When designing a system, there are two methods that can be used to improve the system's reliability without changing the nature of the system: 1) using more reliable components, and/or 2) providing redundant components within the system. The redundancy allocation problem attempts to find the appropriate mix of components & redundancies within a system in order to either minimize cost subject to a minimum level of reliability, or maximize reliability subject to a maximum cost and weight. Redundancy allocation problems can be classified into two groups; one allows the system to have a mix of components with different characteristics incorporated in the system, while the other only allows one type of each component. The former group has a much larger solution space compared to the latter, and therefore obtaining an exact optimal or even a high quality solution for this problem may be more difficult. Optimization techniques, based on meta-heuristic approaches, have recently been proposed to solve the redundancy allocation problem with a mix of components. However, an exact solution method has not been developed. In this paper, we develop an exact solution method, based on the improved surrogate constraint (ISC) method, and use this method to find optimal solutions to problems previously presented in the literature