Joint production and maintenance planning with machine deterioration and random yield

Production, yield and maintenance are three key components for sustaining the competitiveness of a manufacturing firm. In this paper, we investigate a joint production and maintenance planning problem in a periodic review environment subject to stochastic demand and random yields. The manufacturing system deteriorates from period to period according to a discrete-time Markov chain. The objective is to find an integrated lot sizing and maintenance policy for the system such that the aggregate cost associated with production, holding, backlogging and maintenance is minimised. We formulate this integrated planning problem as a Markov decision process and analyse the structural properties of the optimal policies. We prove that the optimal production and the maintenance policies both exhibit a control limit structure and show that the solution to the finite-horizon problems converges to that of the infinite-horizon problem.