Production control of limited inventory manufacturing systems with failures dependent on the production rate

In this paper a failure prone single machine manufacturing system with limited inventory space is considered. The failure/repair process of the machine is characterized by a Markov chain which is non-homogeneous since the failure rate depends on the production rate. The problem is to minimize a cost function which includes a penalty for waiting customers. While the solution for the homogeneous case is well known, the problem becomes much more involved in the non-homogeneous case where, in general, the optimal production control is not of the hedging point type, as in the homogeneous case. We derive the optimal policy for a two value failure rate function. Such an optimal policy still depends on a threshold but is not hedging point. An analytical expression of the threshold is included in the paper together with some examples.