A DEA based approach for identifying the optimal production scale of strongly context-dependent production units

Abstract

In practical management scenarios, decision-makers frequently face the challenge of determining the most effective production scale for a strongly context-dependent decision-making unit (SCD-DMU). A notable hallmark of the SCD-DMU is its substantial reliance on contextual factors when establishing its production scale. This research proposes an approach based on data envelopment analysis (DEA) to estimate the optimal production scale of SCD-DMUs. Firstly, we expand the traditional explicit axioms in DEA to encompass contextual factors, followed by introducing a new DEA model designed to assess the efficiency of SCD-DMUs. Secondly, several models are presented to analyze whether a specific SCD-DMU exhibits increasing, decreasing, or constant returns to scale (RTS). Furthermore, an optimal production scale estimation model is introduced to calculate the optimal production scales for SCD-DMUs while considering their contextual factors. Our approach contributes by introducing a specialized efficiency evaluation model for SCD-DMUs, incorporating techniques for identifying their RTS and estimating the optimal production scale. It should be highlighted that the proposed production scale estimation model can simultaneously estimate the optimal input and output, and the estimated SCD-DMUs are DEA-efficient and operate at the most productive returns to scale. Finally, we apply the proposed approach to a real case study of 31 main airports in China in 2022 and compare it with two representative models.