A Bi-Objective MDP Design approach to redundancy allocation with dynamic maintenance for a parallel system

The reliability of a system can be improved by the addition of redundant elements, giving rise to the well-known redundancy allocation problem (RAP), which can be seen as a design problem. We propose a novel extension to the RAP called the Bi-Objective Integrated Design and Dynamic Maintenance Problem (BO-IDDMP) which allows for future dynamic maintenance decisions to be incorporated. This leads to a problem with first-stage redundancy design decisions and a second-stage sequential decision problem. To the best of our knowledge, this is the first use of a continuous-time Markov Decision Process Design framework to formulate a problem with non-trivial dynamics, as well as its first use alongside bi-objective optimization. A general heuristic optimization methodology for two-stage bi-objective programmes is developed, which is then applied to the BO-IDDMP. The efficiency and accuracy of our methodology are demonstrated against an exact optimization formulation. The heuristic is shown to be orders of magnitude faster, and in only 2 out of 42 cases fails to find one of the Pareto-optimal solutions found by the exact method. The inclusion of dynamic maintenance policies is shown to yield stronger and better-populated Pareto fronts, allowing more flexibility for the decision-maker. The impacts of varying parameters unique to our problem are also investigated.