Modelling Sub-Process Non-Homogeneity in Parallel Network Data Envelopment Analysis

Non-homogeneity in DEA exists where decision-making units (DMUs) have different combinations of inputs and outputs. Parallel network models, on the other hand, are used for the efficiency assessment of DMUs characterised by concurrent sub-processes with dedicated or shared inputs and outputs. A special case of non-homogeneity arises where DMUs have differences in the internal structure of the production process for which some inputs and/or outputs must be optimally apportioned. Where such non-homogeneity exists, current approaches for parallel network DEA and resource allocation fail and will result in incorrect efficiency information for existing and non-existing sub-processes. This is because allocation may be made to non-existing sub-processes resulting in artificially low input and output allocation to existing sub-processes. In this paper, we propose two approaches for resource allocation in parallel network DEA models with non-homogenous sub-processes and shared factors. These approaches differ in terms of the restriction placed on the factor prices. An empirical application is conducted using the electricity generation systems of European states which are characterised by differences in the portfolio of power generation technologies across countries.