The main objective of this paper is to study the optimal components assignment problem for a two-commodity flow network via disjoint minimal paths in the existence of system reliability and total lead-time bands. By using fuzzy membership functions, we formulated the problem as fuzzy linear optimization. An algorithm based on genetic algorithm with fuzzy optimization is suggested for solving the presented problem. The proposed approach achieved success in finding an optimal solution that characterized with maximum reliability and minimum total lead-time. Three studied cases are given four nodes, six nodes and fourteen nodes computer networks to illustrate the efficiency of our proposed approach for solving the presented problem. Three studied cases are given four nodes, six nodes and fourteen nodes computer networks to illustrate the efficiency of our proposed approach for solving the presented problem. Three studied cases are given four nodes, six nodes and fourteen nodes computer networks to illustrate the efficiency of our proposed approach for solving the presented problem.