Heuristics for component assignment problems based on the Birnbaum importance

This article considers the Component Assignment Problem (CAP), which concerns the problem of finding the optimal arrangement of n available components in the n positions of a system so that the system reliability is maximized. The Birnbaum Importance (BI) is a well-known measure that evaluates the relative contributions of components to system reliability. The ordering of BI values of components is a good indicator for the solution of the CAP and has been used to design heuristics for the CAP. This article proposes five new BI-based heuristics and presents their corresponding properties. Based on the numerical testing of the BI-based heuristics, a two-stage approach is proposed to solve the CAP with each stage using different BI-based heuristics. Comprehensive numerical experiments involving both small and large systems are used to evaluate the two-stage approach and to benchmark it against the GAMS/CoinBonmin solver and a randomization method. The numerical results show that the two-stage approach is much more efficient and is able to generate solutions of higher quality than the GAMS/CoinBonmin solver and the randomization method.