面向领域的数据包络分析（DEA）方法研究
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摘要
数据包络分析(Data Envelopment Analysis, DEA)作为一种典型的多准则决策方法,具有很强的实际应用价值,被广泛运用于各个领域解决实际决策问题。本文主要针对工业生产系统有效性评价、决策方案优选及固定成本分摊三个热点应用领域展开DEA方法研究工作。针对上述三个应用领域,本文以创新性的管理思维发掘出决策任务命题,提出与以往不同的决策准则,设计出能够获得全面性、客观性和易接受性决策结果的求解思路,对基础DEA模型进行选择、修改和重构,构建具可操作性的适于问题解决的领域DEA模型。本文具体研究内容如下：
(1)面向工业生产系统有效性评价领域,提出面向社会经济发展水平的工业生产DEA有效性评价策略。该策略的主要依据将工业生产对环境的负外部性和对能源的消耗纳入工业生产有效性评价,且在不同社会经济发展水平下环境负外部性和能源的消耗的参与度不同的评价思想。通过将工业生产系统的投入要素分为能源投入(以吨标准煤计量)和非能源投入,并将工业产品看作期望产出,排放的污染物看作非期望产出,定义能源投入／污染物产出指标动态加权值,构建面向社会经济发展水平的考虑污染物产出动态公共参与度,及同时考虑污染物产出和能源投入动态公共参与度的工业生产有效性DEA动态评价模型,并进行多轮次的有效性评价来实现该评价策略。实验分析表明,这种评价策略全面客观地反映出工业生产系统在不同节能减排标准下的有效性,为决策者制定政策提供更完善的决策信息。
(2)面向决策方案优选领域,以DEA交叉效率评价策略为基础,研究了决策方案排序优选的自适应群评价交叉效率模型。该模型将交叉效率评价方法中自评互评相结合的评价模式看作群决策过程,即每个决策方案既是一个被评对象,又是一个决策“专家”,提出了一种决策方案交叉效率的自适应群评价方法,将决策方案偏好权重的确定和交叉效率有效性分值的去平均化集结作为同一个决策过程,根据每个决策方案的评价结果与群体评价结果的接近程度,同步迭代调整决策方案的“专家”权重和决策方案自评产生的、并提供给其他被评价决策方案的一组确定的偏好指标权重。该模型收敛效果良好,能得到客观稳定的决策方案交叉效率有效性分值及排序,且克服了传统交叉效率评价方法因决策方案偏好权重不唯一而难以操作,因交叉效率有效性分值平均化集结而难以被接受的缺陷。该模型在识别决策方案的可靠性方面具有良好的性能,能够为决策者的方案评价排序决策提供决策支持。
(3)面向固定成本分摊领域,进一步研究了考虑相关投入的决策单元固定成本分摊DEA模型。建模前提是将分摊的固定成本与决策单元相关投入要素合并。为了克服Li等学者的固定成本分摊体系中未能保证成本分摊后决策单元有效性的提高以不降低其它决策单元有效性为前提,以及未能保证在同等规模下,从固定成本使用中的获益更多的分摊后高有效性决策单元比获益更少的低有效性决策单元尽可能承担更多固定成本这两方面的缺陷。证明了当分摊的成本和相关投入要素合并时,决策单元个体分摊后个体CCR有效性和决策单元整体分摊后整体CCR有效性均为关于待分摊固定成本额的递增函数,于是可知当分摊的成本和相关投入要素合并时,一定存在足够大的待分摊固定成本,使得决策单元分摊后个体CCR有效性和分摊后整体CCR有效性均可达到DEA有效；建立了面向虚拟固定成本并同时满足决策单元整体理性和个体理性的成本分摊方案集；提出按决策单元分摊虚拟固定成本额的比例分摊实际的固定成本额的分摊策略；引入纳什讨价还价博弈理论,得出了固定成本的分摊纳什谈判解。最后的算例表明本分摊方法公平可接受,并且弥补了Li等学者的分摊策略中的两方面缺陷。
(4)面向固定成本分摊领域,研究了决策单元有效性和受益性联合决策的固定成本分摊DEA模型。为了克服现有的基于DEA方法解决固定成本分摊问题的研究不能确保在全面客观地反映决策单元投入特征的基础上考虑成本分摊决策；且只考虑将决策单元在固定成本投入后周期的有效性作为固定成本分摊决策的基础的不足,假设已知固定成本投入前后两个连续周期内的决策单元投入/产出,将待分摊的固定成本均等计入决策单元的各项投入要素中。以此假设为建模前提,首先给出考虑分摊固定成本的决策单元超CCR有效性评价模型；继而构建决策单元相对受益识别模型,它面向投入产出的要素变化量和分摊的固定成本；在此基础上提出了同时考虑决策单元有效性和受益性的基于DEA纳什讨价还价合作博弈理论的固定成本分摊模型。实验分析结果表明本章提出的固定成本分摊方法是可行且可接受的。
As a typical multi-criteria evaluation method, Data Envelopment Analysis (DEA) has a strong practical application value, which is widely used in various fields to solve practical decision-making problems. This dissertation commences the DEA methods studies mainly for the three hot application fields of evaluating the effectiveness of industry production systems, decision-making program optimization, and fixed cost allocation. In these three application fields, this dissertation explores the decision-making task propositions by innovative management thinking, and proposes different decision-making criteria, and designs the solving ideas which can obtain the decision-making results of comprehensiveness, objectivity and easy acceptance. Then the basic DEA models are selected, modified or reconstructed. Finally the operable field-oriented DEA models which are suitable for problem-solving are built. The detailed researches of this dissertation are as follows:
(1) In the effectiveness evaluation of industrial production systems-oriented field, the effectiveness evaluation strategy for industrial production systems under the condition of dynamically changing the level of socio-economic development is proposed, the basis of which is that the negative externalities to the environment and energy consumption in the production process should be brought into the efficiency evaluation of the industry production sestems, and the participation level of the negative externalities to the environment and the energy consumption should be determined by the level of socio-economic development. By deviding input elements of the industrial production systems into the energy input(measured by tons of standard coal) and non-energy inputs, treating industrial products as desirable outputs, treating the emissed pollutants as undesirable outputs, and defining dynamic weighted values of energy input/pollutants output indicators, the level of socio-economic development oriented DEA evaluation model for industrial production systems' dynamic relative efficiency with dynamic common participation level of negative externalities to the environment, and simultaneously with dynamic common participation level of negative externalities to the environment&energy input is constructed. By carrying out multi-round of effectiveness evaluations, the above evaluation strategy is achieved. The numerical example demonstrated that this evaluation strategy proposed comprehensively and objectively reflects the effectiveness of industry production sestems under different energy saving and emission reduction criterion, which also provides decision makers with richer decision-making information for policy-making.
(2) In the decision-making program optimization-oriented field, using DEA cross efficiency evaluation strategy, decision-making program optimization model based on an adaptive cross-efficiency group evaluation method is proposed. The adaptive model treats the evaluation model which combines self-evaluation and peer-evaluation as a group decision making process, in which each alternative decision-making program is treated as an "expert" and an opinion object simultaneously, and then an adaptive group evaluating algorithm for alternative decision-making programs' cross efficiency is proposed. According to the close degree of evaluation results which are from each alternative decision-making program and alternative decision-making programs group, the algorithm gets "expert" weight for each alternative decision-making program and deterministic preferential index weight systems for each alternative decision-making program, which are used to evaluate themselves and other alternative decision-making programs, in a single decision making process by iterative adjustments. The experiment illustrates that our algorithm can efficiently converge, which can get objective and stable ultimate efficiency scores to rank all alternative decision-making programs deterministically. The adaptive model can overcome the traditional cross efficiency evaluation method's lacking maneuverability due to that the preferential weight system is always not unique for some or all alternative decision-making programs, and its lacking acceptability due to using the ultimate average cross efficiency scores to rank all alternative decision-making programs. The adaptive model has a good performance in identifying the reliabilities of decision-making programs, and it can provide decision makers with powerful decision making support in evaluating and sorting alternative decision-making programs.
(3) In the fixed cost allocation-oriented field, this dissertation has further studied the DEA model for allocating the fixed cost as a complement of other cost inputs among DMUs. The modeling premise is to combine the allocated fixed cost with one of the current inputs of DMUs which is homogeneous with the fixed cost. To address the two defects in the strategy from Li et al that it can not ensure some DMUs do not improve their effectiveness after cost allocation with the precondition of reducing other DMUs' effectiveness, and it either can not ensure in the same scale, the DMUs which have higher effectiveness after cost allocation actually take on the fixed costs as more as possible than those DMUs which have lower effectiveness after cost allocation, because the former DMUs benefit more than the latter DMUs. Firstly we proved that when the allocated cost and one of the current inputs are combined into one input element, the individual CCR efficiency of each DMU and the overall CCR efficiency of the organization are all the increasing functions of the amount of the fixed cost. So the conclusion can be inferred that when the allocated cost and one of the current inputs are combined, there must be some fixed costs large enough to make the CCR efficiency of each DMU and the CCR efficiency of the overall organization achieve DEA efficient simultaneously. Then the virtual fixed cost oriented cost allocation plans set was constructed, which simultaneously satisfies individual rationality of each DMU and the collective rationality of the organization. Then the strategy that DMUs share the actual fixed cost with the proportion they share the virtual fixed cost was proposed. The fixed cost allocation model was proposed based on Nash bargaining game theory, which can get the Nash bargaining solutions for fixed cost allocation. The final example shows that the cost allocation method proposed is fair and acceptable, and it also can make up for the two defects in the strategy from Li et al.
(4) In the fixed cost allocation-oriented field, this dissertation has studied the DEA model for allocating the fixed cost among DMUs jointly considering relative efficiency and relative benefiting. Current studies on the problem of allocating the fixed cost among DMUs always can't ensure that the cost allocating decision-making to be based on the comprehensive and objective reflection of the DMUs' input features, and also only take the efficiency of DMUs in the period after the cost input as the basis of cost allocating decision-making. This dissertation suppose the production processes of DMUs during the two continuous periods which are before and after the fixed cost input are available, and the modeling premise is that combining the allocated cost with other input elements averagely. Firstly, the DMUs' super CCR efficiency evaluation model considering allocated cost is given. Then the input-output variation and allocated fixed cost oriented DMUs' relative benefit recognition model is built. Based on the Nash bargaining cooperative game theory, the cost allocation model considering relative efficiency and benefit is proposed. The approach is illustrated by a numerical example, which figures that the approach is available and acceptable.
(1)面向工业生产系统有效性评价领域,提出面向社会经济发展水平的工业生产DEA有效性评价策略。该策略的主要依据将工业生产对环境的负外部性和对能源的消耗纳入工业生产有效性评价,且在不同社会经济发展水平下环境负外部性和能源的消耗的参与度不同的评价思想。通过将工业生产系统的投入要素分为能源投入(以吨标准煤计量)和非能源投入,并将工业产品看作期望产出,排放的污染物看作非期望产出,定义能源投入／污染物产出指标动态加权值,构建面向社会经济发展水平的考虑污染物产出动态公共参与度,及同时考虑污染物产出和能源投入动态公共参与度的工业生产有效性DEA动态评价模型,并进行多轮次的有效性评价来实现该评价策略。实验分析表明,这种评价策略全面客观地反映出工业生产系统在不同节能减排标准下的有效性,为决策者制定政策提供更完善的决策信息。
(2)面向决策方案优选领域,以DEA交叉效率评价策略为基础,研究了决策方案排序优选的自适应群评价交叉效率模型。该模型将交叉效率评价方法中自评互评相结合的评价模式看作群决策过程,即每个决策方案既是一个被评对象,又是一个决策“专家”,提出了一种决策方案交叉效率的自适应群评价方法,将决策方案偏好权重的确定和交叉效率有效性分值的去平均化集结作为同一个决策过程,根据每个决策方案的评价结果与群体评价结果的接近程度,同步迭代调整决策方案的“专家”权重和决策方案自评产生的、并提供给其他被评价决策方案的一组确定的偏好指标权重。该模型收敛效果良好,能得到客观稳定的决策方案交叉效率有效性分值及排序,且克服了传统交叉效率评价方法因决策方案偏好权重不唯一而难以操作,因交叉效率有效性分值平均化集结而难以被接受的缺陷。该模型在识别决策方案的可靠性方面具有良好的性能,能够为决策者的方案评价排序决策提供决策支持。
(3)面向固定成本分摊领域,进一步研究了考虑相关投入的决策单元固定成本分摊DEA模型。建模前提是将分摊的固定成本与决策单元相关投入要素合并。为了克服Li等学者的固定成本分摊体系中未能保证成本分摊后决策单元有效性的提高以不降低其它决策单元有效性为前提,以及未能保证在同等规模下,从固定成本使用中的获益更多的分摊后高有效性决策单元比获益更少的低有效性决策单元尽可能承担更多固定成本这两方面的缺陷。证明了当分摊的成本和相关投入要素合并时,决策单元个体分摊后个体CCR有效性和决策单元整体分摊后整体CCR有效性均为关于待分摊固定成本额的递增函数,于是可知当分摊的成本和相关投入要素合并时,一定存在足够大的待分摊固定成本,使得决策单元分摊后个体CCR有效性和分摊后整体CCR有效性均可达到DEA有效；建立了面向虚拟固定成本并同时满足决策单元整体理性和个体理性的成本分摊方案集；提出按决策单元分摊虚拟固定成本额的比例分摊实际的固定成本额的分摊策略；引入纳什讨价还价博弈理论,得出了固定成本的分摊纳什谈判解。最后的算例表明本分摊方法公平可接受,并且弥补了Li等学者的分摊策略中的两方面缺陷。
(4)面向固定成本分摊领域,研究了决策单元有效性和受益性联合决策的固定成本分摊DEA模型。为了克服现有的基于DEA方法解决固定成本分摊问题的研究不能确保在全面客观地反映决策单元投入特征的基础上考虑成本分摊决策；且只考虑将决策单元在固定成本投入后周期的有效性作为固定成本分摊决策的基础的不足,假设已知固定成本投入前后两个连续周期内的决策单元投入/产出,将待分摊的固定成本均等计入决策单元的各项投入要素中。以此假设为建模前提,首先给出考虑分摊固定成本的决策单元超CCR有效性评价模型；继而构建决策单元相对受益识别模型,它面向投入产出的要素变化量和分摊的固定成本；在此基础上提出了同时考虑决策单元有效性和受益性的基于DEA纳什讨价还价合作博弈理论的固定成本分摊模型。实验分析结果表明本章提出的固定成本分摊方法是可行且可接受的。
As a typical multi-criteria evaluation method, Data Envelopment Analysis (DEA) has a strong practical application value, which is widely used in various fields to solve practical decision-making problems. This dissertation commences the DEA methods studies mainly for the three hot application fields of evaluating the effectiveness of industry production systems, decision-making program optimization, and fixed cost allocation. In these three application fields, this dissertation explores the decision-making task propositions by innovative management thinking, and proposes different decision-making criteria, and designs the solving ideas which can obtain the decision-making results of comprehensiveness, objectivity and easy acceptance. Then the basic DEA models are selected, modified or reconstructed. Finally the operable field-oriented DEA models which are suitable for problem-solving are built. The detailed researches of this dissertation are as follows:
(1) In the effectiveness evaluation of industrial production systems-oriented field, the effectiveness evaluation strategy for industrial production systems under the condition of dynamically changing the level of socio-economic development is proposed, the basis of which is that the negative externalities to the environment and energy consumption in the production process should be brought into the efficiency evaluation of the industry production sestems, and the participation level of the negative externalities to the environment and the energy consumption should be determined by the level of socio-economic development. By deviding input elements of the industrial production systems into the energy input(measured by tons of standard coal) and non-energy inputs, treating industrial products as desirable outputs, treating the emissed pollutants as undesirable outputs, and defining dynamic weighted values of energy input/pollutants output indicators, the level of socio-economic development oriented DEA evaluation model for industrial production systems' dynamic relative efficiency with dynamic common participation level of negative externalities to the environment, and simultaneously with dynamic common participation level of negative externalities to the environment&energy input is constructed. By carrying out multi-round of effectiveness evaluations, the above evaluation strategy is achieved. The numerical example demonstrated that this evaluation strategy proposed comprehensively and objectively reflects the effectiveness of industry production sestems under different energy saving and emission reduction criterion, which also provides decision makers with richer decision-making information for policy-making.
(2) In the decision-making program optimization-oriented field, using DEA cross efficiency evaluation strategy, decision-making program optimization model based on an adaptive cross-efficiency group evaluation method is proposed. The adaptive model treats the evaluation model which combines self-evaluation and peer-evaluation as a group decision making process, in which each alternative decision-making program is treated as an "expert" and an opinion object simultaneously, and then an adaptive group evaluating algorithm for alternative decision-making programs' cross efficiency is proposed. According to the close degree of evaluation results which are from each alternative decision-making program and alternative decision-making programs group, the algorithm gets "expert" weight for each alternative decision-making program and deterministic preferential index weight systems for each alternative decision-making program, which are used to evaluate themselves and other alternative decision-making programs, in a single decision making process by iterative adjustments. The experiment illustrates that our algorithm can efficiently converge, which can get objective and stable ultimate efficiency scores to rank all alternative decision-making programs deterministically. The adaptive model can overcome the traditional cross efficiency evaluation method's lacking maneuverability due to that the preferential weight system is always not unique for some or all alternative decision-making programs, and its lacking acceptability due to using the ultimate average cross efficiency scores to rank all alternative decision-making programs. The adaptive model has a good performance in identifying the reliabilities of decision-making programs, and it can provide decision makers with powerful decision making support in evaluating and sorting alternative decision-making programs.
(3) In the fixed cost allocation-oriented field, this dissertation has further studied the DEA model for allocating the fixed cost as a complement of other cost inputs among DMUs. The modeling premise is to combine the allocated fixed cost with one of the current inputs of DMUs which is homogeneous with the fixed cost. To address the two defects in the strategy from Li et al that it can not ensure some DMUs do not improve their effectiveness after cost allocation with the precondition of reducing other DMUs' effectiveness, and it either can not ensure in the same scale, the DMUs which have higher effectiveness after cost allocation actually take on the fixed costs as more as possible than those DMUs which have lower effectiveness after cost allocation, because the former DMUs benefit more than the latter DMUs. Firstly we proved that when the allocated cost and one of the current inputs are combined into one input element, the individual CCR efficiency of each DMU and the overall CCR efficiency of the organization are all the increasing functions of the amount of the fixed cost. So the conclusion can be inferred that when the allocated cost and one of the current inputs are combined, there must be some fixed costs large enough to make the CCR efficiency of each DMU and the CCR efficiency of the overall organization achieve DEA efficient simultaneously. Then the virtual fixed cost oriented cost allocation plans set was constructed, which simultaneously satisfies individual rationality of each DMU and the collective rationality of the organization. Then the strategy that DMUs share the actual fixed cost with the proportion they share the virtual fixed cost was proposed. The fixed cost allocation model was proposed based on Nash bargaining game theory, which can get the Nash bargaining solutions for fixed cost allocation. The final example shows that the cost allocation method proposed is fair and acceptable, and it also can make up for the two defects in the strategy from Li et al.
(4) In the fixed cost allocation-oriented field, this dissertation has studied the DEA model for allocating the fixed cost among DMUs jointly considering relative efficiency and relative benefiting. Current studies on the problem of allocating the fixed cost among DMUs always can't ensure that the cost allocating decision-making to be based on the comprehensive and objective reflection of the DMUs' input features, and also only take the efficiency of DMUs in the period after the cost input as the basis of cost allocating decision-making. This dissertation suppose the production processes of DMUs during the two continuous periods which are before and after the fixed cost input are available, and the modeling premise is that combining the allocated cost with other input elements averagely. Firstly, the DMUs' super CCR efficiency evaluation model considering allocated cost is given. Then the input-output variation and allocated fixed cost oriented DMUs' relative benefit recognition model is built. Based on the Nash bargaining cooperative game theory, the cost allocation model considering relative efficiency and benefit is proposed. The approach is illustrated by a numerical example, which figures that the approach is available and acceptable.
引文
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