A generalized robust data envelopment analysis model based on directional distance function

In the literature of data envelopment analysis, the directional distance function (DDF) model is commonly used to measure efficiency improvement, as it allows the decision-maker to choose an appropriate direction that permits input contraction and output expansion. However, choosing the right direction is challenging in empirical research. Additionally, efficiency measurement becomes problematic when input and output data are uncertain. To address these issues, we present an equivalent DDF model in multiplier form and use the robust optimization approach to construct a technology in order to develop a generalized robust-DDF measure of efficiency. Among the three commonly used predefined directions (input-oriented, output-oriented, and proportional) considered in this study, we define the robust direction as the one with the minimum price that decision-maker must pay to be immune to data uncertainty. To demonstrate the usefulness of our proposed robust direction measure, we apply it a real-life data on life insurance companies in India over eight years (2011–12–2018–19). Our results show that the proportional direction exhibits the lowest price of robustness and is therefore the most appropriate for measuring potential efficiency improvement. Additionally, the increasing efficiency trend in the life insurance industry confirms the evidence of increased work intensity due to competition resulting from insurance reforms, supporting the competition and X-efficiency hypothesis.