数据包络分析中的若干问题研究
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摘要
数据包络分析是一种用来度量多投入多产出决策单元相对效率的“面向数据”的新方法。由于它很少需要各种假设或其他前提条件,经济学、会计学、信息管理、运作管理等不同领域的研究者们都利用DEA方法来度量企业的技术、管理和规模效率。近年来DEA方法广泛应用于医院、大学、法院、商业农场等不同行业以及不同地区和国家的效率度量。
本文关注DEA领域的几个热点问题,在已有研究的基础上进行了拓展。本文的主要创新在于:(1)提出投入导向和产出导向的改进超效率模型,从而彻底解决了已有超效率研究仍存在不可行解的情形,并对数据稳定性进行了灵敏度分析;(2)提出最小调整幅度的效率改进模型,考虑在现有投入产出水平基础上,如何进行最小幅度的调整,将无效单元投影到有效前沿面上;(3)提出基于偏好产出的资源配置模型,将额外投入配置到多个单元中,最大限度的提高偏好产出水平;(4)提出两阶段合作效率模型,调整投入在不同阶段的配置,使得两阶段系统的效率最优;(5)提出基于公共权重和标杆集的两种集成DEA排序方法。文章的组织结构如下:
首先综述了数据包络分析在模型方面的发展和当前研究的进展,概括了本文的研究内容和框架结构。
其次,为了克服传统超效率模型存在不可行解的情形,本文提出了VRS假设下的改进超效率模型。当传统模型无可行解时,该模型仍然可行,且得到有效DMUs的超效率;当传统模型有可行解时,该模型得到的结果与传统模型的结果相一致。本文的研究在一定程度上拓展了MalmquiSt productivity index和DEA benchmarking模型的应用范围。
接着研究如何改变现有的投入产出水平,使得无效单元变为有效。提出了效率改进的一般DEA模型,研究如何通过投入产出的变动来帮助决策者进行效率改进,试图寻找最小调整幅度的投影路径来改善无效决策单元的技术效率,从而使得无效单元投影到有效前沿面,变为有效。
然后研究额外投入既定的情形下,如何合理的配置资源,最大限度的提高产出水平。考虑产出中包含决策者偏好和不偏好两类产出的情形,提出一种改进的集中式资源配置模型,以期获得更多的偏好产出,同时限制不偏好产出的水平。文中还提出了基于期望效率改进的集中式资源配置准则,以此来评价不同资源配置模式之间的优劣。
本文还研究了复杂生产中投入的不同配置方式对整个生产的效率以及每个阶段效率的影响。分析了投入可在不同阶段自由配置的两阶段生产过程,提出了几何平均最优意义下的两阶段合作效率模型。分别讨论了非合作环境下不同阶段占据不同地位的情形,构建了基于CCR和BCC模型的两类几何平均合作效率模型,对多阶段生产过程的技术和规模效率都进行了合理的度量。
进一步提出一种基于公共权重的集成DEA模型。同时考虑所有决策单元,希望找到一组权重系数,使得所有单元的总体无效程度最小,达到系统效率最优。由于这组权重是希望所有单元的无效程度最小,即使得系统的无效程度最小,因此可以尽可能消除不同单元对权重的不同偏好,从而最大程度的被所有单元接受。另一方面,还提出了考虑决策者偏好的基于标杆集的排序方法。
最后对论文全文作了总结,说明了论文的几点创新,指出了论文研究的不足之处,并对论文研究的主题在今后可能的研究方向作了展望。
Data Envelopment Analysis is a relatively new "data oriented" approach for evaluating the performance of a set of peer entities called Decision Making Units which convert multiple inputs into multiple outputs. Because it requires very few assumptions, DEA has also opened up possibilities for use by researchers of various academic areas, such as economics, accounting, information management and operation management, etc. Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as hospitals, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc.
On the basis of the previous researches, this dissertation innovate in several aspects: (1) investigate sensitivity analysis using alternative super efficiency model, which deals with the infeasibility of current super efficiency models; (2) project the inefficient DMUs onto efficient production frontier with minimum amelioration; (3) allocate the additional inputs according to the central decision makers in order to maximize desirable outputs, as well as to restrict undesirable outputs; (4) regulate the allocative factor of the inputs freely among different sub-processes to optimize overall efficiency of the whole process; (5) how various weights influence the efficiency of the DMUs. This dissertation is organized as follows:
Firstly, review models and methodologies development within the context of DEA, lay emphasis on current researches of data variation or uncertainty, and generalize the main ideas and innovations of this dissertation.
Secondly, investigate super efficiency model for sensitivity analysis. The section develops a modified super-efficiency DEA model to overcome the infeasibility issue under the assumption of VRS. The newly developed approach yields (i) an optimal solution and a super-efficiency score for efficient DMUs for which feasible solutions do not exist under the original super-efficiency model; and (ii) super-efficiency scores that are equivalent to those from the original super-efficiency model when feasible solutions do exist. To some extent, the DEA Malmquist productivity index, and the DEA benchmarking models.
Thirdly, study the approach to convert inefficient DMUs into efficient by altering current inputs and outputs. A modified model is proposed to re-allocate the inputs and outputs of inefficient DMUs with minimum amelioration by considering the preference of decision makers and other factors which impact the learning process. A heuristic algorithm is proposed to solve the simplified model based upon the modified one.
Next, explore how to allocate the additional resources in order to maximize the outputs. A centralized resource allocation problem is studied focusing on the desirable outputs according to the overall goals of multi-unit organizations. We proposes modified models to reallocate the additional resources based upon the realized production level. Our problem is to find which units are worth reallocating more resources to maximize desirable outputs, as well as to restrict undesirable outputs, of the overall system. An algorithm is proposed to solve the allocation problem. Further, an criterion to evaluate various resource allocation plans by calculating the average expected system efficiency of each plan is provided.
We also discuss various allocations of inputs among two sub-processes and the overall efficiency as well as the efficiencies of different sub stages. We analysis complex production process with two sub-processes connected serially. Cooperative and non-cooperative game theory was steered to manage the relationship among sub-DMUs, and cooperative efficiency was proceeded to match the actual instance well. Several new models are presented to calculate the efficiency of the sub-DMUs in a non-cooperative manner, whereby the upper and lower bounds of the efficiencies are explicitly determined. A geometric average cooperative DEA model is proposed to evaluate the efficiency of the DMUs, and a heuristic parametric linear programming is suggested to solve the cooperative model. Various situations as constant return to scale and various return scale are discussed separately to evaluate technical and scale efficiency.
Further, we investigate how various weights selection influences the efficiency of the DMUs. an integrated DEA model, which aims at minimizing the total inefficient score of all DMUs and correspondingly optimizing the relative system efficiency based upon the common weights. With such common weights, the efficiency of each DMU is evaluated equitably and effectively, as well as the contribution of each DMU to system, and as a result, a complete ranking order is proposed from it. Also, another ranking approach is proposed, considering the preference of decision makers and management practice. Our problem is to find common weights, putting the best practice and preferable information of decision makers into consideration, as well as concerning about the efficiencies of other DMUs, which is more convincible and feasible and can easily be accepted by all DMUs than that derived from traditional DEA models. We expect the common weights resulted from the proposed integrated DEA models could guarantee those DMUs in BS DEA efficient.
Finally, the concluding section of the full dissertation summarizes some of the breakthroughs made in this dissertation, as well as the shortcomings of this paper and the direction of further researches.
本文关注DEA领域的几个热点问题,在已有研究的基础上进行了拓展。本文的主要创新在于:(1)提出投入导向和产出导向的改进超效率模型,从而彻底解决了已有超效率研究仍存在不可行解的情形,并对数据稳定性进行了灵敏度分析;(2)提出最小调整幅度的效率改进模型,考虑在现有投入产出水平基础上,如何进行最小幅度的调整,将无效单元投影到有效前沿面上;(3)提出基于偏好产出的资源配置模型,将额外投入配置到多个单元中,最大限度的提高偏好产出水平;(4)提出两阶段合作效率模型,调整投入在不同阶段的配置,使得两阶段系统的效率最优;(5)提出基于公共权重和标杆集的两种集成DEA排序方法。文章的组织结构如下:
首先综述了数据包络分析在模型方面的发展和当前研究的进展,概括了本文的研究内容和框架结构。
其次,为了克服传统超效率模型存在不可行解的情形,本文提出了VRS假设下的改进超效率模型。当传统模型无可行解时,该模型仍然可行,且得到有效DMUs的超效率;当传统模型有可行解时,该模型得到的结果与传统模型的结果相一致。本文的研究在一定程度上拓展了MalmquiSt productivity index和DEA benchmarking模型的应用范围。
接着研究如何改变现有的投入产出水平,使得无效单元变为有效。提出了效率改进的一般DEA模型,研究如何通过投入产出的变动来帮助决策者进行效率改进,试图寻找最小调整幅度的投影路径来改善无效决策单元的技术效率,从而使得无效单元投影到有效前沿面,变为有效。
然后研究额外投入既定的情形下,如何合理的配置资源,最大限度的提高产出水平。考虑产出中包含决策者偏好和不偏好两类产出的情形,提出一种改进的集中式资源配置模型,以期获得更多的偏好产出,同时限制不偏好产出的水平。文中还提出了基于期望效率改进的集中式资源配置准则,以此来评价不同资源配置模式之间的优劣。
本文还研究了复杂生产中投入的不同配置方式对整个生产的效率以及每个阶段效率的影响。分析了投入可在不同阶段自由配置的两阶段生产过程,提出了几何平均最优意义下的两阶段合作效率模型。分别讨论了非合作环境下不同阶段占据不同地位的情形,构建了基于CCR和BCC模型的两类几何平均合作效率模型,对多阶段生产过程的技术和规模效率都进行了合理的度量。
进一步提出一种基于公共权重的集成DEA模型。同时考虑所有决策单元,希望找到一组权重系数,使得所有单元的总体无效程度最小,达到系统效率最优。由于这组权重是希望所有单元的无效程度最小,即使得系统的无效程度最小,因此可以尽可能消除不同单元对权重的不同偏好,从而最大程度的被所有单元接受。另一方面,还提出了考虑决策者偏好的基于标杆集的排序方法。
最后对论文全文作了总结,说明了论文的几点创新,指出了论文研究的不足之处,并对论文研究的主题在今后可能的研究方向作了展望。
Data Envelopment Analysis is a relatively new "data oriented" approach for evaluating the performance of a set of peer entities called Decision Making Units which convert multiple inputs into multiple outputs. Because it requires very few assumptions, DEA has also opened up possibilities for use by researchers of various academic areas, such as economics, accounting, information management and operation management, etc. Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as hospitals, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc.
On the basis of the previous researches, this dissertation innovate in several aspects: (1) investigate sensitivity analysis using alternative super efficiency model, which deals with the infeasibility of current super efficiency models; (2) project the inefficient DMUs onto efficient production frontier with minimum amelioration; (3) allocate the additional inputs according to the central decision makers in order to maximize desirable outputs, as well as to restrict undesirable outputs; (4) regulate the allocative factor of the inputs freely among different sub-processes to optimize overall efficiency of the whole process; (5) how various weights influence the efficiency of the DMUs. This dissertation is organized as follows:
Firstly, review models and methodologies development within the context of DEA, lay emphasis on current researches of data variation or uncertainty, and generalize the main ideas and innovations of this dissertation.
Secondly, investigate super efficiency model for sensitivity analysis. The section develops a modified super-efficiency DEA model to overcome the infeasibility issue under the assumption of VRS. The newly developed approach yields (i) an optimal solution and a super-efficiency score for efficient DMUs for which feasible solutions do not exist under the original super-efficiency model; and (ii) super-efficiency scores that are equivalent to those from the original super-efficiency model when feasible solutions do exist. To some extent, the DEA Malmquist productivity index, and the DEA benchmarking models.
Thirdly, study the approach to convert inefficient DMUs into efficient by altering current inputs and outputs. A modified model is proposed to re-allocate the inputs and outputs of inefficient DMUs with minimum amelioration by considering the preference of decision makers and other factors which impact the learning process. A heuristic algorithm is proposed to solve the simplified model based upon the modified one.
Next, explore how to allocate the additional resources in order to maximize the outputs. A centralized resource allocation problem is studied focusing on the desirable outputs according to the overall goals of multi-unit organizations. We proposes modified models to reallocate the additional resources based upon the realized production level. Our problem is to find which units are worth reallocating more resources to maximize desirable outputs, as well as to restrict undesirable outputs, of the overall system. An algorithm is proposed to solve the allocation problem. Further, an criterion to evaluate various resource allocation plans by calculating the average expected system efficiency of each plan is provided.
We also discuss various allocations of inputs among two sub-processes and the overall efficiency as well as the efficiencies of different sub stages. We analysis complex production process with two sub-processes connected serially. Cooperative and non-cooperative game theory was steered to manage the relationship among sub-DMUs, and cooperative efficiency was proceeded to match the actual instance well. Several new models are presented to calculate the efficiency of the sub-DMUs in a non-cooperative manner, whereby the upper and lower bounds of the efficiencies are explicitly determined. A geometric average cooperative DEA model is proposed to evaluate the efficiency of the DMUs, and a heuristic parametric linear programming is suggested to solve the cooperative model. Various situations as constant return to scale and various return scale are discussed separately to evaluate technical and scale efficiency.
Further, we investigate how various weights selection influences the efficiency of the DMUs. an integrated DEA model, which aims at minimizing the total inefficient score of all DMUs and correspondingly optimizing the relative system efficiency based upon the common weights. With such common weights, the efficiency of each DMU is evaluated equitably and effectively, as well as the contribution of each DMU to system, and as a result, a complete ranking order is proposed from it. Also, another ranking approach is proposed, considering the preference of decision makers and management practice. Our problem is to find common weights, putting the best practice and preferable information of decision makers into consideration, as well as concerning about the efficiencies of other DMUs, which is more convincible and feasible and can easily be accepted by all DMUs than that derived from traditional DEA models. We expect the common weights resulted from the proposed integrated DEA models could guarantee those DMUs in BS DEA efficient.
Finally, the concluding section of the full dissertation summarizes some of the breakthroughs made in this dissertation, as well as the shortcomings of this paper and the direction of further researches.
引文
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