end, five artificial or dummy decision making units (DMUs) are defined, the ideal DMU (IDMU), the anti-ideal DMU (ADMU), the right ideal DMU (RIDMU), the left anti-ideal DMU (LADMU) and the average DMU (AVDMU). We form two comprehensive indexes for the AVDMU called the Left Relative Closeness (LRC) and the Right Relative Closeness (RRC) with respect to the RIDMU and LADMU. The LRC and RRC indexes will be used in the new proposed linear programming model to estimate the common set of weights, the new efficiency of DMUs and finally an overall ranking for all the DMUs. The change of the ratio between LRC and RRC indexes is capable to be provoked alternative rankings. One of the best advantages of this model is that we can make a rationale ranking which is demonstrated by the realized correlation analysis. Also, the new proposed efficiency score of the DMUs is close to the efficiency score of the DEA (CCR) methodology. Three numerical examples are provided to illustrate the applicability of the new approach and the effectiveness of the new approach in DEA ranking in comparison with other conventional ranking methods. Also, an "error" analysis proves the robustness of the proposed methodology.     

Determination of weights for ultimate cross efficiency using Shannon entropy

This paper firstly reviews the cross efficiency evaluation method which is an extension tool of data envelopment analysis (DEA), then we describe the main shortcomings when the ultimate average cross efficiency scores are used to evaluate and rank the decision making units (DMUs). In this paper, we eliminate the assumption of average and utilize the Shannon entropy to determine the weights for ultimate cross efficiency scores, and the procedures are introduced in detail. In the end, an empirical example is illustrated to examine the validity of the proposed method. Some future research directions are also pointed out.     

Fuzzy rough DEA model: A possibility and expected value approaches

Uncertainty is certain in the world of uncertainty. Measuring the performance of any entity in such an uncertain environment is unavoidable. Fuzzy rough data envelopment analysis (FRDEA) provides a room to evaluate the relative efficiency of homogenous entities, widely known as decision making units (DMUs) in the data envelopment analysis (DEA) literature. This paper attempts to create a fuzzy rough DEA model by integrating the classical DEA, fuzzy set theory, and rough set theory, which apparently provide a way to accommodate the uncertainty. Moreover, in contrast to the probability approach, this paper provides a pavement to measure the relative efficiency of any given DMUs in line with the possibility approach along with the fuzzy rough expected value operator.