Optimal maintenance policies for multi-level preventive maintenance with complex effects

We consider the problem of optimally maintaining a periodically inspected system with multi-level preventive maintenance whose effects are complex. At each inspection, the maintenance decision concerns whether a preventive maintenance action is needed and which level should be selected if preventive maintenance is desired. The objective is to minimize the total expected discounted cost including inspection and maintenance costs. We formulate an infinite-horizon Markov decision process model and establish sufficient conditions to ensure the existence of an optimal monotone control-limit type policy with respect to the system’s deterioration level and age. We also numerically explore the structure of the optimal policy with respect to two additional system states, the level of the last maintenance action and the time since the last maintenance action. Real-world pavement deterioration data is used in our computational experiments, and the results show that the optimal policy is typically of monotone control-limit type.