Control of manufacturing systems with a two-value, production-dependent failure rate

In this paper we consider a failure prone, single machine, single part-type, limited inventory, manufacturing system subject to a non-homogeneous Markov failure/repair process with the failure rate depending on the production rate through a two-value function. The problem is to minimize a cost function which includes a penalty for waiting customers. We derive and prove the optimality of a policy which depends on a threshold but is not the so-called hedging point policy, optimal for the Markov homogeneous case