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Research on Field-Oriented (Data Envelopment Analysis) DEA Method

Author: ZhangQiPing
Tutor: LiuYeZheng
School: Hefei University of Technology
Course: Management Science and Engineering
Keywords: DEA(Data Envelopment Analysis) DMU(Decision Making Unit) Relative Efficiency Industry Dynamic Evaluation Decision-making Program Optimization CrossEfficiency Adaptive Group Evaluating Fixed Cost Allocation
CLC: C934
Type: PhD thesis
Year: 2012
Downloads: 47
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Abstract


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.

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