Measurement of returns to scale using non-radial DEA models

Abstract

There are some specific features of the non-radial DEA (data envelopment analysis) models which cause some problems under the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using StrongComplementary Slackness Conditions in the optimization theory. However, our investigation and computational experiments show that such methods increase computational complexity significantly and may generate "strange" results. In this paper, we propose and substantiate a direct method for the returns to scale measurement in the non-radial DEA models. Our computational experiments documented that the proposed method works reliably and efficiently on the real-life data sets.

Marginal Values and Returns to Scale for Nonparametric Production Frontiers

“…This general approach effectively removes the need to develop bespoke methods of computation for each type of marginal rate or elasticity (and RTS characterization), for each particular technology, except for the cases where specialist methods offer computational advantages (Krivonozhko et al 2014). …”

On the identification of the global reference set in data envelopment analysis

“…The identification of all the possible reference DMUs for an inefficient unit is an important and interesting problem in DEA, on which we concentrate in this contribution by means of the non-radial range-adjusted model (RAM) of Cooper, Park, and Pastor (1999). This issue has received significant attention in the literature due to its wide range of potential applications in ranking (Jahanshahloo, Junior, Hosseinzadeh Lotfi, & Akbarian, 2007), benchmarking and target setting (Bergendahl, 1998;Camanho & Dyson, 1999), and measuring returns to scale (RTS) (Cooper, Seiford, & Tone, 2007;Krivonozhko, Førsund, & Lychev, 2014;Sueyoshi & Sekitani, 2007a;Sueyoshi & Sekitani, 2007b;Tone, 1996;Tone, 2005;Tone & Sahoo, 2006).…”

“…Furthermore, the economic interpretation of some constraints of their proposed model does not make sense. In a more recent and conscious attempt to overcome these difficulties, Krivonozhko et al (2014) have proposed a primal-dual based procedure based on solving several LP problems. Using computational experiments, they showed that their proposed method works reliably and efficiently on real-life data sets and outperforms Sueyoshi and Sekitani's (2007b) approach.…”

Measuring the Performance of Industrial Green Development Using a Non-Radial Directional Distance Function Approach: A Case Study of Jiangxi Province in China

“…In addition, the major drawback of the radial DDF approach is that it aims to expand the good outputs and contract the bad outputs at the same rate. This is inconsistent with the actual production process, and often leads to many observations under evaluation having the same efficiency value of unity, thus hindering the ranking of observations [22,23]. Therefore, this paper aims to apply a global non-radial directional distance function (GNDDF) approach to analyze the dynamic changes in the performance of industrial green development (PIGD) for Jiangxi Province at the city level in 2003-2015.…”