【作者】 王军；

【导师】 梁樑； 查勇；

【作者基本信息】 中国科学技术大学 ， 管理科学与工程， 2015， 博士

【摘要】 效率评估和改进是决策科学领域中非常重要且有趣的研究内容,对于理论的发展和实践的应用都起着重要的推动作用。随着经济全球化的深入,区域经济的融合和统一,效率的问题关系着各个国家及其企业在市场竞争中的地位和影响力。数据包络分析方法(Data Envelopment Analysis, DEA)是用于评价利用投入来获得产出的生产单元的相对效率的决策分析方法。DEA自1978年提出以来,在理论研究和实践应用中获得了众多学者的青睐,也取得了众多的研究成果。该方法在效率评估领域中存在几个显著的特点：首先,DEA模型在计算过程中不需要预先进行参数的设置,只需要生产过程的输入和输出量；其次,该方法在实际应用中不需要考虑投入与产出之间的函数关系。因此,数据包络分析方法以其独特的特点,使得其在某种程度上能够对决策单元进行客观、公正的评价,从而为决策者提供了生产单元之间的优劣信息以及效率改进的方向。然而,随着DEA方法在理论和实践中的进一步拓展,传统的DEA方法也存在一些亟需解决的问题：第一,DEA模型计算的结果能够区分有效和无效的单元,而对生产前沿面上的点无法进行进一步的区分；第二,传统的DEA方法在进行效率评价的一个隐含的假设是决策单元的同质性。一般地,决策单元需要满足以下的条件：(1)各个决策单元应该有着相同或相似的外部环境；(2)各个单元应有着相同或相似的目标和使命；(3)决策单元单元投入和产出指标应该相同。现实中往往存在异质性的情况,突出的问题是效率评价如何兼顾公平?为了解决上述问题,已有相关的学者和专家提出了一些新的理论和方法去解决实际评价中的非同质性问题。本文基于前人研究成果,对异质性问题作进一步拓展,来丰富决策分析的相关理论和实践。为此,将分别介绍异质性基本问题、影响效率评价的因素、异质性评价方法拓展研究及DEA理论的国内外研究现状和动态,并加以分析和总结。本文将考虑非同质决策单元的效率评价,具体将考虑以下几种情形：处于不同环境下的决策单元的效率评价,多阶段DEA模型的效率评价,考虑非期望产出存在情形下的拥堵问题研究,以及多部门员工之间的绩效评估。具体来说,本文主要从以下几个方面进行详细的论证和分析：第一章为绪论,本文以基本的DEA模型为出发点,简要介绍DEA作为效率评价方法的基本模型、相关概念,以及在实践中的广泛应用。阐述了与本文研究主题的关系和当前形势下存在的主要问题、解决方案和发展方向。然后,提出本文的研究框架,指出现实中常见的异质性问题情形：(1)决策单元处于不同的外部环境,从而导致环境异质性；(2)决策单元的投入、产出指标的不一致从而导致结构的异质性；(3)决策单元的生产规模的差异而导致的规模异质性。最后,我们提出了本文研究的基本方法和目标,以实际问题为导向,拓展理论模型并应用于实践。第二章探讨了考虑非期望产出时的无效和拥堵问题。拥堵是一种广泛存在的经济现象,它的存在会降低决策单元的效率,同时影响效率评价的结果。因此,本文将首先探讨拥堵对效率的影响。本章首先根据无效和拥堵的特点对二者进行区分和构建数学表达式,然后构建相应的数学模型分别计算和识别管理无效、技术无效和拥堵,同时以实际算例说明了先前文献研究中不能够很好地区分技术无效和拥堵的问题。基于这些理论基础,本文在考虑非期望产出和期望产出同时存在的情形下,计算相应的无效和拥堵,同时进一步的将拥堵区分为期望和非期望拥堵。期望拥堵定义为发生在非期望产出和投入之间的拥堵,是管理者所期望发生的；而非期望拥堵是发生在期望产出和投入之间的拥堵,是管理者尽量避免的一种拥堵。最后针对本文提出的模型,选取实际中的算例,进一步验证了本文构建模型的可行性和适用性。第三章提出了在效率评价的过程中,决策单元所处的外部环境对DMU自身的效率也产生重要的影响。本章首先回顾了以往关于外部环境变量对效率评估的影响以及相关的参数和非参数方法如何把环境变量加入到模型中的相关文献,同时指出了已有文献在该问题的解决方法上存在的不足和缺陷,如何把外部环境变量更好的加入模型中及如何量化环境变量的影响等。因此本章在前人研究基础上,提出了三阶段方法来有效的把环境变量对效率的影响剔除,从而来更加合理的对决策单元真实的效率水平进行比较和评价。在第一阶段,选取了SBM-DEA模型来计算初始的效率和获得代表无效程度的松弛变量值；在第二阶段,基于前面的松弛变量值构建前沿分析方法来对松弛变量进行回归和分解为三个部分：个体无效、环境无效和随机误差,基于提出的模型进一步的对原始的投入和产出进行调整,剔除环境的影响部分。同时,本章提供一个统计分析方法来识别这些影响的重要性和外部变量之间的共线性；在第三阶段,基于调整后的投入和产出,使用传统的模型计算决策单元新的效率,从而使得所有的DMUs都能够在统一的环境中进行效率评价。最后,本文将提出的模型应用于中国高校的绩效评价中,来分析高校所处的外部环境对效率的影响。第四章进一步拓展了非同质问题的理论和实践研究,提出了一种基于DEA理论的多部门的员工绩效评价的模型和方法。本章提出的多部门员工绩效评价存在着结构异质性,因为不同部门对员工的要求和所掌握的“技术”是有差异的,而且用于评价员工的关键绩效指标(KPI)也是存在较大差异。基于这样的背景,如何将部门员工纳入企业的层面进行一致性评价。本章首先选取部门员工的KPIs指标,基于构建的公共权重的DEA模型把这些不同部门的多个KPIs指标归集到企业层面的四个维度上来；然后,基于维度的KPIs,构建MPI-alike模型分别来计算员工基于自身部门和其他部门的效率,根据交叉效率的思想来获得员工基于企业层面的效率；本章同时构建了公共前沿面(meta-frontier)模型来获得员工基于自身部门和其他部门以及企业层面效率的差异,从而得到本章开始定义的部门间的技术非同质性；最后,本章采用模拟的数据来对一家汽车制造业的制造和研发部门的员工进行效率评价,从而验证本文模型的有效性。第五章是总结和展望,本章归纳了全文所有的研究内容,同时对每章的内容进行分析和评价,指出目前研究的不足之处,同时基于当前研究现状,提出未来研究方法和研究领域的拓展之处。本文的创新点主要体现在如下几个方面：(1)本文在考虑非期望产出存在的情形下的无效和拥堵问题时,能够很好的将无效和拥堵进行区分,并提出一个合理的模型来计算无效和期望与非期望拥堵；本文同时将提出的方法应用于中国经济发展中遇到的资源拥堵和环境污染问题中。(2)本文在提出的考虑外部环境变量的决策单元的效率评价模型和方法时,采用SBM模型计算得到松弛变量,从而考虑的无效程度更加全面；同时通过新的调整方法可以合理的控制调整量大小,考虑到环境变量的影响的调整(IF)和随机误差影响(EF)调整之间的关系,而不至于使有些投入或者产出的调整量过大；文章同时考虑了投入和产出的调整,在现实中环境变量不仅仅会对投入产生影响,也会对产出产生影响,所以文章考虑的调整更加全面,并通过实际算例来说明提出方法的应用价值。(3)本文探讨了基于企业层面的多部门员工绩效评估方法和模型,首次将多部门员工的不同的评价和考核指标纳入到统一的框架中。为了获得更加合理的员工绩效评估,我们在提出的模型中考虑了部门之间的技术非同质性的影响,来更加合理的获得员工的绩效。更多还原

【Abstract】 Efficiency evaluation and improvement are very significant and interesting in the research field of decision-making science, and play an important role in promoting both the theoretical development and the practical application. With the further development of economic globalization and regional economic integration and unity, efficiency issues are critical to competitive status and influence of various countries and their companies in the market.Data envelopment analysis (DEA) is a decision analysis method used to evaluate the relative efficiency of the decision making units (DMUs) by utilizing the input to obtain the output. DEA has drew a lot of attention from many scholars and numerous research results in the theoretical study and practical application are achieved since it was first proposed in1978. DEA has several significant features in the field of efficiency assessment:firstly, the calculation process of the DEA model does not require preset parameters and only needs the input and output of the process of production; secondly, the functional relationship between input and output needn’t to be taken into consideration in the practical application of DEA. Therefore, with its unique features, DEA can give an objective and fair assessment on the DMUs and hence provide efficiency information for decision-makers as well as the direction of improving the efficiency of production for decision-makers. However, with the theoretical and practical expansion of the DEA, the traditional DEA method also revealed some problems to be solved:first, the calculation results of the DEA model can distinguish between efficient and inefficient units, but the unit in the production frontier cannot be further distinguished; second, the traditional DEA method of conducting efficiency evaluation has an implicit assumption that the homogeneity of the decision-making unit must be satisfied. In general, the DMUs must meet the following conditions:(1) each DMU should have the same or similar external environment;(2) each unit shall have the same or similar goals and mission;(3) the input and output indexes should be the same. However, the outstanding issue is that, when the heterogeneous DMUs occurs in reality, how to do a fair evaluation? To solve this problem, scholars and experts have proposed a number of new theories and methods to solve the non-homogeneity problems in practical evaluation. Based on previous research achievements, this paper aims to further expand the heterogeneity problem and enrich the theory and practice of decision-making analysis. To this end, this paper will introduce the basic problem of heterogeneity, the factors affecting the efficiency evaluation, the expanding research of heterogeneity evaluation methods and the related research status of DEA at home and abroad respectively, which will be further analyzed and summarized. This paper will consider the efficiency evaluation of non-homogeneous DMUs, specifically the following scenarios:the efficiency evaluation of the DMUs under different circumstances; efficiency evaluation of multi-stage DEA model; the research on congestion considering the presence of undesirable outputs; and performance evaluation with multiple department employees. Specifically, this paper carried out a detailed argument and analysis in the following aspects:The first chapter is the introduction. In this paper, with the basic DEA model as a starting point we introduce its basic model, related concepts and some applications. The paper describes the main issues, existing solutions and future directions under the present circumstances and their relationship with the theme of the current research are discussed. Then, the research framework is raised and the heterogeneity situations are highlighted in the paper:(1) the DMUs under different external environment lead to environmental heterogeneity;(2) the DMUs with different inputs and outputs indexes result in structural heterogeneity;(3) the DMUs with different production scale lead to scale heterogeneity. Finally, we present the basic method and expand the theoretical model and apply it into practice under the problem-driven objective.The second chapter discusses the inefficiency and congestion problem when undesirable outputs are yielded. This chapter distinguishes between inefficiency and congestion and constructs the mathematical expressions at first according to the characteristics of them. Then it proposes the models which can identify managerial inefficiency, technical inefficiency and congestion. We also illustrate the problem that cannot be distinguished between technical inefficiency and congestion in previous paper with a practical example. Based on this rationale, the paper calculates the inefficiency and congestion and further differentiates the congestion into desirable and undesirable congestion when undesirable output and desirable output are co-existed. The desirable congestion is defined as occurring between undesirable outputs and inputs, which is expected by the managers; and instead undesirable congestion occurs between the desirable output and input, and the manager expected to avoid this kind of congestion. Finally, the proposed approach is applied and verified by identifying resource congestion and environmental inefficiencies of China’s economic development.The third chapter discusses the problem of environmental nonhomogeneity. The external environmental variable is an important issue that makes an indispensable impact on the productivity of decision making units (DMUs). In this paper, we first investigate whether and how these variables influence performances of the DMUs based on slack-based measurement. We extend the implicit assumption of prior studies and suggest that environmental variables can be a catalyst to increase productivity. Impact and error factors, which are derived from regression analysis and stochastic frontier analysis (SFA), are defined to better represent the composition of two contradictory impacts, catalyst and depressant, of contextual variables. A statistical analysis is provided to identify the significance of such impacts and recognize multicollinearity among contextual variables. The two factors are also moderated flexibly by decision makers in accordance with various production scenarios. Accordingly, original inputs and outputs are appropriately adjusted to well depict individual, contextual, and statistical error inefficiencies. Further, modified slack-based DEA models are proposed to incorporate DEA and regression methodology within an integral framework. Several properties are presented to better describe the characteristics of the models. An empirical example is shown to verify the feasibility of the proposed approach.The fourth chapter further expands the theory and practice of non-homogeneous problem. In this research, we study the performance of the employees in heterogeneous departments with distinctly different key performance indicators (KPIs). We begin with the identification of the characteristics of KPIs and explore widely accepted criteria to collect the appropriate indicators for each department in a consistent way. We then make a classification of the departmental indicators and orient various KPI indices to a framework composed of four unified dimensions. An approach incorporating data envelopment analysis (DEA) and common weights is proposed to integrate various KPIs and obtain objective scores for each employee. Since the KPI scores of employees are also significantly related to the "technology" of a department and may be preferred by the managers of department, we propose a Malmquist productivity index alike (MPI-alike) model to evaluate the performance of an employee in different departments which represent different technology and identify the employee’s efficiency based on the idea of cross efficiency. In this way, the inconsistency caused by different frontier facets is eliminated when estimating the employees’performance. Specifically, the subjective preference and inconsistence of the managers are also eliminated or reduced. Further, we propose a modified meta-frontier model to estimate the technology heterogeneity among departments.The final chapter is a summary and outlook. This chapter summarizes all research contents of the full text, and gives the detailed analysis and evaluation of the content of each chapter. We also identify shortcomings of the present study. At last, we propose future research methods and research areas based on the current research situation.Innovation of this paper is mainly reflected in the following aspects:(1) We first classify conventional congestion into a new congestion and technical inefficiency based on priori researches and real applications. Modified definitions and mathematical expression of congestion, managerial and technical inefficiencies are proposed to better illustrate the differences among them. The proposed approach is applied and verified by identifying resource congestion and environmental inefficiencies of China’s economic development.(2) In this paper, we apply the SBM-DEA model to calculate slack variables which can make the inefficiency more comprehensive when considering the impact of the external environment variable on the DMUs efficiency. At the same time, through the new adjustment method, the amount of the adjustment can be controlled properly. We also consider the relationship between the impact factor (IF) and error factor (EF). In reality, environment variables will not only affect inputs, but also have the impact on outputs, so the adjustment in this paper is more comprehensive. Numerical analysis validates the influence of environment variables on productivity.(3) This paper discusses the performance assessment methods and models indifferent departments and incorporates the different evaluation and examination index into a unified framework based on the enterprise level. In order to obtain a more reasonable employee performance, the proposed models considers the impact of the technological heterogeneity on the employee’s efficiency among multiple departments. Numerical analysis of an auto company validates the proposed models.更多还原