Solve condition-based replacement and inventory control problem in a K-out-of-N system with the concept of divided-and-conquer

The maintenance of complex industrial equipment is often modeled as the Markov Decision Process through joint optimization of components replacement and spare inventory control. However, the size of state space is overwhelming for the practical problem, which is intractable for Value/Policy Iteration algorithms. This paper focuses on a K-out-of-N system, where the structure dependencies are emphasized by the model. To tackle the “curse of dimension” problem, we propose a heuristic algorithm with the concept of Divided-and-Conquer. In the “Divided” part, the multiple components and spare inventory are separated into N subproblems. In the “Conquer” part, we integrate the subsystems to make the spare purchase decision, which balances the risk of performance loss and the cost of holding. A numerical study is conducted by analyzing a 2-out-of-3 system. The result shows the satisfactory performance of the proposed algorithm.