# Ranking Models in Data Envelopment Analysis Technique

Z. Moghaddas (Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran) and M. Vaez-Ghasemi (Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran)
DOI: 10.4018/978-1-5225-0596-9.ch007

## Abstract

Data envelopment analysis as a mathematical technique formulated based on linear programming problems which enables decision makers to evaluate Decision-Making Units (DMUs) with multiple inputs and outputs. One of the important issue in DEA technique which is widely discussed by researchers is ranking efficient units. Since these units are not comparable among each other. Ranking DMUs is an important issue in theory and practice and many applications in this field are performed. Considering the ranking order senior managers try to better guiding the system. In literature there exist different ranking models each of which tries to make improvements in this subject. Many researchers try to make advances in theory of ranking units and overcome the difficulties exist in presented methods. Each of the existing ranking method has its own specialties and advantages. As each of the existing method can be viewed from different aspects, it is possible that somewhat these groups have overlapping with the others.
Chapter Preview
Top

## Introduction

Data envelopment analysis is a mathematical programming technique introduced by Charnes et al.(1978) and then developed Banker et al. (1984). With this technique managers can obtained the relative efficiency of a set of decision making units. This technique is based on evaluating units in optimistic viewpoint to acquire the weights of inputs and outputs. Data envelopment analysis as a mathematical tool was initiated by Charnes et al.(1978). They formulated a linear programming problem with which it is possible to evaluate decision-making units (DMUs) with multiple inputs and outputs. Note that in this technique it is not necessary to know the production function. Considering the optimal weights those units whoes weighted outputs to weighted inputs is equal to 1 are called best practice units. Since they used inputs and produced outputs efficiently. In accordance to the efficacy score obtained for each unit it is possible to rank them. But, efficient units are not ranked considering their efficiency scores. Thus, ranking efficient units gains an important attention in theory and application. Many researchers provided variety of ranking methods each of which rank efficient units from different aspects. Cross efficiency method is another important filed in ranking introduced by Sexton et al.(1986), Contreras (2012), Wu et al.(2012), Mustafa et al.(2013), Wu (2012), Rodder and Reucher (2011), Wang et al.(2011), Orkju and Bal (2011), Jafatri et al.(2011). Super efficiency is one of the important fields in ranking units as first introduced by Andersen and Petersen (1993), Mehrabian et al. (1999), Tone (2002), Jahanshahllo et al.(2004), Tohidi et al. (2004), chen et al.(2004), Amirteimoori et al.(2005), Pourkarimi et al.(2006), Li et al.(2007), Omrani et al.(2011), Gholam abri et. al (2011), Moazami Goudarzi et al.(2011), Fanati Rashidi et al.(2011), Ashrafi et al.(2011), Chen et a.(2011), Rezai Balf et al. (2012) and Chen et al.(2013). Considering Multi-criteria decision analysis (MCDA) is another significant fields in ranking, Hosseinzadeh Lotfi et al. (2013),Wang and Jiang (2012), Jablonsky (2011), Chen (2007), Strassert and Prato (2002) introduced different ranking methods. Benchmarking method is another important field in ranking units introduced by Torgersen et al. (1996), Jahanshahloo et al.(2007),Lu et al.(2009) and Deng et al. (2011). There exist other methods based on finding optimal weights in DEA analysis by Jahanshahloo et al.(2004), Hosseinzadeh Lotfi et al.(2005), Alirezaee and Afsharian (2007), Liu and Peng (2008), Wang et al.(2007),Wang et al (2011) and Reshadi et al. (2011). Considering the application of statistical tools for ranking units first suggested by Friedman and Sinuany-Stern (1997) and Mecit and Alp (2013). In addition to those papers discussed theatrical aspects of ranking efficient units, there exist different paper consider applicational issues such as, Martic and Savic (2001), Leeneer and Pastijn (2002), Estellita Lins et a.(2003), Paralikas and Lygeros (2005), Ali and Nakosteen (2005), Martin and Roman (2006), Raab and Feroz (2007), Wang et al.(2007), Williams and Van Dyke (2007), Giokas and Pentzaropoulos (2008), Darvish et al.(2009), Lu and Lo (2009), Feroz et al.(2009), Sadjadi et al.(2011), Ramn et al.(2012) and Sitarz (2013). There exist some papers which review the ranking methods, as Adler et al. (2001), Adler et al.(2002), and Hosseinzade et al.(2013).

## Complete Chapter List

Search this Book:
Reset