Summary: Conventional data envelopment analysis (DEA) methods are useful for estimating the performance measure of decision making units (DMUs) that each DMU uses multiple inputs to produce multiple outputs without considering any partial impacts between inputs and outputs. Nevertheless, there are some real-world situations where DMUs may possess several production lines with a two-stage network structure that each production line use inputs according to their needs. The current paper extends the recent work by J. Ma [“A two-stage DEA model considering shared inputs and free intermediate measures”, Expert Syst. Appl. 42, No. 9, 4339–4347 (2015; doi:10.1016/j.eswa.2015.01.040)] to consider partial impact between inputs and outputs for two-stage network production systems. Toward this end, we consider several input-output bundles in each stage for production lines. We formulate a couple of new mathematical programming models in the DEA framework with the aim of considering partial impact between inputs and outputs for calculating aggregate, overall, and subunit efficiencies along with resource usage by production lines for a two-stage production system Finally, an application in refinery industries is provided as an example to illustrate the potential application of the proposed method.