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.Index Terms-Budgeted uncertainty, cold standby redundancy allocation, mixed integer nonlinear programming, robust optimization, series-parallel system.

h i g h l i g h t s• A robust approach for quadratic assignment problem (RQAP) with budgeted uncertainty. • An exact and two heuristic methods to solve RQAP.• Extensive experiments to show performance of methods and quality of solutions.• RQAP can be solved significantly faster than minmax regret QAP. • RQAP has adjustable conservativeness while minmax regret QAP has not. a b s t r a c tWe consider a generalization of the classical quadratic assignment problem, where material flows between facilities are uncertain, and belong to a budgeted uncertainty set. The objective is to find a robust solution under all possible scenarios in the given uncertainty set. We present an exact quadratic formulation as a robust counterpart and develop an equivalent mixed integer programming model for it. To solve the proposed model for large-scale instances, we also develop two different heuristics based on 2-Opt local search and tabu search algorithms. We discuss performance of these methods and the quality of robust solutions through extensive computational experiments.