Lot sizing and maintenance planning for a deteriorating machine with random yields

In this paper we investigate a production and maintenance planning problem in a periodic review environment with stochastic demand and random yields. We focus on a single-period, single-product, single machine production-inventory system with random yields, and aim to optimize the production and maintenance policies. 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 strategy for the system that minimizes the expected sum of production cost, holding cost, backlogging cost and maintenance cost. We formulate a single-period problem and analyze the structural properties of the optimal policies.