含有偏好的DEA-BWM评价方法研究

针对传统的DEA模型在评估过程中并未考虑决策者对相关指标权重的偏好,将最优最差方法(BWM)嵌入到传统DEA模型中,基于决策者偏好排序的判断矩阵,构建一种含有偏好的DEA-BWM评价方法。首先在保持传统DEA方法的优势基础上,构建了CCR-BWM评价模型对各DMU进行评价。同时考虑为了便于各决策单元在统一权重基础上相互比较,构建了CSW-BWM公共权重模型。另外考虑决策单元自评和互评,构建了NCE-BWM中立型交叉效率。然后采用min-max方法分别将上述三种多目标评价模型转换为单目标线性规划进行求解。最后,选择一组算例对三种模型的有效性与合理性进行验证。     

考虑偏差值的中立型区间交叉效率研究

在不确定性环境下,当决策单元(DMU)的投入产出数据为区间数形式时,为解决决策单元之间既不是合作也不是竞争关系时的交叉评价问题,本文提出一种中立型区间交叉效率模型。从所有被评价者的角度出发解决评价权重的选取问题,以决策单元投入得分的平均偏差与产出得分的平均偏差之和最小化为目标,建立决策单元在最佳和最差两种生产状态下的中立型区间交叉效率模型。在本文提出的中立型模型视角下,DMU的投入得分平均偏差和产出得分平均偏差之和达到最小。算例结果表明该中立型区间交叉效率模型的有效性,解决了不确定性环境下的交叉评价问题,保证评价的客观公正,更加符合现实。     

区域性物流园区竞合策略的演化博弈分析

针对我国物流园区发展现状,探讨了区域性物流园区之间的竞合策略。建立了区域性物流园区竞合策略的演化博弈模型,据此分析了物流园区间竞争合作关系演变发展的趋势。研究表明,区域性物流园区之间长期竞争合作演化的结果是完全竞争或完全合作;在一定条件下,物流园区竞合策略选择的动态演化过程收敛于哪一个均衡点受到博弈发生的初始状态的影响,演化的路径和最终状态与转化能力、风险水平以及资源水平密切相关。     

具有偏好锥的面向输出的超效率DEA模型分析

鉴于传统DEA模型无法区分有效决策单元,超效率DEA模型未考虑决策者的偏好,现提出面向输出的权重受限的综合超效率DEA模型及其投影概念,并讨论该模型与其他超效率DEA模型之间的关系.接着,分析模型的最优目标函数值与决策单元有效性之间的关系,并讨论面向输出的权重受限的综合超效投影与多目标规划问题的非支配解之间的关系.最后,通过对中国西部12个地区工业企业科技创新效率综合评价,并与原有方法进行比较研究,得出本文方法更具优势和合理性.     

具有偏好锥的面向输出的超效率DEA模型分析

鉴于传统DEA模型无法区分有效决策单元,超效率DEA模型未考虑决策者的偏好,现提出面向输出的权重受限的综合超效率DEA模型及其投影概念,并讨论该模型与其他超效率DEA模型之间的关系.接着,分析模型的最优目标函数值与决策单元有效性之间的关系,并讨论面向输出的权重受限的综合超效投影与多目标规划问题的非支配解之间的关系.最后,通过对中国西部12个地区工业企业科技创新效率综合评价,并与原有方法进行比较研究,得出本文方法更具优势和合理性.     

Interval DEA模型中决策单元的投影问题

在传统的DEA模型中,最优相对效率模型是在不大于1的范围内研究决策单元的效率的,最差相对效率模型是在不小于1的范围内研究决策单元的效率,这两种模型在研究投影问题时,是在不同的范围内进行的,有一定的片面性.将在interval DEA模型中,研究决策单元的投影问题,该模型是在相同的约束域内研究最优和最差相对效率模型,得出的结论将更加全面,通过两个定理给出了非DEA有效的决策单元在DEA有效面上的投影表达式和非DEA无效的决策单元在DEA无效面上的投影表达式.同时,通过一个实例对决策单元在interval DEA模型中的投影结果与在传统的DEA模型的投影结果进行了比较,发现投影结果比传统模型得到的投影结果对实际的生产有更强的指导意义.     

基于松弛变量方法的动态网络系统效率测度及分解

传统数据包络分析(DEA)方法以静态"黑箱"的视角分析系统效率,无法体现出决策单元(DMU)生产的实际运作情况,从而造成结果与实际效率存在较大偏差.文章引入合作博弈思想,考虑系统的内部结构和不同时期的动态联系,构建动态网络系统的松弛变量方法(SBM)模型.同时,探讨系统存在非期望要素情况下的效率评价问题.此外,基于多目标规划理论,构建效率分解模型.分析不同时期和不同过程对整体系统效率的影响,并解决了效率分解方案不唯一的问题.最后,给出一个应用实例来说明模型的可行性与实用性.     

基于动态网络DEA模型的机场绩效研究

在已有网络DEA的基础上加入时间维度,构建了多时段下具有串联决策单元内部结构的复杂系统动态网络DEA效率评价模型.模型与传统DEA模型相比,既克服了传统DEA无视系统内部结构的缺陷,又在传统DEA的决策空间和目标空间基础上加入了时间维度,可以考察决策单元在不同时段的效率变化,从而对解决多时段内的复杂系统效率评估问题具有更为现实的应用价值.运用模型对区域多机场系统中的机场运营效率进行了计算,结果表明:1)动态网络DEA模型综合机场多年的投入产出,引入联系变量将相邻两时段连接起来,系统全面地评价多年来机场的整体运营水平,避免了传统模型将各年度独立评价的不足.2)江苏7家机场在2006-2010年仅南京禄口机场动态效率值为1,其余机场效率值都比较低,说明这些机场5年整体运营不佳,需要进一步加强管理和改进.     

基于熵权法的DEA/AR交叉效率知识化制造模式评价

用模糊DEA/AR交叉效率方法,解决制造模式的评价与排序问题.首先,构建了四种不同的DEA/AR交叉效率模型—任意型、对抗型、友好型和博弈型.然后,应用熵权法确定每一种交叉效率模型的最终交叉效率值,目的是用保证域来避免传统模型的权重偏差,从而实现了决策单元的相对有效评价和精确排序.同时,引入奇异指数的概念来衡量最终交叉效率的合理性及可靠性.最后,通过实例验证本文模型和方法的可行性及有效性:与采用简单DEA效率模型进行评价比较,我们的方法会使得效率更加精准、排序更加合理.     

基于交叉评价策略的DEA灰色关联排序模型北大核心

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

Interval cross efficiency for fully ranking decision making units using DEA/AHP approach

Data envelopment analysis (DEA) is a popular technique for measuring the relative efficiency of a set of decision making units (DMUs). Fully ranking DMUs is a traditional and important topic in DEA. In various types of ranking methods, cross efficiency method receives much attention from researchers because it evaluates DMUs by using self and peer evaluation. However, cross efficiency score is usual nonuniqueness. This paper combines the DEA and analytic hierarchy process (AHP) to fully rank the DMUs that considers all possible cross efficiencies of a DMU with respect to all the other DMUs. We firstly measure the interval cross efficiency of each DMU. Based on the interval cross efficiency, relative efficiency pairwise comparison between each pair of DMUs is used to construct interval multiplicative preference relations (IMPRs). To obtain the consistency ranking order, a method to derive consistent IMPRs is developed. After that, the full ranking order of DMUs from completely consistent IMPRs is derived. It is worth noting that our DEA/AHP approach not only avoids overestimation of DMUs’ efficiency by only self-evaluation, but also eliminates the subjectivity of pairwise comparison between DMUs in AHP. Finally, a real example is offered to illustrate the feasibility and practicality of the proposed procedure.     

Competition strategy and efficiency evaluation for decision making units with fixed-sum outputs

This paper develops a DEA (data envelopment analysis) model to accommodate competition over outputs. In the proposed model, the total output of all decision making units (DMUs) is fixed, and DMUs compete with each other to maximize their self-rated DEA efficiency score. In the presence of competition over outputs, the best-practice frontier deviates from the classical DEA frontier. We also compute the efficiency scores using the proposed fixed sum output DEA (FSODEA) models, and discuss the competition strategy selection rule. The model is illustrated using a hypothetical data set under the constant returns to scale assumption and medal data from the 2000 Sydney Olympics under the variable returns to scale assumption.     

A DEA game model approach to supply chain efficiency

Data envelopment analysis (DEA) is a useful method to evaluate the relative efficiency of peer decision making units (DMUs). Based upon the definitions of supply chain efficiency, we investigate the efficiency game between two supply chain members. It is shown that there exist numerous Nash equilibriums efficiency plans for the supplier and the manufacturer with respect to their efficiency functions. A bargaining model is then proposed to analyze the supplier and manufacturer's decision process and to determine the best efficiency plan strategy. DEA efficiency for supply chain operations is studied for the central control and the decentralized control cases. The current study is illustrated with a numerical example.     

Overall performance evaluation: new bounded DEA models against unreachability of efficiency

Data envelopment analysis (DEA) performance evaluation can be implemented from either optimistic or pessimistic perspectives. For an overall performance evaluation from both perspectives, bounded DEA models are introduced to evaluate decision making units (DMUs) in terms of interval efficiencies. This paper reveals unreachability of efficiency and distortion of frontiers associated with the existing bounded DEA models. New bounded DEA models against these problems are proposed by integrating the archetypal optimistic and pessimistic DEA models into a model with bounded efficiency. It provides a new way of deriving empirical estimates of efficiency frontiers in tune with that identified by the archetypal models. Without distortion of frontiers, all DMUs reach interval efficiencies in accordance with that determined by the archetypal models. A unified evaluation and classification result is derived and the efficiency relationships between DMUs are preserved. It is shown that the newly proposed models are more reliable for overall performance evaluation in practice, as illustrated empirically by two examples.     

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.     

Output–input ratio analysis and DEA frontier

Data envelopment analysis (DEA) is a mathematical programming technique for identifying efficient frontiers for peer decision making units (DMUs). The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, we present mathematical properties which characterize the inherent relationships between DEA frontier DMUs and output–input ratios. It is shown that top-ranked performance by ratio analysis is a DEA frontier point. This in turn allows identification of membership of frontier DMUs without solving a DEA program. Such finding is useful in streamlining the solution of DEA.     

Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis

It has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units. This paper proposes a new methodology for ranking decision making units (DMUs). The new methodology ranks DMUs by imposing an appropriate minimum weight restriction on all inputs and outputs, which is decided by a decision maker (DM) or an assessor in terms of the solutions to a series of linear programming (LP) models that are specially constructed to determine a maximin weight for each DEA efficient unit. The DM can decide how many DMUs to be retained as DEA efficient in final efficiency ranking according to the requirement of real applications, which provides flexibility for DEA ranking. Three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between DMUs, particularly DEA efficient units.     

Network DEA: A slacks-based measure approach

Traditional DEA models deal with measurements of relative efficiency of DMUs regarding multiple-inputs vs. multiple-outputs. One of the drawbacks of these models is the neglect of intermediate products or linking activities. After pointing out needs for inclusion of them to DEA models, we propose a slacks-based network DEA model, called Network SBM, that can deal with intermediate products formally. Using this model we can evaluate divisional efficiencies along with the overall efficiency of decision making units (DMUs).