Exact cost minimization of a series-parallel reliable system with multiple component choices using an algebraic method

The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple component choices while ensuring a given system reliability level. The obtained model is a nonlinear integer programming problem with a nonlinear, nonseparable constraint. We propose a method based on the construction of a test set of an integer linear problem, which allows us to obtain an exact solution of the problem. It is compared to other approaches in the literature and standard nonlinear solvers.