DEA-based Research On Ranking Dmus And Performance Measurement Of Two-stage Network Structures

In real-world situations, many governmental/non-governmental organizations, corporations, health care sectors, etc., possess a series of homogeneous operating units that consume the same set of resources to produce the same set of products, such as parallel-level universities, branch banks, and supermarket chains. Decision makers are always quite interested in the differentiating and ranking of their performance. Furthermore, focusing on the internal structures of these operating units or decision making units (DMUs), two-stage processes with intermediate measures are one of the most representative types. Comparatively speaking, data envelopment analysis (DEA) is an effective and relatively objective mathematical programming method to evaluate the efficiency for DMUs with multiple inputs and multiple outputs. Based on the basic framework of DEA theory, this paper studies ranking DMUs and performance measurement of two-stage network structures.This thesis involves seven chapters, and the essence is summarized as follows.Chapter 1 firstly introduces some important conceptions, analysis mechanisim, major models and application areas of DEA; then it discusses the significance and main achievements in DEA-based ranking methods and two-stage efficiency analysis.Chapter 2, 3 and 4 propose three different DEA-based methods to differentiating and ranking decision making units, especially those efficient ones. Chapter 2 extends Tone's (2002) super-efficiency model into the additive DEA model proposed by Charnes et al. (1982), and develops additive slacks-based measure of (SBM) super-efficiency DEA models. According to the corresponding results, an additive SBM super-efficiency is introduced to further discriminate the efficient DMUs. Based upon the research on slacks in DEA models, Chapter 3 defines aδ-efficiency score and considers the influence of eachδ-efficient DMU on all other DMUs. The measurement on such influence is used to differentiate the efficient DMUs, and achive a thorough ranking on all DMUs. Chapter 4 finds a way to measure the influence of one efficient DMU on all the other DMUs in order to discriminate among efficnet DMUs. The more influential one efficient DMU on the remaining DMUs, the more important it is viewed as, thus a higher ranking it gets. The numerical examples and real-world applications illustrate that these three ranking methods are reasonable and demonstrate farely good differenting effects. They are able to provide support for decision makers in evaluating DMUs'performance, and to assist them in making corresponding managerial decisions.Chapter 5 and 6 discuss the overall efficiency and efficiency decomposition in two-stage production structures. From the perspective of game theory, Chapter 5 applies Nash bargaining model into the efficiency analysis within a two-stage process.Two individual stages are viewed as two players bargaining with each other for a better payoff from a cooperative manner. A Nash bargaining DEA model is proposed to measure the efficiency score for each individual stage and the overall process. It can be proved that in the case of only one intermediate measure, the Nash bargaining DEA approach yields the same efficiency results as obtained from the separately-applied standard DEA approach. Focusing on the two-stage network processes with shared resources, Chapter 6 develops a set of DEA models to obtain the overall efficiency and the corresponding efficiency decomposition within this typical structure. The proposed models reasonably and correctly consider the roles taken by intermediate measures and shared inputs, and effectively avoid the possible conflict resulted from the intermediate measures.Chapter 7 summarized the main research work in this thesis, and points out possible extensions for future study and improvement.The major contributions of this thesis are briefly summarized as follows: (1) In the case of multiple efficient DMUs, an additive slacks-based measure of super-efficiency DEA model and the corresponding additive super-efficiency are proposed in order to further differentiate the efficient DMUs; (2) A way is found to measure the influence of one efficient DMU upon all other DMUs, based on which a further discrimination among all efficient DMUs can be achieved; (3) From the perspective of game theory, a Nash bargaining DEA model is proposed to measure the efficiency score for each individual stage and the overall process with a two-stage structure; (4) It is proved that in the case of only one intermediate measure, the Nash bargaining DEA approach yields the same efficiency results as obtained from the separately-applied standard DEA approach; (5) An efficiency analysis and an efficiency decomposition are studied in a two-stage network structure with shared resources and intermediate measures.