The Parallel Multi-component Network DEA Model with Variable Returns to Scale

This paper presents the parallel multi-component network DEA model in the case of variable returns to scale. It turns out that the convexity constraint in the proposed model is different from that in the conventional variable-returns-to-scale DEA model as it accounts for the number of sub-DMUs, i.e., components, is each DMU. This is in accordance with the centralised resource allocation structure of the model, where DMUs supervise a number (not necessarily equal) of sub-DMUs and they are allowed to reallocate resources and activities across them. We demonstrate that optimising the model with a parallel multi-component structure, as proposed by Kao (2017), is equivalent to finding weights that maximise the relative efficiency of virtual DMUs with average inputs and outputs values of the constituent sub-DMUs in a conventional DEA model. This has important implications as we can solve a problem having a parallel network structure using a conventional DEA model, which includes average productions units. The results hold both for the case of constant and variable returns to scale. We investigate these cases using data on national forest districts in Taiwan, each with multiple subdistricts.