Several Issues On Data Envelopment Analysis

Data Envelopment Analysis is a relatively new "data oriented" approach for evaluating the performance of a set of peer entities called Decision Making Units which convert multiple inputs into multiple outputs. Because it requires very few assumptions, DEA has also opened up possibilities for use by researchers of various academic areas, such as economics, accounting, information management and operation management, etc. Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as hospitals, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc.On the basis of the previous researches, this dissertation innovate in several aspects: (1) investigate sensitivity analysis using alternative super efficiency model, which deals with the infeasibility of current super efficiency models; (2) project the inefficient DMUs onto efficient production frontier with minimum amelioration; (3) allocate the additional inputs according to the central decision makers in order to maximize desirable outputs, as well as to restrict undesirable outputs; (4) regulate the allocative factor of the inputs freely among different sub-processes to optimize overall efficiency of the whole process; (5) how various weights influence the efficiency of the DMUs. This dissertation is organized as follows:Firstly, review models and methodologies development within the context of DEA, lay emphasis on current researches of data variation or uncertainty, and generalize the main ideas and innovations of this dissertation.Secondly, investigate super efficiency model for sensitivity analysis. The section develops a modified super-efficiency DEA model to overcome the infeasibility issue under the assumption of VRS. The newly developed approach yields (i) an optimal solution and a super-efficiency score for efficient DMUs for which feasible solutions do not exist under the original super-efficiency model; and (ii) super-efficiency scores that are equivalent to those from the original super-efficiency model when feasible solutions do exist. To some extent, the DEA Malmquist productivity index, and the DEA benchmarking models.Thirdly, study the approach to convert inefficient DMUs into efficient by altering current inputs and outputs. A modified model is proposed to re-allocate the inputs and outputs of inefficient DMUs with minimum amelioration by considering the preference of decision makers and other factors which impact the learning process. A heuristic algorithm is proposed to solve the simplified model based upon the modified one.Next, explore how to allocate the additional resources in order to maximize the outputs. A centralized resource allocation problem is studied focusing on the desirable outputs according to the overall goals of multi-unit organizations. We proposes modified models to reallocate the additional resources based upon the realized production level. Our problem is to find which units are worth reallocating more resources to maximize desirable outputs, as well as to restrict undesirable outputs, of the overall system. An algorithm is proposed to solve the allocation problem. Further, an criterion to evaluate various resource allocation plans by calculating the average expected system efficiency of each plan is provided.We also discuss various allocations of inputs among two sub-processes and the overall efficiency as well as the efficiencies of different sub stages. We analysis complex production process with two sub-processes connected serially. Cooperative and non-cooperative game theory was steered to manage the relationship among sub-DMUs, and cooperative efficiency was proceeded to match the actual instance well. Several new models are presented to calculate the efficiency of the sub-DMUs in a non-cooperative manner, whereby the upper and lower bounds of the efficiencies are explicitly determined. A geometric average cooperative DEA model is proposed to evaluate the efficiency of the DMUs, and a heuristic parametric linear programming is suggested to solve the cooperative model. Various situations as constant return to scale and various return scale are discussed separately to evaluate technical and scale efficiency.Further, we investigate how various weights selection influences the efficiency of the DMUs. an integrated DEA model, which aims at minimizing the total inefficient score of all DMUs and correspondingly optimizing the relative system efficiency based upon the common weights. With such common weights, the efficiency of each DMU is evaluated equitably and effectively, as well as the contribution of each DMU to system, and as a result, a complete ranking order is proposed from it. Also, another ranking approach is proposed, considering the preference of decision makers and management practice. Our problem is to find common weights, putting the best practice and preferable information of decision makers into consideration, as well as concerning about the efficiencies of other DMUs, which is more convincible and feasible and can easily be accepted by all DMUs than that derived from traditional DEA models. We expect the common weights resulted from the proposed integrated DEA models could guarantee those DMUs in BS DEA efficient.Finally, the concluding section of the full dissertation summarizes some of the breakthroughs made in this dissertation, as well as the shortcomings of this paper and the direction of further researches.