Robust optimization on redundancy allocation problems in multi-state and continuous-state series–parallel systems

In this paper, we consider the redundancy allocation problem (RAP) with uncertainties in component parameters for multi-state series–parallel system (MSSPS) and continuous-state series–parallel system (CSSPS). In real-world cases, the component parameters such as costs and reliabilities are often uncertain due to epistemic uncertainty. The existing research works mainly focused on binary-state RAP with data uncertainties. Few studies considered the epistemic uncertainty in MSSPS RAP. To the knowledge of the authors, nearly no research work addressed it in CSSPS. Therefore, in this paper we focus on MSSPS RAP and CSSPS RAP with uncertainties and propose a common model suitable for both of them. Moreover, the epistemic uncertainty of component state is handled by a state distribution distributed in an ambiguity set. The uncertain cost parameters are considered as the interval values. Given the partial information of the probability distribution of uncertain data, we establish a robust model to deal with different types of uncertain parameters. The robust model we proposed has a strong risk-averse capacity against the epistemic uncertainties and can help the ambiguity-averse managers design a system where all parameters are evaluated over the worst-case situation within the ambiguity set. Due to its intractability, we reformulate this proposed model as a mixed-integer linear programming problem via duality theory. The performance of the proposed model is illustrated by numerical experiments on the well-known benchmark problem for MSSPS RAP from three aspects: the robustness of the solutions under different conservative levels; the performance of robust solutions to hedge against the uncertainty of component state; the comparison of stochastic programming model and robust model to hedge against the uncertainties of component cost and state.