Exact cost minimization of a series-parallel system
  The redundancy allocation problem is formulated minimizing the design cost for a series-parallel system with multiple component choices whereas ensuring a given system reliability level. The obtained model is a nonlinear integer programming problem with a non linear, non separable constraint. We propose an algebraic method, based on Gr\"obner bases, to obtain the exact solution of the problem. In addition, we provide a closed form for the required Gr\"obner bases, avoiding the bottleneck associated with the computation, and promising computational results. 
F. Castro and J. Gago and I. Hartillo and J. Puerto and J.M. Ucha
math.OC math.AC