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.     

Two-stage DEA models with undesirable input-intermediate-outputs

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks.     

Internal resource waste and centralization degree in two-stage systems: An efficiency analysis

Internal resource waste refers to the waste in the intermediate resources between the upstream stage and downstream stage in a production or service system. This study examines a system with a two-stage structure, in which the outputs from the first stage are taken as the inputs for the second stage. Two-stage systems can exist in centralized, decentralized, or mixed organizational modes. In this paper, we propose two-stage DEA models considering a degree of centralization that makes it possible to measure internal resource waste in different system modes. Some managerial insights are tested and verified from the perspective of efficiency analysis. We find that: 1) when there is only one intermediate measure in a centralized two-stage system, internal resource waste can be eliminated completely, and 2) a higher degree of centralization in a two-stage system can lead to less internal resource waste and more expected outputs. Finally, we present a numerical example and two practical real-world examples that illustrate our approach and findings.     

Stage efficiency evaluation in a two-stage network data envelopment analysis model with weight priority

Conventional DEA models treat the entire production system as a black box and ignore its internal structures. To address this issue, many studies have examined the DEA efficiencies of two-stage systems in which all outputs of the first stage are the only inputs to the second stage. Based on game theory, the non-cooperative model and centralized model were developed for such a two-stage network structure. However, for the centralized model with multiple optimal solutions and the non-cooperative model, an assumption is required as to whether the first or second stage should be assigned the absolute priority for optimization. In many cases, certain circumstances might exist in which one stage does not completely dominate the other stage. In this paper, we develop a methodology for assessing the overall and stage efficiencies by considering the different and DMU-specific degree of priority given to the stages. Particularly, the non-cooperative model and the centralized model can be deemed as special cases. Moreover, we compare the proposed approaches with the existing approaches, which indicates that our approaches can greatly reduce the computational burden. Two empirical examples are used to demonstrate the proposed approach.     

Measurement of tourist hotels׳ productive efficiency,occupancy, and catering service effectiveness using a modified two-stage DEA model in Taiwan

This study develops a modified two-stage model to evaluate productive efficiency, occupancy, and catering service effectiveness of Taiwan׳s international tourist hotels. The difference between the modified and original two-stage model is that the modified two-stage model allows for multiple efficiencies to be calculated in the unique stage and the concept of intermediate input is introduced.The modified model was tested using 58 Taiwanese international hotels and the results show the modified model offers a more efficient and effective approach in calculating all the efficiencies in a single data envelopment analysis (DEA) implementation as opposed to independent efficiency calculations.     

A fair evaluation of certain stage in a two-stage structure: revisiting the typical two-stage DEA approaches

The efficiency of decision processes with a two-stage structure has been studied by some modified versions of Data Envelopment Analysis (DEA) methodology, such as the relational or centralized model, and the non-cooperative model. After revisiting the rationale of the centralized model provided by the literature, we find that some unfairness exist in its efficiency evaluation of certain stage. This unfairness leads to the usual underestimation of the overall efficiency by the centralized model. Furthermore, because the independent DEA model for one stage ignores its relation and coordination with the other stage and the two-stage system, externalities between these members may arise and lead to the seeming contradiction in efficiencies derived by independent DEA models for the stages and the black box system. Therefore, we argue that the efficiency of certain stage in the context of a two-stage structure should be reevaluated instead of simply using the independent DEA model. A sequence of leader-follower procedures, with data adjustment on intermediates, is proposed to eliminate the externalities and to ensure a fair evaluation. We find that, after this data adjustment, the reevaluation of the second stage for a given Decision Making Unit (DMU) yields the same result as obtained by the standard DEA model regarding the two-stage as a black box. Moreover, some explicit relations are established between the black box model, the centralized model, and the non-cooperative model. Two typical examples taken from the literature illustrate our main results. Our findings also imply that more emphasis should be placed on the game theoretic DEA approach to model the efficiency evaluation of two-stage processes.     

部分中间产出作为最终产品的两阶段合作效率

网络DEA模型研究多个进程和多个子系统的复杂系统的效率度量.针对中间产出无法为第2阶段完全消耗的情形,传统DEA模型对系统效率的评价偏高,已有网络DEA模型则对系统效率的评价偏低.本文提出部分中间产出作为最终产品,进入流通渠道的两阶段效率模型,用来测度两阶段生产过程的真实效率.采用乘积形式描述两阶段合作的特征,给出不同...     

Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA

Measuring and improving the efficiency of the Chinese commercial banking system has recently attracted increasing interest. Few studies, however, have adopted the two-stage network DEA to explore this issue in the Chinese context. Because the entire operational process of the banking system could be divided into two sub-processes (deposit producing and profit earning), the evaluation of the sub-process efficiencies could be used to assist in identifying the sources of the inefficiency of the entire banking system. In this study, we utilize the network DEA approach to disaggregate, evaluate and test the efficiencies of 16 major Chinese commercial banks during the third round of the Chinese banking reform period (2003–2011) with the variable returns to scale setting and the consideration of undesirable/bad output. The main findings of this study are as follows: (i) the two-stage DEA model is more effective than the conventional black box DEA model in identifying the inefficiency of banking system, and the inefficiency of the Chinese banking system primarily results from the inefficiency of its deposit producing sub-process; (ii) the overall efficiency of the Chinese banking system improves over the study period because of the reform; (iii) the state-owned commercial banks (SOBs) appear to be more overall efficient than the joint-stock commercial banks (JSBs) only in the pre-reform period, and the efficiency difference between the SOBs and the JSBs is reduced over the post-reform period; (iv) the disposal of non-performing loans (NPLs) from the Chinese banking system in general explains its efficiency improvement, and the joint-equity reform of the SOBs specifically increases their efficiencies.     

非合作博弈两阶段生产系统的环境效率评价

本文研究了环境效率评价中广泛存在的一类典型问题:两阶段非合作博弈的效率评价问题,该问题有两个明显的特点:(1)决策单元由经济生产子系统和污染物处理子系统两个阶段的子系统构成,(2)经济生产子系统产生的污染物由污染物处理子系统进行处理,且经济生产子系统居于主导地位,而污染物处理子系统居于从属地位.文章在分析各个决策单元整体效率与其子系统效率之间关系的基础上,提出一种能够同时评价决策单元整体效率和其子系统效率的DEA方法;然后引入非合作博弈思想,提出了基于两阶段非合作博弈的环境效率评价的DEA方法;最后采用中国各地区的工业系统的环境效率评价的实例分析说明了该方法的合理性和有效性.由于文章提出的方法能够有效地分析决策单元内部子系统的有效性水平,能够反映子系统之间的主从关系,能够发掘影响决策单元效率的关键因素,因而能够给出更为有效的环境管理信息,为决策者的决策提供科学的依据.     

两阶段DEA前沿面投影问题研究——兼对我国上市银行运营绩效进行评价

DEA方法,即数据包络分析方法,是一种用于评价决策单元(Decision Making Units,DMUs)相对有效性的实证方法。近年来DEA方法已经广泛的应用于各行各业的绩效评价中,并发展出两阶段DEA方法。两阶段DEA方法相对于传统DEA方法的优势在于,它不但可以提供被评价对象的总体效率值,还可以分别生成每一阶段的效率值。但正是由于中间要素的存在,按照传统的DEA方法来调整两阶段DEA投入、产出要素的优化过程已不能成功投影在有效前沿面上。本文基于两阶段DEA方法,通过加入"虚拟中间要素"在两阶段DEA中嵌入一个"虚拟阶段",这样不但完善了两阶段DEA的逻辑结构,而且成功的将被评价单元投影到有效前沿面。最后本文应用以上方法对我国上市银行的运营绩效进行了实证分析。实证结果令我们意外的是,国有商业银行运营绩效优于股份制银行。     

考虑满意度的两阶段DEA固定成本分摊方法

考虑具有相同的投入和产出的两阶段决策单元的固定成本分摊问题。将待分摊的固定成本作为一种新的投入，建立两阶段加性DEA模型。首先证明了各决策单元从自身角度出发可以找到至少一种分摊方案，使其自身整体和阶段效率都达到Pareto有效。然后证明了在公共的权重下，至少存在一种分摊方案可以使得各决策单元整体和阶段效率都达到Pareto有效。并给出了这样的有效成本分摊方案集。为了得到公平的成本分摊方案，定义了各DMU各阶段对分摊方案的满意度，最大化最小的满意度，可以得到最终的成本分摊方案。将问题拓展到两阶段存在共享投入的生产系统中，这些性质定理同样成立。数值算例部分将本文与Yu等（2016）的研究结果进行了对比，验证了本文方法的有效性，指出了本文方法的优越性。本文的方法综合考虑了效率和公平，得到的固定成本分摊方案公平合理。     

DEA models for extended two-stage network structures

Liang et al. (2008) [1] developed DEA models based upon game approach to decompose efficiency for two-stage network structures where all outputs of the first stage are the only inputs to the second stage. This paper extends Liang et al. (2008) [1] by assuming that the inputs to the second stage include both the outputs from the first stage and additional inputs to the second stage. Two models are proposed to evaluate the performance of this type general two-stage network structures. One is a non-linear centralized model whose global optimal solutions can be estimated using a heuristic search procedure. The other is a non-cooperative model, in which one of the stages is regarded as the leader and the other is the follower. The newly developed models are applied to a case of regional R&D of China.     

具有双重角色和非期望要素的供应商评价两阶段DEA模型

在基于DEA方法的供应商评价过程中,会出现供应商同时具有双重角色要素和非期望输出要素的情形。文章提出了一个处理双重角色要素的新思路,认为DEA模型中双重角色要素同时扮演了输入和输出两个角色,所有双重角色要素本质上就是网络DEA模型中的中间变量,并同时认为包含双重角色要素的生产系统一定能分解成为多个子系统,其中的双重角色要素既是一个子系统的输入,同时又是另一个子系统的输出。为测度供应商的效率,基于已有关系型两阶段DEA模型,将供应商的生产运营视为两阶段过程,其双重角色要素视为两阶段过程的中间变量,并通过将所有输出以加权和的形式表达,但对非期望输出用负的权重的方式,提出了一个具有双重角色和非期望输出要素的供应商评价两阶段DEA模型,最后用一个实例验证了方法的可行。     

工业用水系统效率评价:考虑污染物可处理特性的两阶段DEA

提高水资源使用效率和污水处理效率是解决目前水资源短缺的重要途径。中国工业用水系统可分为生产用水子系统和污水处理子系统。本文考虑两个子系统之间的联系,并区分污染物在两个子系统中的弱处理和强处理特性,提出了一种基于DEA的两阶段评价模型。应用本文提出的新模型分析中国30个省级区域的工业用水系统的效率,结果表明: 中国省级区域工业用水整体效率不高,且地域分布特征明显,东部、西部、中部效率依次递减; 中国工业用水系统的非有效性主要源于污水处理效率的影响;工业用水系统效率与地区水资源禀赋存在一定的关系,水资源短缺的地区用水效率相对较高。文章所提出的方法兼顾生产用水子系统和污水处理子系统之间的相互影响,能够同时评价两个子系统效率和工业用水系统的整体效率,能有效发现系统中影响整体效率的关键环节,且可以应用于其他能源效率评价问题,具有明显的实际应用价值。     

Efficiency decomposition in network data envelopment analysis with slacks-based measures

Conventional data envelopment analysis (DEA) treats the production system as a black box when measuring efficiency, ignoring its internal structure. By taking the operations of the component processes of the system into consideration, several network DEA models have been developed. Of these, the slacks-based measure (SBM) approach has attracted much attention for its ability to provide suitable efficiency measures, especially for weakly efficient production units. This paper proposes a general SBM model for network systems, and is able to decompose the system efficiency into a weighted average of the process efficiencies. This relationship holds for all types of network structure. An example shows that the network model has stronger discriminating power than the conventional black-box model, and the system efficiency is indeed a weighted average of the process efficiencies. The decomposition of the system efficiency helps identify key factors to improve the performance of a production unit.     

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。     

非独立并联生产系统的DEA效率评价研究

对复杂生产系统进行效率评价,是改善其生产效率的基础.针对非独立并联结构生产系统的效率评价问题开展研究.首先,将两阶段非独立并联生产系统等价为先并联后串联结构的混联生产系统;其次,将混联生产系统的整体效率定义为各串联子系统效率的乘积,而各个串联子系统的效率则定义为内部各并联子系统效率的加权和,并给出了对应的DEA效率评价模型;最后,有关定理和算例分析证实了该模型能更合理地评价此类生产系统的技术效率,能够更大程度地挖掘系统整体性能改善的潜力.     

Hierarchical network systems: An application to high-technology industry in China

In real world situations, there is a hierarchical structure exists in a specific organization and each component has its network process. However, such hierarchical network system has not been well studied in previous literature, and misleading results often are produced. The current paper discusses a data envelopment analysis (DEA) modelling technique for a network structure where a hierarchical system consists of components having two-stage series processes. An additive network DEA is proposed to evaluate the performance of this type of network structure. The overall and divisional efficiencies of the system and each component can be derived, and the relationship between system efficiency, divisional efficiency and the ones of components is discussed. The newly developed additive network DEA is nonlinear and cannot be converted into a linear program. A semidefinite programming (SDP) approach is developed for effectively solving this model and the global solution can be guaranteed. Another linear multiplicative network DEA also developed for this hierarchical system. The two newly developed models are illustrated with a case of the performance evaluation of high-technology industry in China.     

Efficiency evaluation of banks in China: A dynamic two-stage slacks-based measure approach

Operational processes of banks in China can be divided into productivity and profitability stages. Within this, non-performing loans can be treated as a carry-over variable, an undesirable output of the profitability stage in the previous period but an input to the profitability stage in the current period. Using this framework, this paper proposes a dynamic two-stage slacks-based measure model to evaluate the efficiencies of Chinese banks. Based on the proposed model, the measures of stage, period and period stage efficiencies are defined. The proposed approach is applied to evaluate the operational efficiency of banks in China during 2008–2012. Key findings are that banks in China show both technical and scale inefficiency during 2008–2012, which results from the inefficiencies of both the productivity stage and profitability stage; city-owned commercial banks are more overall technically efficient than state-owned commercial banks and joint-stock commercial banks although state-owned commercial banks show best practice for pure technical efficiency, and city-owned commercial banks perform better than joint-stock commercial banks for pure technical efficiency.     

两阶段生产系统的DEA效率评价模型

数据包络分析(DEA)作为一种数学规划方法,已经被广泛用来评价一个决策单元相对于其它决策单元的效率。经典的DEA模型把决策单元看作一个“黑箱”,对决策单元的内部运行机制不作深入的研究。本文以一个两阶段生产系统为例,从生产系统的内部过程出发,提出一个基于DEA的模型以合理评估该决策单元的相对效率。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,但确实有助于管理者确定生产过程(如供应链)的非有效来源及其效率改进方向。