Optimization models for complex recovery block schemes

In this paper we consider three complex recovery block schemes: (1) nested recovery block; (2) modified recovery block; and (3) nested consensus recovery block. For all the three models: (1) we derive simple expressions for calculating the system reliability; (2) we investigate how to arrange the versions in a nested recovery block and in a nested consensus recovery block; and (3) we develop optimization models where the objective is to optimize the reliability satisfying a budget constraint. The paper also includes efficient branch and bound procedures to solve the optimization problems. Two numerical example problems are solved to illustrate the branch and bound technique.