We present an optimization problem for the maintenance of a multi-component system subject to random deteriorations or failures of its components, resulting in the evolution of the overall system's state. The system can be required to perform missions with deterministic occurrences and durations. Our long term objective is to set up an optimized maintenance policy to ensure the smooth running of missions while minimizing maintenance costs. The main idea of this work is to propose a mathematical model for the evolution of the system by using the formalism of a Markov Decision Processes (MDP). Through Monte Carlo simulations, we compare the performances of several reference policies.