具有非期望产出的混联网络DEA模型

数据包络分析(DEA)是评价系统相对有效性的分析方法,网络DEA模型在评价企业的经济效益、管理效益等实际问题中有着广泛的应用.在网络DEA模型的基础上考虑非期望产出要素,提出了具有非期望产出的混联网络DEA模型.研究了新模型的系统弱DEA有效与各子阶段弱DEA有效之间的关系,找到了无效决策单元的无效阶段,通过有针对性的改进能够提高系统的整体效率.最后通过数值算例验证了模型的可行性.     

具有阶段最终产出的广义链式网络DEA模型

传统网络DEA方法通过打开生产过程中的"黑箱",考虑生产过程的中间环节,对生产过程进行相对效率评价.但是传统网络DEA方法只能相对于决策单元集而不能相对于非决策单元集进行相对效率评价.给出能够相对于任意参考集对决策单元进行相对效率评价的基于C2R模型的具有阶段最终产出的广义链式网络DEA方法,初步讨论相应性质并进行算例演示.     

具有偏好锥的链式网络DEA模型

对链式网络DEA模型进行推广,将"偏好锥"引入网络DEA模型.针对中间产出重要性以及决策者评价时的偏好,建立带有产出锥和投入锥相应的两阶段生产可能集,对具有"偏好锥"的链式网络DEA模型,证明了决策单元为网络DEA有效的充要条件,给出了网络DEA有效性与各阶段弱DEA有效性的关系.另外,文章结合具体算例说明了偏好锥的变化对效率评价的影响.关于两阶段的模型以及相关结论可以推广到多阶段网络结构.     

链式网络DEA模型

数据包络分析(DEA)是评价决策单元(DMU)相对有效性的一种工具,现已得到广泛的应用.传统的DEA不考虑系统内部结构,而是将系统作为一个"黑箱"来度量效率.针对多阶段网络结构提出一个新的网络DEA模型—链式网络DEA模型.研究网络决策单元的网络DEA有效性及各个阶段的弱DEA有效性之间的关系,给出了网络DEA有效的充分必要条件.若网络决策单元不是网络DEA有效的,根据模型可以指出系统在哪些阶段是无效的.     

考虑投入和产出指标偏好的广义DEA模型

广义DEA是一种基于决策单元和非决策单元自由选择参考集的扩展DEA模型.传统DEA模型的最优解大多是由线性规划随机计算的,未能充分考虑投入和产出指标的重要程度.将投入和产出指标的决策者偏好引入到广义DEA模型约束条件中,首先定义投入和产出指标偏好矩阵,再将该矩阵纳入广义DEA模型的约束条件,构建了带投入和产出指标偏好的广义DEA模型(GDEA-IP).接下来给出决策单元GDEA-IP有效性与评价指标的量纲选择无关性的证明,以及决策单元为GDEA-IP弱有效和有效的理论证明.算例分析说明GDEA-IP模型的有效性,通过和其它经典模型的对比分析,进一步说明该模型比广义DEA模型具有更大的灵活性和通用性,拓展了DEA方法的理论研究.     

基于C~2R模型的广义链式网络DEA模型

传统网络DEA方法是将传统DEA方法评价过程中的"黑箱"打开,考虑输入到输出的中间环节,对生产过程中的各个环节分别评价。传统网络DEA方法获得的是相对于有效决策单元评价的结果,但有时可能要相对于非有效决策单元或者非决策单元进行评价,传统网络DEA方法无法解决该类问题。为此给出相对于非有效决策单元或者非决策单元进行评价的基于C~2R模型的广义链式网络DEA模型,并探讨相关性质.     

只有产出(投入)BC~2模型中决策单元效率的几何刻画

在DEA方法中,DEA有效和弱DEA有效的决策单元位于生产前沿面上,非弱DEA有效的DEA无效决策单元位于生产可能集的内部而非生产前沿面上.通过引入生产可能集与生产前沿面移动的思想,证明只有产出(投入)的BC²模型评价下的决策单元的最优值与相应的生产前沿面的移动值存在倒数关系,以双产出(投入)情形图示说明,明确了决策单元在生产可能集中所处的位置.     

一种基于虚拟决策单元的排序方法的完善和扩展

本文对文[1]中提出的基于虚拟决策单元的排序方法进行了完善和扩展。首先,根据CCR模型,给出了两类特殊的DEA模型,分别是仅有投入数据的DEA模型和仅有产出数据的DEA模型;其次,基于这两个模型,应用上述方法实现了对仅有投入(或产出)数据的决策单元的排序;第三,给出了排序方法中参数a的计算方法;最后,通过修正排序模型,有效提高了排序方法的计算精度。改进后的排序方法避免了两个决策单元因为相对效率值过小而不能排序的情形,其应用范围也进一步扩大。     

基于数据包络分析的并行生产系统效率评价方法

数据包络分析(DEA)是一种评价具有多投入、多产出决策单元的相对效率的线性规划方法.在现实世界中,决策单元有时呈现出由多个独立子系统构成的复杂并联网络系统,各子系统的投入/产出之和构成了系统的总投入/产出.目前,用于评价这种具有并联网络生产系统相对效率的模型主要有三种:网络DEA模型、多部门DEA模型和关联DEA模型.现有这些模型的基本特性和相互关系存在着不足,即子系统的效率分解和优化指数不唯一.为解决这一问题,提出了改进的并联DEA模型,并采用加拿大银行系统实例来说明所提出模型的合理性和有效性.     

基于样本评价的广义数据包络分析方法

传统DEA方法是一种依据自评体系评价的方法,而无法自主选择参照系.为了解决DEA方法可以同时依据自评体系和其它参照系进行评价问题,首先给出了广义DEA有效的概念.然后,给出了一类基于样本单元评价的广义数据包络分析模型,包括面向输入的广义DEA模型、面向输出的广义DEA模型以及加性广义DEA模型.最后,分析了上述这些模型与传统DEA模型之间的关系,探讨了广义DEA有效与相应多目标规划Pareto有效之间的关系,并给出了决策单元的投影性质以及决策单元的有效性排序方法.     

Network DEA efficiency in input–output models: With an application to OECD countries

We undertake network efficiency analysis within an input–output model that allows us to assess potential technical efficiency gains by comparing technologies corresponding to different economies. Input–output tables represent a network where different sectoral nodes use primary inputs (endowments) to produce intermediate input and outputs (according to sectoral technologies), and satisfy final demand (preferences). Within the input–output framework it is possible to optimize primary inputs allocation, intermediate production and final demand production by way of non-parametric data envelopment analysis (DEA) techniques. DEA allows us to model the different subtechnologies corresponding to alternative production processes, to assess efficient resource allocation among them, and to determine potential output gains if inefficiencies were dealt with. The proposed model optimizes the underlying multi-stage technologies that the input–output system comprises identifying the best practice economies. The model is applied to a set of OECD countries.     

A network-based approach for increasing discrimination in data envelopment analysis

Data envelopment analysis (DEA) is known to produce more than one efficient decision-making unit (DMU). This paper proposes a network-based approach for further increasing discrimination among these efficient DMUs. The approach treats the system under study as a directed and weighted network in which nodes represent DMUs and the direction and strength of the links represent the relative relationship among DMUs. In constructing the network, the observed node is set to point to its referent DMUs as suggested by DEA. The corresponding lambda values for these referent DMUs are taken as the strength of the network link. The network is weaved by not only the full input/output model, but also by models of all possible input/output combinations. Incorporating these models into the system basically introduces the merits of each DMU under various situations into the system and thus provides the key information for further discrimination. Once the network is constructed, the centrality concept commonly used in social network analysis—specifically, eigenvector centrality—is employed to rank the efficient DMUs. The network-based approach tends to rank high the DMUs that are not specialized and have balanced strengths.     

Optimal system design series-network DEA models

There is an urgent need in a wide range of fields such as logistics and supply chain management to develop effective approaches to measure and/or optimally design a network system comprised of a set of units. Data envelopment analysis (DEA) researchers have been developing network DEA models to measure decision making units’ (DMUs’) network systems. However, to our knowledge, there are no previous contributions on the DEA-type models that help DMUs optimally design their network systems. The need to design optimal systems is quite common and is sometimes necessary in practice. This research thus introduces a new type of DEA model termed the optimal system design (OSD) network DEA model to optimally design a DMUs (exogenous and endogenous) input and (endogenous and final) output portfolios in terms of profit maximization given the DMUs total available budget. The resulting optimal network design through the proposed OSD network DEA models is efficient, that is, it lies on the frontier of the corresponding production possibility set.     

Network-based method for ranking of efficient units in two-stage DEA models

This study presents a methodology that is able to further discriminate the efficient decision-making units (DMUs) in a two-stage data envelopment analysis (DEA) context. The methodology is an extension of the single-stage network-based ranking method, which utilizes the eigenvector centrality concept in social network analysis to determine the rank of efficient DMUs. The mathematical formulation for the method to work under the two-stage DEA context is laid out and then applied to a real-world problem. In addition to its basic ranking function, the exercise highlights two particular features of the method that are not available in standard DEA: suggesting a benchmark unit for each input/intermediate/output factor, and identifying the strengths of each efficient unit. With the methodology, the value of DEA greatly increases.     

Two-stage network DEA: when intermediate measures can be treated as outputs from the second stage

This paper investigates efficiency measurement in a two-stage data envelopment analysis (DEA) setting. Since 1978, DEA literature has witnessed the expansion of the original concept to encompass a wide range of theoretical and applied research areas. One such area is network DEA, and in particular two-stage DEA. In the conventional closed serial system, the only role played by the outputs from Stage 1 is to behave as inputs to Stage 2. The current paper examines a variation of that system. In particular, we consider settings where the set of final outputs comprises not only those that result from Stage 2, but can include, in addition, certain outputs from the previous (first) stage. The difficulty that this situation creates is that such outputs are attempting to play both an input and output role in the same stage. We develop a DEA-based methodology that is designed to handle what we term ‘time-staged outputs’. We then examine an application of this concept where the DMUs are schools of business.     

使决策单元变为DEA有效的偏差和最小法

某决策单元为非 DEA有效 ( C2 R或 C2 GS2 ) ,为了将它变为 DEA有效 ,在找出其对应点附近的一些有效前沿面的基础上 ,给出了使其对应点与这些有效前沿面上的点的输入、输出的偏差和最小的方法 .