A novel method is presented here for solving certain classes of separation-network synthesis (SNS) problems, which are inherently non-linear, using branch-and-bound framework and linear programming. The proposed method determines effectively the structure and flowrates of the optimal separation network. The examined problem contains simple and sharp separators, mixers, and dividers; its aim is to produce three pure product streams from two three-component feed streams with minimal cost. The cost of the network is the sum of the costs of the separators and the cost of a separator is a concave function of its mass load. The mathematical programming model generated from the rigorous super-structure is non-linear. The goal of our work is to determine the optimum of the aforementioned model effectively. The splitting ratios of the dividers are handled as intervals. A B&B method operates on them. The cost functions of the separators are approximated with lower estimating functions. (C) 2013 Elsevier Ltd. All rights reserved.