A survey on measuring efficiency through the determination of the least distance in data envelopment analysis

Abstract

Purpose -The purpose of this paper is to provide an outline of the major contributions in the literature on the determination of the least distance in data envelopment analysis (DEA). The focus herein is primarily on methodological developments. Specifically, attention is mainly paid to modeling aspects, computational features, the satisfaction of properties and duality. Finally, some promising avenues of future research on this topic are stated. Design/methodology/approach -DEA is a methodology based on mathematical programming for the assessment of relative efficiency of a set of decision-making units (DMUs) that use several inputs to produce several outputs. DEA is classified in the literature as a non-parametric method because it does not assume a particular functional form for the underlying production function and presents, in this sense, some outstanding properties: the efficiency of firms may be evaluated independently on the market prices of the inputs used and outputs produced; it may be easily used with multiple inputs and outputs; a single score of efficiency for each assessed organization is obtained; this technique ranks organizations based on relative efficiency; and finally, it yields benchmarking information. DEA models provide both benchmarking information and efficiency scores for each of the evaluated units when it is applied to a dataset of observations and variables (inputs and outputs). Without a doubt, this benchmarking information gives DEA a distinct advantage over other efficiency methodologies, such as stochastic frontier analysis (SFA). Technical inefficiency is typically measured in DEA as the distance between the observed unit and a "benchmarking" target on the estimated piece-wise linear efficient frontier. The choice of this target is critical for assessing the potential performance of each DMU in the sample, as well as for providing information on how to increase its performance. However, traditional DEA models yield targets that are determined by the "furthest" efficient projection to the evaluated DMU. The projected point

Interactive multiobjective DEA target setting using lexicographic DDF

“…That is the case, for example, of those DEA approaches that search for the least distant target (e.g. Aparicio et al 2007, 2017, Aparicio 2016 or compute a stepwise benchmarking path that divides the total improvement effort so that it does not have to be made all in one step (e.g. Lozano and Villa 2005, Lozano and Calzada-Infante 2018.…”

A modified distance friction minimization approach in data envelopment analysis

“…In this context, Ando et al (2012) gave weakly monotonic least distance measure with the incorporation of a free disposable set and showed that it satisfies weak monotonicity over the strongly efficient frontier. Aparicio andPastor (2013, 2014a) proposed an output-oriented strongly monotonic measure based on least distance. Fukuyama et al (2014a) by extending the free disposable set and introducing the so-called tradeoff set, developed a least distance p-norm efficiency measure satisfying strong monotonicity over the strongly efficient frontier.…”

“…For recent and up-to-date developments on the least distance projections, the reader is referred to Aparicio (2016) and Aparicio et al (2017d).…”

A sequence of targets toward a common best practice frontier in DEA

“…The issue of least distance to the frontier has been used in other applications of DEA, such as ranking units (e.g., see Ziari 2016;Aghayi and Tavana 2018). The concept of benchmarking based on least distance has also been developed by Pastor and Aparicio (2010), Ando et al (2012Ando et al ( , 2017, Aparicio andPastor (2013, 2014a, b) and Aparicio et al (2014). On the other hand, some authors like Cherchye and Van Puyenbroeck (2001) and Silva Portela et al (2003) have developed some benchmarking approaches based in the issue of similarity and closeness.…”

“…However, benchmarking is considered as an important field of research in DEA and can be viewed from different perspectives such as neural network as discussed in Shokrollahpour et al (2016), artificial units in Didehkhani et al (2018) or Fuzzy De-Novo programming by Sarah and Khalili-Damghani (2018). For a complete review of other benchmarking models, the reader is referred to Aparicio (2016), Aparicio et al (2017a, b).…”