Determining the optimal production–maintenance policy of a parallel production system with stochastically interacted yield and deterioration

In this paper, we study the integrated production–maintenance optimization problem of a multi-component deteriorating machine. The deterioration of each component is described by a discrete-time Markov chain with finite state space. To meet a constant demand, production planning is scheduled based on the system deterioration and the inventory level. We consider the mutual dependence between the production and the system deterioration. For each component, its deterioration transition probabilities depends on its own characteristics and its production quantity. Production yield is stochastically decreasing with the system deterioration. Maintenance is scheduled immediately if at least one component failure occurs. Otherwise, the decision-maker need to determine whether to schedule a preventive maintenance or to continue producing. We formulate the problem into a Markov decision process framework. The total discounted costs including the production costs, maintenance costs and holding/backlogging costs in the infinite horizon is obtained. Some structural properties of the optimal policy with respect to the machine condition, the inventory level are presented under mild conditions. The proposed model is further examined by a numerical example, where the properties of the production and maintenance planning and the corresponding cost are investigated. It can provide theoretical reference in managing the production and maintenance problems in multiple production lines.