Joint optimization of condition-based maintenance and condition-based production of a single equipment considering random yield and maintenance delay

In this paper, we study the integrated production-maintenance optimization problem of a deteriorating machine where random yield and maintenance delay are considered. The system deterioration is described by a discrete-time Markov chain. The production system faces a constant demand and a random yield which is proportional to the input quantity. A corrective maintenance needs to be scheduled if the machine enters into its failure state. Otherwise, the decision-maker can choose to schedule a preventive maintenance or decide how much to produce. The maintenance delay is considered in this work, where the maintenance crew arrival time is assumed to be non-negligible. We formulate the problem into a Markov decision process framework where the total discounted production-maintenance costs in the infinite horizon is minimized. Some structural properties of the optimal policy with respect to the machine condition, the inventory level are presented under mild conditions. A numerical example is given to present the model applicability. We also compare the model with the sequential approach to illustrate the characteristics and advantages of the proposed model. It may provide some managerial insight to the decision-maker when developing production schedules.