Research On The Matrix-type Network DEA Model, Method And Applications

Efficiency evaluation is reagarded as an important task of economic and social activities, and also is a difficult task. The paper studies how to evaluate the efficiency of the decision-making unit in the economic and social activities. The method used in the paper is Data Envelopment Analysis (DEA) method. DEA is a useful tool to evaluate the efficiency of the comparable DMUS, and has become one of the most important methods for efficiency evaluation since the first DEA model was established in1978.The traditional DEA models regard DMUS as the whole and ignore the internal inputs and outputs of the DMUs, then the efficiency scores are not reflect the true efficiency scores of the DMUs. The purpose of the paper is to open the DMUs and put forward DEA models can effectively evaluate the efficiency of the DMUs, the DEA method can be extended to the evaluation of the complex systems.So-called matrix-type network system is a kind of common complex system in the economic and social activities, such as circulatory system, supply chain system based on life cycle et al. This system has no starting subsystem or ending subsystem, which has some subsystems with external inputs and outputs. And there are some kinds of bidirectional supply and demand relationships between each two subsystems. This paper will construct matrix-type network DEA models that more effective and suitable for the management practice base on the characteristics of the system. According to the different study methods, the main contents of the paper can be divided into five chapters, including analysis of the system, establishment and analysis of the NCCR model, establishment and analysis of the NCCGSS model, establishment and analysis of the NSBM model and the practical application of the models in the economic society.In Chapter3, the complex system construct will be analyzed and corresponding production possibility set theory and muti-objective programming are built based on religious mathematical and economic logic.In Chapter4to6, the NCCR model, the NCCGSS model and the NSBM model are built aiming to the characters of matrix-type network system; numerical calculation and validity judgment methods is proposed according to the models; the equivalence between matrix-type network DEA efficiency and Pareto efficient solutions is proved and the numerical examples analysis are given at the same time.In Chapter7, the paper will give some empirical research to evaluate the performance of agricultural recycle economy system, the second industry based inputs-outputs table and electric power enterprises. The practical significance of the results is given and also the practical application value of the study in the paper is shown.Not only the matrix-type network DEA model and method system theoretically will be created but also some quantitative methods will be given that can used to evaluate the management efficiency and decision-making validity of macro-economy or micro-economy recycle system.In short, in this paper, not only the matrix-type network DEA model and method system theoretically are created but also some quantitative methods are given that can used to evaluate the management efficiency and decision-making validity of macro-economy or micro-economy recycle system.