A branch and bound algorithm for designing reliable systems at a minimum cost

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

“…In the exact method described in [12], there appear only illustrative examples, and they do not consider different types of components within a subsystem.…”

“…There are lots of heuristic methods to obtain such a point. In our case, we use a greedy algorithm similar to [12] or [16].…”

“…There are very few papers looking for their exact solutions, due to the difficulty of the problems. Those works use essentially dynamic programming [21], branch and bound methods [12], or Lagrangian relaxation [16], among other techniques. On the contrary, in the literature there are many heuristics and metaheuristic algorithms, such as those based on Genetic Algorithms [7], Tabu Search [15] or Ant Colony Optimization [2], among others.…”

“…For a fixed subsystem, its inner components can be considered equal, as in [12], or different, as in [16] and [21]. If the components are equal, the reliability function is separable and convex, and the problem can be reduced to a linear knapsack problem [12].…”

“…The first relaxation consists of deleting the nonlinear reliability constraint, and adding certain linear constraints, one for each subsystem. The second relaxation assumes that the same type of component is going to be used in every subsystem, so that the problem reduces to one similar as in [12].…”