Ranking using l1-norm in data envelopment analysis

An alternative transformation in ranking using $$l_1$$ l 1 -norm in data envelopment analysis

“…In these regards, several methods have been proposed for ranking of the extreme efficient DMUs, see Andersen and Petersen (1993), Mehrabian et al (1999) and Jahanshahloo et al (2004). A DMU is called extremely efficient if it cannot be represented as a linear combination (with nonnegative coefficients) of the remaining DMUs (Charnes et al 1991).…”

“…Mehrabian et al (1999) suggested the MAJ model for complete ranking of efficient DMUs, but their approach lacks feasibility in some cases, too. To overcome the drawbacks of the AP (Andersen and Petersen 1993) and MAJ (Mehrabian et al 1999) models, Jahanshahloo et al (2004) presented a method to rank the extremely efficient DMUs in DEA models with constant and variable returns to scale using L 1 -norm. Their proposed model is a nonlinear programming form which has the higher order of complexity in solving.…”

“…Their proposed model is a nonlinear programming form which has the higher order of complexity in solving. In addition, a complex procedure was applied in Jahanshahloo et al (2004) to provide the nonlinear model into a linear one which obtains an approximately optimal solution. Wu and Yan (2010) have also suggested an effective transformation to convert the nonlinear model in Jahanshahloo et al (2004) into a linear model.…”

“…In addition, a complex procedure was applied in Jahanshahloo et al (2004) to provide the nonlinear model into a linear one which obtains an approximately optimal solution. Wu and Yan (2010) have also suggested an effective transformation to convert the nonlinear model in Jahanshahloo et al (2004) into a linear model. Recently, Ziari and Raissi (2016) proposed an approach to rank the efficient DMUs in DEA based on minimizing distance of the under evaluation DMU to the frontier of efficiency.…”

“…Recently, Ziari and Raissi (2016) proposed an approach to rank the efficient DMUs in DEA based on minimizing distance of the under evaluation DMU to the frontier of efficiency. Following this trend, the present paper is an attempt to provide an alternative transformation to convert the nonlinear model in Jahanshahloo et al (2004) into a linear model. The proposed model in this paper linearizes model in Jahanshahloo et al (2004) in a way which is different from the presented method in Wu and Yan (2010).…”