DEA-based Evaluation On Fixed Outputs’ DMU And Allocation With Satisfaction Degree

In some organizations, in order to save costs, they tend to build a common platform for resources sharing. At this time, each decision-making unit (DMU for short) must bear the corresponding cost of common expenses when obtaining benefits from the common platform. For example, bank headquarter will build a united trading systems for its branches. Therefore, to design a fair and reasonable cost-allocation mechanism is particularly necessary. Data envelopment analysis (DEA for short) has been proved to be a more and more important tool to solve this allocation problem. However, traditional DEA-based approaches for fixed cost allocation are only from the perspective of efficiency, which do not consider whether the DMU satisfies with the results of allocation. In order to make the results to be more reasonable, this paper firstly proposes a fixed cost allocation method based on DEA and satisfaction degree from the perspective of DMUs’satisfaction relative to the results of allocation.In real life, we often encounter with the situation that some DMUs whose outputs’ sum are fixed. For example, the sum of an industry’s market share is a constant (1). In the fixed outputs environment, one DMU expanding its outputs may reduce others’ outputs to make up for the increase. However, traditional DEA models do not take this constraint into account during the evaluation, and the existing researches relative to this field are rare, therefore, this paper also will research on evaluating DMUs with fixed outputs.This paper contains six chapters, and the main contents of each chapter are displayed as follows.In the first chapter, we introduce the basic knowledge about data envelopment analysis (DEA), including some basic concepts, some basic models, the basic principle of evaluation as well as some relative applications of DEA. Then, we view the above knowledge as the background of our research and clarify two key points of this study:fixed cost allocation and DMUs with fixed outputs evaluation. Lastly, we respectively introduce the meaning and the status of these two researches briefly.Chapter2proposes a fixed cost allocation approach based on DEA and satisfaction degree, which firstly consider the DMUs’satisfaction degree to the results of allocation. In the beginning of this chapter, we calculate the maximum and minimum fixed cost of each DMU according to allocation scheme equations, which are used to constitute the cost interval. Then we define the concept of satisfaction degree by the cost interval. This concept meets the following two conditions. One is that the DMU most satisfies with its cost allocation when its satisfaction degree reaches its maximum value1. The other is that, on the contrary, the DMU most dissatisfies with its cost allocation when its satisfaction degree reaches its minimum value0. Then we construct a Maxmin model based on this satisfaction degree. In light of this model, we get a unique allocation, which can be accepted by all DMUs。Chapter3proposes a method named equilibrium efficiency frontier DEA (EEFDEA) to evaluate DMUs with fixed outputs. First of all, we review some of prior DEA literatures relative to evaluation on DMUs with fixed outputs and point out the shortages of them such as they evaluated DMUs based on different efficient frontiers and so on. To fill those gapes, this chapter first proposes an equilibrium efficiency frontiers constructed model based on minimum adjustment strategy. By this model, all DMUs can achieve efficient frontier one by one with a given order and, finally, an equilibrium efficient frontier is formed. Then all DMUs are evaluated based on such a common equilibrium efficient frontier.Consider the proposed EEFDEA method in Chapter3needs multiple steps and a given order for constructing a common equilibrium frontier, in order to simplify steps of equilibrium frontier achievement, Chapter4proposes a general equilibrium efficient frontier DEA (GEEFDEA for short) approach to evaluate DMUs with fixed outputs. According to GEEFDEA method, the equilibrium efficient frontier can be achieved by only one step and without any given adjusted order, which reduce the computational complexity greatly. Finally, we applied GEEFDEA method to2012London Olympic Games. Consider the importance of three fixed outputs of Olympics (gold, silver and bronze medal) is different, we add the constraint of assurance region in the model to ensure the results of evaluation more reasonable.Chapter5extends the fixed outputs in Chapter4to undesirable outputs. In the beginning of this chapter, we review some DEA literatures relative to undesirable outputs. From literatures we find that although there have been so many the researches about undesirable outputs, few researches consider the situation regards to undesirable fixed outputs. Therefore, this chapter proposes a GEEFDEA model which takes undesirable fixed outputs into account. The proposed model not only maintains all advantages of GEEFDEA model, but also overcomes the shortage in prior models that those models may appear infeasibility solution when evaluating DMUs with undesirable fixed outputs. In the end, we utilize the proposed model to evaluate the environmental efficiency of industry of31provinces and autonomous regions.Chapter6is conclusion and future research. We first conclude the main contents in all previous chapters, respectively. Meanwhile, we point out the shortcomings of this study. In order to overcome these shortcomings, we put forward some key points for future research.The main innovations of this paper are listed as follows:1) this paper firstly takes DMUs’satisfaction degree to the results of allocation into account when allocating fixed cost via DEA method. We get a unique and acceptable allocation.2) The proposed equilibrium efficiency frontier DEA approach is unique one which can satisfy the following four conditions simultaneously when evaluating competitive DMUs with fixed outputs:(i) evaluating based on a common efficient frontier,(ii) taking account of fixed outputs,(iii) extending fixed outputs from one dimension to multi-dimensions, and (iv) providing a full rank order of DMUs.3) This paper firstly proposes a general equilibrium efficiency frontier DEA approach. It not only maintains all advantages of EEFDEA model, but also reduces the computational complexity greatly since the equilibrium efficient frontier can be achieved by only one step and without any given adjusted order.4) This paper firstly proposes undesirable fixed outputs GEEFDEA model which overcomes the shortage in prior models that those models may appear infeasibility solution when evaluating DMUs with undesirable fixed outputs.