考虑系统内部平行结构的DEA资源分摊方法

如何将一定数量的资源在一组决策单元中进行有效地分摊是决策者在实际工作中常面临的问题。本文将决策单元看作系统,研究系统内部为平行结构的资源分摊方法。在将待分摊的资源作为一种新的独立投入要素的前提下,采用数据包络分析(DEA,data envelopment analysis)方法得到能够使得所有的总系统和子平行系统同时达到Pareto有效状态(效率值为1)的资源分摊方案集,并确定每个子平行系统的有效分摊区间。进而定义效用函数以反映各子平行系统对分摊额的满意程度,并基于满意度max-min公平原则和Pareto有效原则建立资源分摊模型。最后通过我国2008年31个省市或地区三大产业的相关数据验证了资源分摊模型的有效性,具有一定的理论与现实指导意义。     

基于DEA联盟博弈核仁解的固定成本分摊方法研究

本文结合DEA(Data Envelopment Analysis)和联盟博弈理论研究了固定成本分摊问题.本文首先证明了在固定成本作为决策单元(Decision Making Unit,DMU)新投入要素的条件下,那么DMU个体和整体将同为DEA有效,在此结论的基础上,本文结合联盟博弈理论,定义了联盟博弈的特征函数,提出了基于核仁解的固定成本分摊模型,并给出了相应的求解算法,最终通过算例说明了本文方法的合理性和求解算法的可行性.     

基于最近距离投影的DEA两阶段效率评价方法研究

数据包络分析是进行效率评价最重要的方法之一。传统的数据包络分析理论主要寻找有效前沿面上的最远距离投影，在极大化无效性指数的同时也面临着效率改进的巨大难度和高额成本。对于具有两阶段内部生产结构的决策单元，本文从考虑最小改进难度的视角出发，提出了最近距离投影的两阶段效率评价方法。该方法首先得到所有强有效决策单元的线性组合，且这些组合均占优于被评价的两阶段决策单元。然后建立了两阶段范围调整效率评价模型，在确定具有最近投影距离的占优组合的同时，得到了两阶段评价效率。最后，本文运用我国32家上市银行的年度数据对所提出方法进行了应用验证。     

考虑环境因素的三阶段半参数效率评价模型与实证研究

数据包络分析方法自提出以来,因其在评价决策单元相对有效性的诸多优势而得到了广泛应用,但其局限性之一在于要求决策单元具有相同的投入和产出性质。为了突破这一局限性,本文将参数方法引入DEA评价模型,以考虑外部环境因素对生产系统的影响;构建了一个新的三阶段半参数效率评价模型,其突出特点在于对"环境变量"和"非自由处置变量"的有效处理;选取国内某石油企业下属的各大油田作为分析对象,对上述三阶段模型进行了实证研究,证明了该三阶段模型的实用性和有效性。     

基于未来效率的兼顾公平与效率的资源分配DEA模型研究——以各省碳排放额分配为例

根据需要实现的目标，评估各生产决策单元的投入产出效率及改进潜力，可以为资源分配提供重要参考。构建一个基于未来效率的兼顾公平与效率的资源分配DEA模型可以有效、灵活地解决该问题。该DEA模型首先根据历史数据计算每个生产决策单元过去各期的技术增长率，并预测各DMU未来的技术增长率，从而获得未来的生产前沿面。以此为基础，在九个硬性目标约束下，分三个步骤分别解决三个追求的软性目标：最大化期望总产出、最小化非期望总产出、最小化可变要素总投入。管理者不仅可以改变九个硬性目标的参数值，以及调整三个软性目标的优先顺序和软性目标参数值，进而形成各种兼顾效率与公平的资源分配方案。最后，运用该DEA模型评估了我国各省碳排放削减潜力，并形成了能够实现管理者期望目标的各省碳排放削减责任分配方案。     

盟员行为偏好下生鲜农产品供应链生鲜努力激励机制与协调研究

本文建立了"合作社+核心企业"模式下两阶段折扣定价的二级生鲜农产品供应链，基于消费者生鲜偏好、价格敏感度对市场需求的影响，选取Nash谈判解作为公平参考点，引入合作社公平偏好理论，研究供应链盟员保鲜投入决策。针对合作社保鲜努力激励，探讨供应链盟员偏好对保鲜努力水平以及收益共享契约激励协调效果的影响。研究发现，消费者生鲜偏好的提高能够促进收益共享契约的激励效果，并且提高合作社公平效用。同时，收益共享契约在第一阶段对保鲜努力水平的激励效果优于第二阶段，而在第二阶段联合使用收益共享和成本分摊能够显著提高该阶段的保鲜投入。     

依托平台协作配送成本分摊的有效方法研究

依托平台的协作配送问题,在合理时间内有效计算公平成本分摊方案至关重要.核仁解是公认的公平分摊方案,但需要通过复杂的优化计算.提出了一个能通过公式近似快速计算核仁解的方法,发现任意满足总体理性分摊方案x的2~n-1(n为大联盟N中成员数)个子联盟S(S为N的子集)的满意度e(S, x)之和为常数,且不同x对应的任意子联盟S与互补联盟NS的满意度之和,即L_S=e(S, x)+e(NS, x)为常数.基于子联盟满意度越均衡,分配方案越合理的准则,构造了分配方案x对应的所有子联盟满意度均衡量化函数f(x)=∑[e(S, x)-0.5L_S]~2.显然,f越小表示子联盟满意度越均衡.证明了存在分配方案x*使f取到极小值,且x~*满足总体理性、唯一性、可加性、策略等价相对不变性、一致性、匿名性和可比性等众多分摊方案合理属性.最后,采用文章所提方法和核仁解求解方法,计算了诸多已有文献中的成本分摊算例,求解结果表明文章提出的方法计算速度比传统核仁解求解方法快数万倍以上,与最新求解核仁解及Shapley值的有效算法相比也具有明显的性能优势,且求解结果与核仁解的结果平均偏差只有5%左右.更重要的是,提出的新方法本身具有科学内涵,可以应用于任何支付可转移的合作博弈成本分摊问题.     

基于整体效率的区间DEA方法研究

针对现有的区间DEA方法采用非统一指标数据进行效率评价的不足,本文在分析现有区间DEA方法的基础上,提出一种基于整体效率的区间DEA方法。该方法能够在多决策单元系统整体效率最大化的同时,得到统一的各决策单元投入/产出的精确数据及各指标权重,一次性求解出所有决策单元的效率。最后,采用一个算例分析说明文章所提方法的合理性和优越性。     

具有共享产出固定和约束的DEA两阶段效率评价方法研究

数据包络分析方法是组织绩效评价的重要方法。传统的数据包络分析方法都假设所有决策单元的产出水平可以自由调整，但在许多管理实践中都普遍存在着产出固定和的约束，这使得决策单元间产出水平的调整不再满足独立性假设。虽然考虑产出固定和约束的效率评价方法得到了一定的发展，但网络生产结构下具有产出固定和约束的效率评价方法研究仍较缺乏。有鉴于此，本文考虑了具有共享产出的两阶段生产结构，并建立了满足共享产出固定和约束的两阶段效率评价模型与子阶段效率分解模型。最后，本文运用碳达峰政策背景下我国30个省级地区能源生产-能源利用的实证数据进行了方法验证。     

非合作博弈两阶段生产系统DEA并购效率评价

如何选择并购对象及预测并购可行性是企业管理者在并购决策过程中常面临的问题。针对企业并购预测问题,本文以两阶段生产系统的决策单元为研究对象,研究数据包络分析方法在预测并购可行性方面的应用。该生产系统有两个明显的特点:(1)决策单元由两个阶段串行子系统构成,(2)两个子系统一个处于主导地位,而另一个处于从属地位。两个或者两个以上决策单元并购为一个虚拟决策单元。本文在分析由决策单元整体效率与其子系统效率之间关系的基础上,引入非合作博弈的思想,提出了基于非合作博弈的DEA模型评估虚拟决策单元两阶段生产系统的并购效率:即在保持现有的产出水平和生产效率的前提下,分别求解虚拟决策单元及其子系统的并购效率,分析虚拟决策单元如何通过两个子系统实现整个系统的成本节约。最后,将模型应用于台湾24家非寿险保险公司的仿真分析。由于文章提出的方法能够有效地分析虚拟决策单元内部子系统的并购有效性水平,同时考虑子系统之间的主从关系,因此,能够发掘影响虚拟决策单元并购效率的内部因素,因而能够为管理者并购决策提供更精确有效的管理信息,提高并购决策的科学性。     

Allocating a fixed cost based on data envelopment analysis and satisfaction degree

This paper uses the Data Envelopment Analysis (DEA) technique to solve the problem of allocating a fixed cost across a set of comparable decision making units (DMUs) in a fair way. It first investigates the effect of the fixed cost on each DMU and on the collection of DMUs. Next we prove that there exist some cost allocations which can make each DMU and the collection of DMUs efficient. We show that such a cost allocation is unique and equivalent to the proportional sharing method if the fixed cost allocation problem is a one-dimensional case. In a multidimensional case, the fixed cost allocations may not be unique. This paper defines the concept of satisfaction degree, and proposes a maxmin model and a corresponding algorithm to generate a unique fixed cost allocation. Finally, the proposed approach has been applied to a data set from prior literature.     

DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches

This paper proposes new fixed cost allocation approaches for allocating a fixed cost among decision-making units (DMUs) with two-stage structures under the framework of data envelopment analysis (DEA). Firstly, we give the set of possible fixed cost allocations, prove that all DMUs can be overall efficient when evaluated by a common set of weights after fixed cost allocation. Secondly, from a centralized point of view, we consider the competition between the DMUs’ two stages in fixed cost allocation and regard these two kinds of stages as two unions. Then, we incorporate leader-follower models to propose a fixed cost allocation approach to handle the situation in which the two unions make decisions sequentially. Based on the result of these models, a concept of satisfaction degree of each union on a fixed cost allocation is presented. A satisfaction degree bargaining game model is then proposed to obtain a fixed cost allocation which is a bargaining equilibrium of the two unions. We show that the proposed approaches always obtain a fixed cost allocation that is proportionally invariant. Additionally, the satisfaction degree bargaining game approach automatically guarantees the uniqueness of the fixed cost allocation. These properties make the fixed cost allocation generated by our approaches more stable and more acceptable. Finally, a numerical example and an application of fixed cost allocation among bank branches are given to illustrate the proposed approach and to compare it with a benchmark approach among the current studies, respectively.     

Allocating a fixed cost across the decision making units with two-stage network structures

A prominent issue in many organizations involves the fair allocation of a total fixed cost among a group of entities. This paper extends the traditional fixed cost allocation problem to situations where the decision making units (DMUs) have a two-stage network structure. To this end, this paper first uses the data envelopment analysis (DEA) methodology to determine the relative efficiency while taking the internal structure and possible allocated costs into account. It shows that each DMU can separately maximize its relative efficiency to one through determining a series of allocations and selecting a set of relative weights. Next, we demonstrate that there exists an efficient allocation set based on a set of common weights, using which all DMUs and their two sub-stages can be simultaneously efficient. However, there are alternative allocation plans in the efficient allocation set. According to this non-uniqueness problem, we further optimize the allocation plans by taking the size of operation units into account, such that the allocation result is proportional to current input usages and output productions from a size point of view. In addition, we suggest a min–max model and a feasible computation algorithm for it to generate the final allocation plan in a way that minimizes the deviation between the efficient allocations and size allocations. More importantly, by repeatedly minimizing the maximum deviation, our proposed method can guarantee a unique allocation plan for all DMUs and sub-stages. Finally, both a numerical example modified from previous literature and an empirical application of bank activities are used to demonstrate the efficacy and usefulness of the proposed approach.     

A slacks-based measure of super-efficiency in data envelopment analysis: An alternative approach

The current paper proposes a slack-based version of the Super SBM, which is an alternative super-efficiency model for the SBM proposed by Tone. Our two-stage approach provides the same super-efficiency score as that obtained by the Super SBM model when the evaluated DMU is efficient and yields the same efficiency score as that obtained by the SBM model when the evaluated DMU is inefficient. The projection identified by the Super SBM model may not be strongly Pareto efficient; however, the projection identified from our approach is strongly Pareto efficient.     

Centralized resource allocation based on efficiency analysis for step-by-step improvement paths

The existing centralized resource allocation models often assume that all of the DMUs are efficient after resource allocation. For the DMU with a very low efficiency score, it means the dramatic reduction of the resources, which can cause the organizational resistance. In addition, in reality, it is particularly difficult for the DMUs to achieve their target efficiencies in a single step, especially when they are far from the efficient frontier. Thus, gradual progress towards benchmarking targets is gaining importance. In this paper, we present a new approach for resource allocation based on efficiency analysis under a centralized decision-making environment. Through our approach, the central decision-maker can obtain a sequence of intermediate benchmark targets based on efficiency analysis, which provide a level-wise improvement path to direct the DMUs to reach their ultimate targets on the efficient frontier in an implementable and realistic manner. Numerical examples are presented to illustrate the application procedure of the proposed approach.     

基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。     

基于DEA的两阶段系统中间产品公平设定研究

在由两个子决策单元串联组成的两阶段系统中,公平设定中间产品目标对确保和激励两阶段相互合作以达到整个系统的最佳性能至关重要.数据包络分析(DEA)作为系统绩效评估的一种非参数方法吸引了众多学者的注意;基于此方法,本文提出一个考虑公平关切的两阶段DEA模型用于设定两阶段系统中间产品目标,并证明据此模型获得的设定方案正是一个纳什讨价还价博弈的均衡解.     

资源约束型两阶段生产系统的DEA效率评价模型

经典的数据包络分析(DEA)模型将决策单元看作"黑箱",忽视决策单元的内部过程,必然会高估决策单元的效率。本文研究了一种资源约束型两阶段生产系统的DEA效率评价方法,针对此类生产过程的内部过程,研究其内部运行机制对整体效率的影响。本文提出的模型实质上是一类特殊的网络DEA模型,其评价原理有别于已有的研究成果,但更有助于管理者确定生产过程的非有效来源及其效率改进方向。实例证实本文方法的合理性。