A Robust Optimization Approach for Estimating the Most Productive Scale Size in Uncertain Data Envelopment Analysis

Productivity measurement, ranking, performance assessment, and benchmarking of homogeneous decision-making units (DMUs), as well as estimating the most productive scale size (MPSS) and returns to scale (RTS), are among the most significant challenges faced by managers and decision-makers (DMs) in various real-world situations and problems. Data envelopment analysis (DEA), a widely used and powerful approach, can be applied to address all of these challenges. It is important to note that, in the presence of uncertain and ambiguous data, traditional DEA approaches cannot be utilized effectively. Therefore, this research presents a novel method for estimating the most productive scale size in DEA within a deep uncertainty environment. Notably, the robust optimization (RO) method, recognized for its effectiveness and practicality in uncertain programming, is employed to propose the robust most productive scale size (RMPSS) model. The implementation of the developed robust MPSS method is demonstrated through a numerical example and a real-life case study from the Iranian healthcare system. Furthermore, the results indicate the effectiveness and efficacy of the proposed approach in estimating MPSS within uncertain DEA.