Summary: In recent Data envelopment analysis (DEA) literature, many researchers have examined systems with a two-stage network structure and its pitfalls. In these studies, two-stage network systems operations for converting inputs into outputs have been performed in two stages, meanwhile the intermediate products were considered as the outputs from the first stage and as inputs to the second stage. This duality in dealing with intermediate products imposes restrictions on the pricing of these products. In this paper by focusing on the convexity axiom, we define a new production possibility set. The main contributions of this paper are fourfold: (1) we propose models for evaluating the overall efficiency measure of decision making units (DMUs) in a two-stage network structure based on the convex hull in intermediate products; (2) we propose a procedure to determine the target unit of each inefficient DMU; (3) we explain how to calculate the divisional efficiency; (4) we demonstrate the feasibility and richness of the obtained solutions in the context of two examples.