A DEA Based Approach for Identifying the Optimal Production Scale of Strongly Context-Dependent Production Units

In real managerial decisions, situations frequently occur when the decisionmakers need to estimate the optimal production scale (the amount of input and output) for a strongly context-dependent decision-making unit (SCD-DMU) for decision support. While for the SCD-DMU, the obvious feature is that its production scale is strongly dependent on the surrounding contextual factors. In this paper, a data envelopment analysis (DEA)-based approach is proposed to yield estimation of the optimal production scale of SCD-DMUs. First, the traditional explicit axioms in DEA are extended considering the contextual factors and a new DEA model is further proposed for efficiency evaluation of the SCD-DMUs which considers the contextual factors. Second, we give some models for analyzing whether increasing, decreasing or constant returns to scale (RTS) prevails at those special SCD-DMUs. Further, an optimal production scale estimation model is proposed to estimate the optimal production scales for the SCD-DMUs according to their contextual factors. The proposed approach provides details on how to estimate simultaneously the optimal input and output (production scale) of the SCD-DMU based its contextual factors. The estimated optimal SCD-DMUs have not only the DEA efficient property (i.e., the SCD-DMUs will make productions on the efficient frontier) but also the maximum returns to scale. Finally, the proposed production scale estimation approach is applied to a real example of airports in Spain