Optimal Allocation of Redundant Components for Large Systems

TLDR: Two new exact algorithms are presented for the case where the objective and constraint functions are stagewise separable, both are branch and bound algorithms.

Abstract: This paper discusses allocating redundant components subject to resource constraints so as to optimize some measure of system performance. Two new exact algorithms are presented for the case where the objective and constraint functions are stagewise separable. Both are branch and bound algorithms. The first, BLE1, is based on an underlying knapsack structure, while the second, BLE2, exploits a multiple-choice knapsack structure. BLE1 can solve problems with 100 stages and 10 constraints in just a few seconds of CPU time on an IBM 3033. For larger problems, BLH, a heuristic procedure, is proposed. The heuristic is based on the ``slippery algorithm'' for knapsack problems. Computational testing indicates BLH often finds the optimal solution, and when it doesn't, the solutions are quite close to optimal.