Research On Theory, Modelling And Application Of Integer DEA

Data envelopment analysis (DEA) is one of the most popular tools to measure the performance of Decision making units (DMU) with considering multiple input and output variables. In the past several decades, thousands of researches have been done to extend DEA theory and apply DEA methodology into all kinds of fields, while many new DEA models were constructed to deal with all kinds of problems. Lozano and Villa firstly propose integer-valued DEA models to measure integer-valued data, which is very common in real-life. After that, many scholars focus on improving the capability of integer-valued DEA models and proposing some new models to improve the accuracy on efficiency results. Also, a lot of application studies have been done based on integer-valued DEA models. However, the existing integer-valued DEA models are not perfect, which still have some shortcomings such as efficiency scores overestimation. In this paper, we have done a lot of researches to fill the gap and solve some problems of the existing integer-valued DEA models. The structure of this paper should be listed as following:Chapter1introduces DEA methodology and its development in the past decades, expose the basic hypothesis and axiom, and then illustrate some original DEA models and their use. After that, we show the importance and difficulties of constructing integer-valued DEA models. We point out the existing integer-valued DEA models and their development and applications in the past several years. Lastly, we briefly provide some problems of existing integer-valued DEA models we have found and. their solutions.In Chapter2, we introduce the preference between different indicators into integer-valued DEA models and propose new models which could be used to evaluate the integer-valued variables with considering the given preference rate from managers. An application study have also been illustrated in this chapter, which use the new presented models to calculate the efficiency of participated nations in Beijing2008Olympic Games.All the traditional integer-valued DEA models are on either input-oriented projection of DMU onto the production frontier by reducing input variables as much as possible while keeping the present output levels, or output-oriented projection that increases output levels at the present input consumption. Chapter3focus on developing integer-valued DEA models that can be used to measure input excesses and output shortfalls simultaneously based on integer dataset.Chapter4focuses on the problem that the existing integer-valued DEA models applied radial projection and access non-radial efficiency results by using a set of slacks which always lend to over-estimation of the efficiency of DMU. We re-establish the possible production set (PPS) and construct a set of non-radial integer-valued DEA models, in which the substitutability between different input variables are also be considered. Finally, an application study has been shown to illustrate the use and advantages of the new proposed models.In Chapter5, we construct a set of three-steps integer-valued DEA models which should be used to measure the fixed-sum outputs which also been restricted to take integer values. Different from the existing fixed-sum DEA model, these models are composed based on the principle of maximizing the efficiency scores of DMU. A simple numerical example has been used in this section to show the use of our iterative models.Chapter6briefly summarize the contribution and the disadvantages of this paper, and then point out the possible improvements in the future.