Optimality condition and Branch and Bound algorithm for constrained redundancy optimization in series systems

This paper considers the constrained redundancy optimization problem in series systems. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall systems reliability under limited resource constraints. By exploiting special features of the problem, we derive a new necessary condition for optimal redundancy assignments. This condition leads to a new fathoming condition in the branch and bound method that may result in a significant reduction of computational efforts, as evidenced in our numerical calculation for linearly constrained redundancy optimization problems.