Integrated optimization of scheduling and maintenance in multi-state production systems with deterioration effects

To explore the influence of deterioration effects on coupling relationship of maintenance and production scheduling, an integrated optimization was investigated for production scheduling and preventive maintenance in multi-state production systems. Based on preventive maintenance cost, production cost and finished job rewards, the integrated optimization problem was formulated as a Markov Decision Process (MDP) model of long-run expected average reward over finite-horizon. After analyzing and proving the existence of optimal stationary policy, an optimal equation was obtained for MDP model. To solve the difficulty that the traditional dynamic programming methods suffered from the curse of dimensionality and modeling, a model-free reinforcement learning algorithm was presented to solve the established MDP model on the basis of optimal equation. To evaluate the performance of reinforcement learning, a concise heuristic algorithm was proposed, and the experiments indicated that the reinforcement learning algorithm provide very effective solutions for the problem in comparison with the heuristic algorithm. A parameter sensitivity analysis was performed for the reinforcement learning algorithm, which provided the experiment reference for further design and improvement of the algorithm.