Fuzzy random multi-objective optimization using a novel mixed fuzzy random inverse DEA model in input-output production

Abstract

Inverse data envelopment analysis (DEA), which is an effective tool for determining inputs and outputs, is commonly applied in areas such as output prediction, resource allocation, and target setting. However, existing inverse DEA methods typically assume precise and deterministic data, which limits applicability in uncertain production environments, particularly when both random and fuzzy environments are present. This study introduces a novel inverse DEA approach for optimizing inputs and outputs in mixed uncertainty environments. The proposed model allows decision-makers to achieve target efficiency and meet various input/output targets under different production scale assumptions. First, a new optimality principle for multi-objective fuzzy random problems is presented and the necessary theoretical conditions for input/output calculations are derived. Second, an equivalent linear model is introduced to solve the inverse DEA problem with fuzzy random variables, thereby overcoming the challenges associated with nonlinear programming. Notably, the proposed model offers enhanced flexibility as it does not rely on specific fuzzy numbers or predefined assumptions regarding random distributions. Finally, the effectiveness of the model is validated through numerical examples and a case study, demonstrating its practical application in complex decision-making scenarios.