مقاله انگلیسی رایگان در مورد یک مدل DEA برای تصمیم گیری – اسپرینگر 2017

Based on the CCR model, we propose an extended data envelopment analysis to evaluate the efficiency of decision making units with historical input and output data. The contributions of the work are threefold. First, the input and output data of the evaluated decision making unit are variable over time, and time series method is used to analyze and predict the data. Second, there are many sample decision making units, which are divided into several ordered sample standards in terms of production strategy, and the constraint condition consists of one of the sample standards. Furthermore, the efficiency is illustrated by considering the efficiency relationship between the evaluated decision making unit and sample decision making units from constraint condition. Third, to reduce the computation complexity, we introduce an algorithm based on the binary search tree in the model to choose the sample standard that has similar behavior with the evaluated decision making unit. Finally, we provide two numerical examples to illustrate the proposed model.

Introduction

In conventional data envelopment analysis (DEA) models, such as CCR model named after Charnes et al. [] and BCC model proposed by Banker et al. [], the inputs and outputs are assumed to be precise. In addition, the constraint condition consists of the evaluated decision making units (DMUs). In practical studies, the input and output data of the evaluated DMUs are frequently variable over multiple time periods (time series data), and it is important to analyze the change of efficiency over time. For example, in the evaluation of travel agencies, transportation, ticket price, accommodation, and labor are always regarded as the inputs, whereas profits and satisfaction of tourists are the outputs. The inputs and outputs are affected by various influential factors, such as the tourism policy, investment of infrastructure, level of starred hotel, annual per-capita income, and level of economic development. However, since the influential factors are variable over time, the inputs, outputs, and efficiencies of travel agencies are variable over time accordingly. Given the current upsurge in interest in DEA, it is surprising that the dynamic DEA attracts very little attention. The only methods we know of this area are Malmquist Productivity Index (MPI) and window analysis. MPI was originally proposed by Caves et al. [] to estimate changes in the overall productivity growth of each DMU over a two-year period by calculating the efficiency value. To deal with the productivity changes of DMUs over time, Färe et al. [] constructed a DEA-based MPI by combining the efficiency measurement of Farrell [] with the productivity measurement of Caves et al. Window analysis, proposed by Charnes et al. [], is adopted to overcome the constraint of limited DMUs and is a benefit to detect the tendency of DMUs over long period with large inputs and outputs. Since then, some improved approaches on the DEA-based MPI or window analysis have been proposed [–]. However, both the DEA-based MPI and window analysis models suffer from one shortcoming: they neglect predicting efficiency of the evaluated DMU. In many practical evaluation problems, efficiency of every evaluated DMU in a particular period may not be contrasted with the evaluated DMUs, but rather with sample standards determined by manufacturing parameters. The purpose of the contrast is not only to evaluate efficiency, but also to locate the standard with which the evaluated DMU has similar behavior. For instance, there are many grade standards for the evaluation of travel agencies. Travel agencies from the same region can be evaluated by the same standards separately, and those from different regions should not be evaluated by the same standards because of regional disparities. The standards should be formulated by the regional parameters. Taking outbound tourism as an example, it is an important part for travel agency business in developed regions, but it may not be contained in the travel agency business in some developing regions. Clearly, it is unreasonable that the outbound tourism is included in input measures to evaluate the travel agencies from different regions, and then grade standards in different regions should be formulated in terms of different manufacturing parameters.