A compromise programming approach for target setting in DEA

Abstract

This paper presents a new Data Envelopment Analysis (DEA) target setting approach that uses the Compromise Programming (CP) method of multiobjective optimization. This method computes the ideal point associated to each Decision Making Unit (DMU) and determines an ambitious, efficient target that is as close as possible (using an lp metric) to that ideal point. The specific cases p=1, p=2 and p= are separately discussed and analyzed. In particular, for p=1 and p=, a lexicographic optimization approach is proposed in order to guarantee uniqueness of the obtained target. The original CP method is translation invariant and has been adapted so that the proposed CP-DEA is also units invariant. An lp metric-based efficiency score is also defined for each DMU. The proposed CP-DEA approach can also be utilized in the presence of preference information, non-discretionary or integer variables and undesirable outputs. The proposed approach has been extensively compared with other DEA approaches on a dataset from the literature.

Multiobjective centralized DEA approach to Tokyo 2020 Olympic Games

“…Getting as close to it as possible, however, is a sensible strategy. This is the idea behind several multiobjective optimization methods, such as Compromise Programming (e.g., Lozano et al, 2020) and the WTM (e.g., Gutiérrez & Lozano, 2016). As mentioned above, the WTM, in particular, uses the weighted Tchebychef distance, which, in this context, means the maximum weighted deviation from the output targets to their corresponding ideal values.…”

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

“…(2021), who use a pseudo‐Malmquist index, Lozano et al. (2020), who use compromise programming, Silva et al. (2020), Stumbriene 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.…”

Common set of weights in data envelopment analysis under prospect theory

“…Yu (1973) proposed the compromise programming (CP) method of multi-objective optimization. This method have been applied in many DEA studies, for example, Kao and Hung (2005) and Lozano, Soltani, and Dehnokhalaji (2020). Based in the concept of Yu (1973), it is noted that for 0 < α < 1 and 0 < β < 1, V…”

“…Yu (1973) proposed the compromise programming (CP) method of multi‐objective optimization. This method have been applied in many DEA studies, for example, Kao and Hung (2005) and Lozano, Soltani, and Dehnokhalaji (2020). Based in the concept of Yu (1973), it is noted that for 0 < α < 1 and 0 < β < 1, and are a strictly increasing function of and , respectively, which is simpler in its mathematical expression.…”