Non-radial two-stage network DEA model to estimate returns to scale

Purpose As returns to scale (RTS) describes the long run connection of the changes of outputs relative to increases in the inputs, the purpose of this study is to answer the following questions: If the proportionate changes exist in the inputs, what is the rate of changes in outputs with respect to the inputs' variations in the two-stage networks over the long term? How can the authors investigate quantitative RTS in the two-stage networks? In other words, the purpose of this research is to introduce a different approach to estimate the performance, RTS and scale economies (SE) in network structures. Design/methodology/approach This paper proposes a novel non-radial approach based on data envelopment analysis to analyze the performance and to investigate RTS and SE in two-stage processes. Findings The findings show that the range adjusted measure (RAM)/RTS approach can identify reference sets for overall systems and each stage. In addition, the models presented in this paper can classify decision-making units and determine the increasing/decreasing trends of RTS. Originality/value The majority of previous RTS studies have been examined in black-box structures and have been discussed in a radial framework. Therefore, in this study, RTS and SE in the two-stage networks are dealt with using an extended RAM approach. Actually, the efficiency and RTS for each stage and the overall model are calculated using the proposed technique.