The Robust Cold Standby Redundancy Allocation in Series-Parallel Systems With Budgeted Uncertainty

This paper studies a redundancy allocation problem (RAP) with cold standby strategy in non-repairable series-parallel systems. We assume that the components´ reliabilities are uncertain values in a budgeted uncertainty set, with unknown probability distributions. Because the system reliability is a nonlinear function of the components´ reliabilities, classical robust optimization approaches cannot be directly applied to construct the robust counterpart of this problem. Therefore, this paper for the first time proposes linear mixed integer programming (MIP) and binary equivalent models for the cold standby RAP; and by exploiting the problem structure, robust counterparts are developed to deal with budgeted uncertainty in this problem. Then, two exact solution methods are proposed: one of them solves a MIP model iteratively in a Benders´ decomposition framework, and the other one solves a single binary linear model. The validity and the performance of the proposed approach are tested through a Monte Carlo simulation, and computational results.