Research On DEA Efficiency Based On Multi-Objective Programming

Data envelopment analysis (DEA) is a non-parametric technique for measuring and evaluating the relative efficiencies of DMUs which stand for decision making units with common input and output terms. As soon as the DEA method appeared in 1978, with the unique characteristic and superiority, it becomes the focus of study. It has been got rapid development in theory study and application, and now it becomes the common and important analysis tool and research way in management science, system engineering, decision analysis, evaluating technique and other fields. DEA has done its actions that it should do in society developing. Even now, there are many problems should be researched deeply in DEA theory and DEA method. In this dissertation the deeply study on extremely DEA efficient, DEA models based on multi-objective programming, and fuzzy DEA efficiency, will have the academic significance and great practical significance in DEA theory and applications.The main contents of this dissertation are listed below:1. By means of some equivalent propositions on evaluation the DEA extremely efficient of a DMU relative to a reference set grouped by all other DMUs, the robustness analysis of the DMU which is extreme efficient has been studied in this paper. Sufficient and necessary conditions for upward variations of inputs and for downward variations of the outputs of an extremely efficient DMU to remain extremely efficient are presented. Some approaches to judge the DMU whether keeping the extreme efficient after inputs or outputs are changed are illustrated as well, and these approaches don't require the calculation of the inverse optimal basis matrix in [47] and the solution of the linear equations in [100]. It has been applied in AMT(Advanced Manufacturing Technology) evaluation to obtain the variety ranges of inputs and outputs as an example.2. In order to avoid the faults of the traditional DEA models in assessing the relative efficiencies of a DMU to other DMUs. A multiple objective programmingDEA model (MP) has been built. Based on (MP) and other models, some equivalent propositions on evaluation the DEA extremely efficient of a DMU relative to other DMUs have been given. And the sensitivity analysis of the DMU which is extreme efficient has been studied either in this paper.3. Based on the reference set To, from two objectives of input and output, to assess the relative efficiencies of a DMU, a new DEA model based on the biobjective programming has been built, a arithmetic by ideal point methodology to solve the problem has been given, and some qualities about it have been discussed as well.4. The conventional data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making unit (DMU) via single objective linear programming are limited to crisp data. In order to improve assessing the DMU with fuzzy data, we introduce a fuzzy DEA model based on the multiple programming, to transform the fuzzy DEA model to a pessimistic and a optimistic crisp DEA model by applying a cut approach, some qualities about it have been discussed, via which the more information of the inputs and outputs are derived. As an illustration, a numerical example is shown.Via the studies in this dissertation, some beneficial discussions have been done on the DEA theoretics bases for its deeper applications. The Robustness of DEA extremely efficiency, reflected the variety ranges of input or output vectors for an extremely efficient DMU to remain the extremely DEA efficiency. It would have definite guidance meaning for jugement decision-making in practice. Compared with the given-methods, the approaches showen in the paper reduced workload. It is a practicality-doable one.In allusion to localization in conventional DEA models in evaluating the relatively efficiencies of a DMU to other DMUs, based on the new multiple objective programming DEA model, some propositions on DMU which was extremely DEA efficient have been studied. It would be a new viable way in estimating DEA efficiency or extremely DEA efficiency for a DMU, it could beused in improving on a DMU which was not DEA efficient either.The new biobjective programming DEA model (CCR) based on reference set To, given a new method in discussing the DEA efficiency. This was a simple and practical way, the ratios of downward input variations and upward output variations have been obtained, and it could be extended in multiple objective programming DEA models.The new fuzzy DEA model based on multiple objective programming could estimate the DEA efficiency for DMUs with fuzzy data. The varieties of the components in input vector and output vector were shown under the possible level a. More information of the DMU could be derived.