An epsilon-based data envelopment analysis approach for solving performance measurement problems with interval and ordinal dual-role factors

Abstract

Data envelopment analysis (DEA) is a linear programming method for measuring the performance and efficiency of units called decision-making units (DMUs). In many real-world performance measurement problems, the input and output data are not precisely known. Furthermore, the data may include dual-role factors that can be considered an input and output factor simultaneously. We propose a novel DEA model in the presence of imprecise data and imprecise dual-role factors by developing a new pair of mixed binary linear epsilon-based DEA models. The proposed models estimate the lower and upper bound efficiency scores in the presence of interval input, output, and dual-role factors by considering a fixed and unified production frontier for all DMUs. We then extend our models by including the weak ordinal dual-role factors. In contrast to the existing methods that exclude the dual-role factors, we include the dual-role factors and find a strictly positive value for the lower bound of the weights of inputs, outputs, and dual-role factors. We present a case study to demonstrate the applicability and exhibit the superiority of our approach over the existing methods.

Methods of regulatory impact assessment: critical analysis and alternative method

“…Concerning the proposed method, it provides optimal and therefore objective weights and uses substitute indicators that can take various forms: quantitative, qualitative, negative and in the form of an interval (Ebrahimi et al , 2021). Also, it is a noncompensatory and non-trade-off method, which avoids the problem of disagreements among the decision-makers.…”

“…As a response to the research question, AVRM avoids the drawbacks of the current methods used in the RIA field: cost–benefit method, event study and multicriteria methods, taking into account the intrinsic disadvantages of these methods in the literature review section and their comparison with the proposed method according to relevant criteria in the discussion section. At the same time, it ensures functionalities that the other methods do not ensure, such as optimization with negative values, benchmarking and dealing with various kinds of indicators, whether positive or negative, physical or monetary, visible or hidden, cardinal or ordinal, quantitative or qualitative, punctual or in the form of an interval (Ebrahimi et al , 2021). Other distinctive functionalities of the AVRM reside in adequately quantifying the improvements to be made via slack and radial movements (Coelli et al , 2005) and establishing budget constraints at the regulatory level.…”

Exact and stochastic methods for robustness analysis in the context of Imprecise Data Envelopment Analysis

“…A similar aim of deriving an efficiency interval for each DMU-though in different settings-was considered in Ebrahimi and Toloo (2020) and Park (2007). Also, in this context, Ebrahimi et al (2021) and Toloo et al (2021) accounted for the dual-role factors, which can be interpreted as input and output at the same time. In turn, Haghighat and Khorram (2005) proposed non-linear models for deriving the maximal and minimal numbers of efficient units when the input and output performances are given as intervals.…”