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Reliability and cost are two most important issues in network design optimization that is extensively applied into various optimization problems such as supply chain network design, telecommunication network design, and transportation engineering. This paper proposes an efficient deterministic optimization approach for solving the problem of designing a reliable network. The problem discussed in this paper considers the minimization of the total cost subject to demand, flow balance, and capacity constraints while simultaneously employing mitigation resources to reduce the risk of network failures. Such a problem is typically formulated as a nonconvex mixed-integer program that cannot be easily solved to obtain a global optimum. The proposed optimization method transforms the original nonconvex program into a mixed-integer linear program by linearization techniques and is thus guaranteed to reach a global optimum. In addition, an extended model of minimizing the total weighted loss subject to resource constraints is discussed and globally solved by the proposed method. Experimental results show that the proposed approach effectively solves the reliable network design problem with the minimal total cost or the minimal total weighted loss under an appropriate allocation of mitigation resources. [ABSTRACT FROM AUTHOR]