Efficiency assessment of two-stage systems with fixed-sum outputs: a bi-objective DEA model with application to green innovation development
针对两阶段系统中产出总和固定的情况，提出一个双目标DEA模型，同时最大化两阶段效率，并应用于中国省级绿色低碳创新发展评价。
In numerous real-world scenarios, decision-making units (DMUs) are organized into two-stage structures, with the total outputs of the DMU set remaining fixed. The fundamental approaches to two-stage structure with fixed-sum output analysis are the centralized models, global perspective models, and non-cooperative game models. While these approaches are valuable, they face persistent challenges such as non-unique stage efficiency decomposition, difficulties in defining stage prioritization, and imprecise measurement of stage-level efficiencies. In this study, we propose a bi-objective two-stage fixed-sum output DEA model, aiming to simultaneously maximize the efficiencies of both stages. We transform the bi-objective model into a single-objective optimization problem using the Tchebycheff norm scalarization method and devise an algorithm to calculate both stage efficiency and overall efficiency. Finally, to demonstrate the applicability of our approach, we apply the proposed model to evaluate the performance of China’s provincial-level green low-carbon innovation development (GLID).