An interval efficiency analysis with dual-role factors

Abstract

Data envelopment analysis (DEA) is a data-driven and benchmarking tool for evaluating the relative efficiency of production units with multiple outputs and inputs. Conventional DEA models are based on a production system by converting inputs to outputs using input-transformation-output processes. However, in some situations, it is inescapable to think of some assessment factors, referred to as dual-role factors, which can play simultaneously input and output roles in DEA. The observed data are often assumed to be precise although it needs to consider uncertainty as an inherent part of most real-world applications. Dealing with imprecise data is a perpetual challenge in DEA that can be treated by presenting the interval data. This paper develops an imprecise DEA approach with dual-role factors based on revised production possibility sets. The resulting models are a pair of mixed binary linear programming problems that yield the possible relative efficiencies in the form of intervals. In addition, a procedure is presented to assign the optimal designation to a dual-role factor and specify whether the dual-role factor is a nondiscretionary input or output. Given the interval efficiencies, the production units are categorized into the efficient and inefficient sets. Beyond the dichotomized classification, a practical ranking approach is also adopted to achieve incremental discrimination through evaluation analysis. Finally, an application to third-party reverse logistics providers is studied to illustrate the efficacy and applicability of the proposed approach.

Selection of strategy for reverse logistics implementation

“…According to Scopus data, till July 2021, more than 60 articles (published in journals and conferences) have been found which did research in this area using various MCDM methods as well as mathematical models. Most of the authors consider this as a MCDM problem and used a wide variety of methods such as analytic hierarchy process (AHP) (Abdel-Basset et al , 2021; Zarbakhshnia et al , 2020; Govindan et al , 2019; Ilgin, 2017; Prakash and Barua, 2016; Khodaverdi and Hashemi, 2015; Senthil et al , 2014), analytic network process (ANP) (Tavana et al , 2018; Tavana et al , 2016), technique for order performance by similarity to ideal solution (Abdel-Basset et al , 2021; Govindan et al , 2019; Ilgin, 2017; Prakash and Barua, 2016; Senthil et al , 2014), stepwise weight assessment ratio analysis (Zarbakhshnia et al , 2018; Mavi et al , 2017), multi-objective optimization on the basis of ratio analysis (Zarbakhshnia et al , 2020; Mavi et al , 2017) and data envelopment analysis (DEA) (Toloo et al , 2021; Momeni et al , 2015; Saen, 2011) to solve it. Some authors developed this problem as a modelling problem and used various theories and programming tool to solve it.…”

Evaluation of Road Safety Performance Based on Self-Reported Behaviour Data Set

“…When collecting self-reported data on behaviour, the main focus is on their final presentation, since, in many cases, respondents are not able to clearly express their judgments, and it is assumed that all final values derived from such data are uncertain [21]. Recently, in an uncertain DEA framework, imprecise DEA approaches [22], fuzzy DEA methods [23], and robust DEA methods [24] have been used. In [25,26], it was shown that both imprecise DEA and fuzzy DEA models can give robust composite index scores, which implies the effectiveness and reliability of these two approaches for modelling qualitative data.…”

Weight restrictions for the DEA model in the presence of dual-role factors: An application to the Iranian banking sector

“…In estimating the efficiency of each DMU by their model, a dual-role factor can simultaneously take both input and output roles, but in the previous DEA models, after the evaluation, a dual-role factor can only take one role. Toloo et al [35] presented DEA models in the presence of dual-role factors for the interval data. The formulated models are a pair of mixed binary linear programming problems to calculate the relative efficiencies in the interval forms.…”