基于网络DEA的共享投入与(非)期望产出的两部门并行系统效率评价——以中国道路运输业为例

研究了一类典型并行系统的效率评价问题:1)决策单元由两个并行的子单元组成;2)两个子单元之间存在部分共享投入资源的同时,也共同产生(非)期望产出,且我们无法明显区别该资源及(非)期望产出在不同子单元之间的分配比例.分别基于固定和可变规模收益,文章在分析决策单元整体效率及内部子单元效率的基础上,提出一种能同时确定系统整体效率及内部子单元效率的评价方法,该方法能够在评价系统效率的同时,实现共享资源与(非)期望产出的有效分配.最后,以中国道路交通运输业为实例对所提方法进行了说明.     

存在中间产品退出的混合型生产系统效率测度与分解研究

混合型生产系统是系统内部同时存在串联子系统和并联子系统的复杂生产系统.以存在中间产品退出的混合型生产系统为研究对象,针对其效率测度与分解问题在总系统效率函数表达、中间产品退出比例确定和子系统效率分解三方面的表征,构建了一种基于DEA理论框架的效率测度与分解模型.在求解该模型的过程中,借鉴交叉效率思想解决复杂模型非线性求解问题,并提出一种中立的第二目标规划优化效率分解中最优解不唯一问题.最后通过一个算例验证该模型的可行性和有效性.     

DEA效率分解与规模收益评价

使用输出DEA模型CCR、BCC、FG、ST和WY给出了整体效率的四种分解公式,并利用分解公式判别决策单元规模收益状况(包括拥挤),是对前人研究的整体效率分解公式的一种推广和应用.使用输出DEA模型CCR相对于WY的效率分解公式,可以判断决策单元是否为规模收益不变;使用BCC相对于WY的效率分解公式,可以判别是否出现拥挤.联合使用输出DEA模型FG相对于WY的效率分解公式,和ST相对于WY的效率分解公式,可以判断决策单元是否为规模收益递增、不变、递减或拥挤.     

基于“零和收益”的SBM效率分配方法及应用

在松弛变量度量(slacks-based measure,SBM)效率评价方法的基础上,首先明确投入(产出)要素固定的生产系统中,投入(产出)要素在各决策单元间的竞争性关系;然后采用比例分配策略对SBM无效决策单元的投入(产出)松弛进行效率分配,以构建一个基于零和收益的SBM(zero sum gains SBM,ZSG-SBM)效率分配方法;再通过分析ZSG-SBM模型与SBM模型效率评价结果的关系,给出了比例分配策略ZSG-SBM模型的求解方法;最后应用实例研究验证了本文模型在要素存在竞争性的复杂生产系统效率评价和资源分配中的优势。     

投入变量缺失系统DEA效率评价

针对投入变量缺失生产服务系统,提出一种基于DEA的相对效率评价方法.由于该系统的投入无法确知,首先需要依据产出对各决策单元(DMU)进行分组,并将其相对效率分解为组内效率与组间效率.对于组内效率,引人虚拟投入变量利用传统超效率DEA模型进行评价.而对于组间效率,则建立扩展的超效率DEA模型.最终以两类效率之积评价所有决策单元之间的相对效率.理论分析表明:投入缺失系统内决策单元有效的充要条件是其组内效率及其所在组的组间效率均有效.文章最后以基金项目评审为例进行实证分析,说明了本方法的合理性与可行性.     

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.     

考虑环境因素的中国城市经济效率评价研究

在考虑环境因素情形下,实证考察中国城市经济效率水平.引入环境因素,构建中国城市经济效率评价指标体系;运用DEA-BCC模型对中国31个省会城市和计划单列市的经济效率进行评价,计算得出各决策单元的DEA评价值,并进行效率分析、投入冗余产出不足分析和区域比较分析.考虑环境因素情形下,中国城市经济效率总体上较好,综合效率、纯技术效率和规模效率平均值分别达0.912、0.855和0.940,但个体差异较大,存在个体间的非均衡发展;从规模报酬来看,太原、福州、南昌等10个决策单元的经济规模应适当增加;长春、哈尔滨、南京等9个决策单元的经济规模应适当减少;太原、长春、哈尔滨等16个决策单元存在不同程度的投入冗余和产出不足,亟待改进;中国城市经济效率存在区域间的非均衡发展,综合效率平均值呈现东部地区最高,中部地区次之,西部地区最低的格局.     

“21世纪海上丝绸之路”沿线国家商业银行全要素生产率评价研究——基于两阶段Dynamic Network Malmquist-Luenberger指数和Tobit模型

现有文献对商业银行的全要素生产率进行了大量研究,但未同时考虑中间产品和结转产品对整个经营过程的影响,得到的测算结果存在一定的偏差。本文使用"21世纪海上丝绸之路"沿线29个国家2011-2016年的商业银行数据,将商业银行的经营过程看成是一个两阶段的动态网络结构,采用动态网络方向距离函数构造了一种新的动态网络Malmquist-Luenberger指数研究商业银行整体和子阶段的全要素生产率变化,并进行了影响因素分析和β收敛检验。得到的结论有:(1)"21世纪海上丝绸之路"沿线国家商业银行整体全要素生产率年均下降0.61%,呈现N型趋势,两个子阶段的全要素生产率年均下降0.06%,呈现V型趋势,技术进步是整体和子阶段全要素生产率增长的主要动力。(2)四个地区和四种收入类型国家整体的全要素生产率都是下降的,各子阶段全要素生产率变化有所差异。(3)人均GDP水平、信贷市场结构、外商投资、银行经营年限、银行规模、银行资产配置等因素会对全要素生产率产生影响。(4)"21世纪海上丝绸之路"沿线国家商业银行整体和子阶段的全要素生产率都存在绝对β收敛和条件β收敛,不同地区和不同收入类型国家的收敛特征不尽相同。     

区域高技术产业技术创新效率测度与提升路径研究——基于共享投入关联型两阶段DEA模型

将高技术产业创新过程划分为技术研发和经济转化两个阶段,考虑初始创新投入在两阶段分配、非研发投入及新产品开发费用等因素对创新产出的影响,构建共享投入关联型两阶段DEA模型,并测度了2013~2015创新年度中国大陆30个省份的高技术产业技术创新整体效率与两阶段效率。结果表明:大多数区域高技术产业初始创新投入对研发产出和经济产出均有影响;高技术产业技术创新整体效率与两阶段效率都较低,且各区域创新效率水平差异较大;技术研发效率水平高于整体效率水平,而经济转化效率水平低于整体效率水平。最后,依据高技术产业技术创新两阶段效率及其在整体效率中的权重对各区域进行重分类,有针对性地提出了单边突破式、双向协调式等多条技术创新效率提升路径。     

管理有效性与管理贡献率的测算

生产单元的管理有效性具体体现在优化配置所有参与生产过程的物质资源和人力资源,适时调整生产规模.在这一含义之下,利用等效益面生产函数可将一个生产单元的经济增长分解为三个要素的代数和.他们分别是投入要素的贡献、技术进步和管理效应.其中管理贡献反映的是技术效率的改善,其本质就是偏要素生产率的变化和规模效应即资源配置效率.在其离散型分解式的基础上,可以根据这些要素的不同变化情况,进一步测算管理贡献率.基于等效益面生产函数上的管理贡献率测算方法同时考虑了管理有效性概念的内涵和外延,具有明确的经济意义和几何意义.     

A ranking method based on a full-inefficient frontier

Since in evaluating by traditional data envelopment analysis (DEA) models many decision making units (DMUs) are classified as efficient, a large number of methods for fully ranking both efficient and inefficient DMUs have been proposed. In this paper a ranking method is suggested which basically differs from previous methods but its models are similar to traditional DEA models such as BCC, additive model, etc. In this ranking method, DMUs are compared against an full-inefficient frontier, which will be defined in this paper. Based on this point of view many models can be designed, and we mention a radial and a slacks-based one out of them. This method can be used to rank all DMUs to get analytic information about the system, and also to rank only efficient DMUs to discriminate between them.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

Deriving the DEA frontier for two-stage processes

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently DEA has been extended to examine the efficiency of two-stage 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 provides not only an overall efficiency score for the entire process, but as well yields an efficiency score for each of the individual stages. Due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores, as in the standard DEA approach, does not necessarily yield a frontier projection. The current paper develops an approach for determining the frontier points for inefficient DMUs within the framework of two-stage DEA.     

具有包容关系的结构异质DEA效率评价方法

指标结构同质是数据包络分析（DEA）方法的基本假设之一;然而,现实问题的复杂性使得该假设常常难以完全被满足.针对具有包容关系的产出结构异质问题,通过解析决策单元（DMU）之间生产结构的内在关系来构建一种分阶段的DEA效率评价方法.该方法充分考虑了不同结构DMU的主观偏好,较好地规避了传统DEA方法在结构异质DMU效率评价过程中的不公平性.随后,该方法分别被拓展至投入结构异质和多重结构异质的情境中.最后,通过两个算例来说明本文方法的有效性与实用性.     

Fuzzy data envelopment analysis (DEA): Model and ranking method

Data Envelopment Analysis (DEA) is a very effective method to evaluate the relative efficiency of decision-making units (DMUs). Since the data of production processes cannot be precisely measured in some cases, the uncertain theory has played an important role in DEA. This paper attempts to extend the traditional DEA models to a fuzzy framework, thus producing a fuzzy DEA model based on credibility measure. Following is a method of ranking all the DMUs. In order to solve the fuzzy model, we have designed the hybrid algorithm combined with fuzzy simulation and genetic algorithm. When the inputs and outputs are all trapezoidal or triangular fuzzy variables, the model can be transformed to linear programming. Finally, a numerical example is presented to illustrate the fuzzy DEA model and the method of ranking all the DMUs.     

A generalized model for data envelopment analysis with interval data

Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

Sensitivity and stability analysis on the first and second levels of efficiency score relative to data error

In data envelopment analysis (DEA), efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for a category DMUs and finds the stability radius for all efficient DMUs. By means of combining some classic DEA models and with the condition that the efficiency scores of efficient DMUs remain unchanged, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalizes the conventional sensitivity analysis approach in which the inputs of efficient DMUs increase and their outputs decrease, while the inputs of inefficient DMUs decrease and their outputs increase. We find the maximum quantity of perturbations of data so that all first level efficient DMUs remain at the same level.     

Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.