Lexicographic hyperbolic DEA

Abstract

The hyperbolic distance function (HDF) reduces all inputs and increases all outputs simultaneously and at the same rate. Although the corresponding data envelopment analysis (DEA) model is non-linear, for constant returns to scale it can be linearized and for variable returns to scale an efficient iterative approach based on the directional distance function (DDF) model can be used. However, HDF does not necessarily project onto an efficient target. To remedy this, lexicographic hyperbolic DEA (LexHDEA) is proposed in this paper. Thus, before solving the HDF model, the input or output dimensions that can be improved are determined. A reduced HDF model is then solved, looking for improvements only in these dimensions. If the corresponding target is efficient, then no further steps are necessary. Otherwise, a reduced HDF model that improves only those dimensions that can be further improved is solved. If this improved target is efficient the process stops. Otherwise the process is repeated until eventually the efficient frontier is reached. In addition to guaranteeing an efficient target the proposed approach also computes an efficiency measure that has indication of efficiency and units invariance. The proposed approach can be extended to handle a preference structure, nondiscretionary variables and undesirable outputs.

Data Envelopment Analysis Approach to Energy-Saving Projects Selection in an Energy Service Company

“…There are many DEA models that can be used in different situations [9][10][11][12][13]. In particular, several specific DEA approaches have been proposed for project selection.…”

Identifying suitable benchmarks in the way toward achieving targets using data envelopment analysis

“…Some recent papers dealing with these issues include Korhonen et al. (2018), who use a lexicographic approach to reach the efficient frontier, Lozano and Soltani (2020c), who address target setting with the hyperbolic distance function, Camanho et al. (2021), who use a pseudo‐Malmquist index, Lozano et al.…”

“…A large number of models and approaches have been developed within DEA for purposes of benchmarking and target setting, often in combination with other methodologies. Some recent papers dealing with these issues include Korhonen et al (2018), who use a lexicographic approach to reach the efficient frontier, Lozano and Soltani (2020c), who address target setting with the hyperbolic distance function, Camanho et al (2021), who use a pseudo-Malmquist index, Lozano et al (2020), who use compromise programming, Silva et al (2020), Stumbriene et al (2020), andVan Puyenbroeck et al (2021), who use composite indicators, Chen and Wang (2019), who propose a target setting approach within the framework of cross efficiency, Lim (2018), who deal with forecasting targets in presence of infeasibility, Moreno and Lozano (2018), who combine DEA and network DEA, Wu et al (2020), who combine DEA and game theory, An et al (2020), who use agency theory also in combination with games, and Park and Lee (2018), Lozano and Calzada-Infante (2018), Ramón et al (2018), Nasrabadi et al (2019), Dehnokhalaji and Soltani (2019), An et al (2021) and Lozano and Soltani (2020a), who propose stepwise benchmarking approaches.…”