A heuristic approach to optimal assignment of components to a parallel-series network

In a parallel-series network the required n components are to be selected from the available m(⩾n) components and assigned to the n positions in the network with the objective of maximizing the reliability of the system. Any component can be assigned to any of the n positions, but the reliability of a component is affected by the position to which it is assigned. Obtaining an exact solution to this problem is highly complex. Therefore, a heuristic method that requires solving k(k+1)/2 classical assignment problems, where k is the number of pathsets in the network, is developed. The results of an extensive computational experiment show that the heuristic method obtains exact solutions in a vast majority of cases, and when it fails to give an exact solution, the deviation from the exact solution is small in most cases