Data envelopment analysis (DEA) can be used to evaluate the efficiencies of decision‐making units (DMUs) in various areas like education, healthcare, and energy. Several DEA methods are proposed for this purpose; however, some of these methods cannot provide a full ranking and others often overlook some considerations that arise with special characteristics of DMUs. We propose a new DEA‐based approach to achieve a full ranking of DMUs. Our approach takes various issues into account such as the initial efficiency score of the DMU, the DMUs that should be removed from the set for it to become efficient (if any) and its effects on the efficiency scores of other DMUs. We demonstrate the shortcomings of several other DEA methods and discuss how our approach overcomes these. We apply our approach to evaluate 50 MBA programs from Financial Times 2018 rankings and compare the results with the evaluations of other methods. As opposed to some methods, our approach has the advantage of differentiating between all efficient DMUs as well as inefficient ones. In addition, the results demonstrate that we can achieve a consistent ranking that considers different aspects of the problem setting. The generated scores are also used to sort DMUs in classes of preference.

ÖzGünümüzün rekabetçi ortamında organizasyonların önem vermesi gereken stratejik kararlardan biri de tesis yer seçimi problemidir. Tesis yer seçimi problemlerinden biri olan p-medyan problemi, n adet düğüm noktasını kullanarak p tane tesisin konumunu, düğüm noktaları ile tesisler arasındaki taşımalardan kaynaklanan maliyetin minimize edilmesini sağlayarak elde etmeyi amaçlamaktadır. Bir diğer ifade ile p-medyan problemi p adet tesisin hangi aday bölgelere kurulacağının ve hangi müşterilerin hangi tesise atanacağının belirlenmesi problemidir. Problemde düğüm noktalarının talepleri sabit, hizmete sunulan tesislerin sayısı ve konumlarının bilindiği varsayıldığından problem kesikli uzayda tesis yer seçimi problemi içerisinde sınıflandırılmaktadır. Bu çalışmada ise p-medyan probleminde yer alan alternatif tesislerin konumlarının bilinmediği varsayılmış ve Karar Verici (KV) tarafından belirlenmiş olan p adet tesisin konumu matematiksel model yardımı ile elde edilmiştir. Sürekli uzayda tesis yer seçimi problemi olarak adlandırılan bu problem için Karesel Öklid uzaklığı kullanılarak doğrusal olmayan matematiksel model ele alınmıştır. Matematiksel modelin çözümü için GAMS 22.5 programı BARON çözücüsünden yararlanılmıştır.

 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...

The Vehicle Routing Problem (VRP), which has many sub-branches, is a difficult problem that cannot be solved using classical methods. This study includes a case study for Service Routing Problem, which is one of the sub-branches of VRP. The case study is a problem of determining service routes for staffs of a company. In this context, we first assigned the employees to the stations, and then we reached a solution using the route first-cluster second heuristic method. We used the Genetic Algorithm (GA) to improve the route and compared the results by creating different scenarios in clustering methods.