Veri zarflama analizinde tüm alternatiflerin sıralanmasına yeni bir yaklaşım: ASES

Abstract

 Full ranking of DMUs  Fair ranking of nonextreme DMUs  Application to evaluate European countries with respect to environmental technologies Data Envelopment Analysis (DEA) is a nonparametric method used to evaluate the efficiency of Decision Making Units (DMUs). In classical DEA, DMUs are categorized as efficient or inefficient. In addition, there are various studies in the literature that propose DEA-related measures to rank DMUs. Some methods can provide a ranking of only efficient or inefficient DMUs, not a full ranking. Furthermore, these methods cannot account for the special characteristics of the data set or DMUs. The limited number of studies that provide full ranking are also prone to this disadvantage. The proposed method (Area of Super Efficiency Score Graph-ASES) can evaluate all types of DMUs fairly and can consider special cases of the data set like crowded and sparse regions and outliers. ASES provides a ranking score that takes the proximity of the DMUs to the efficient frontier, their positions with respect to each other, their competitors, clustering and outliers of the data set into account. To calculate this score, the super efficiency of each DMU is computed while other DMUs are removed from the set one by one. These scores are summed and normalized for each DMU to achieve the final score. ASES is first introduced and discussed with a toy example of 10 DMUs and its strengths relative to other methods from the literature are illustrated. In the case study, 18 European countries are evaluated with respect to their environmental awareness and technology; related data is taken from OECD statistics. Figure 1 illustrates the ASES super efficiency change graphs of the four efficient countries. Although the four countries have close initial scores, the fourth one manages to improve its score more substantially and thus achieves the first rank. ASES is able to differentiate between efficient DMUs, even when they are convex combinations of other efficient DMUs, an issue overlooked by previous studies. Figure A. Efficiency change of efficient DMUs 1, 2, 3 and 4 Purpose: The proposed method ASES aims to overcome the shortcomings and disadvantages of previous ranking methods in DEA. ASES is able to evaluate all types of efficient and inefficient DMUs. It can also consider various potential issues related to problem sets to be studied and offers a compact efficiency score. Theory and Methods: DEA is a linear programming-based methodology used to measure the relative efficiencies of DMUs that produce similar outputs with similar inputs. There are several DEA models in the literature to evaluate DMUs. Some of these are discussed in this study and a new DEA model is proposed to rank efficient and inefficient DMUs. Results: ASES is demonstrated to perform as desired in applications. As opposed to benchmark models, it is able to provide a full ranking and it can take various characteristics of the data set into account. Conclusion: The proposed method ASES overcomes the mentioned disadvantages of benchmark...