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This study explores the additive decomposition method in which the overall efficiency is a weighted average of the two stage efficiencies in a feedback system. In the additive decomposition method, the weight is often expressed as the proportion of total resources devoted to each stage, reflecting the relative importance of the stage. When this approach of determining weights is used in the additive two-stage data envelopment analysis (DEA) model with feedback, we find that the weight of the first stage is never less than that of the second stage, indicating that the first stage is favored, which causes a biased efficiency evaluation. Additionally, the weight of the first stage decreases when its efficiency increases, which does not conform to the belief that to maximize the overall efficiencies, a larger weight should be assigned to the stage with higher efficiency. In this study, we build an improved feedback two-stage DEA model with constant weights and develop a heuristic method to solve it. An empirical dataset covering the high-tech industry of 30 regions in mainland China in 2019 is studied to illustrate the applicability and superiority of our improved model.

Efficiency evaluation of a two-stage production process with feedback: an improved DEA model