We present in this paper a network DEA approach to deal with efficiency assessments in two-stage processes. Our approach complies with the composition paradigm, where the efficiencies of the stages are estimated without a prior definition of the overall efficiency of the system. The overall efficiency is obtained by aggregating the stage efficiencies a posteriori. We use multi-objective programming as modeling framework. This provides us the means to assess unique and neutral efficiency scores. We apply our approach to the assessment of the academic performance of forty faculty members in a Greek University