Optimality of a two threshold feedback policy for the control of a manufacturing system with a two - value , production dependent failure rate ∗

In this report we consider a failure prone, single machine, single part-type, 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 long term average expected cost function which penalizes both the presence of waiting customers both a finite inventory surplus. We derive and prove the optimality of a policy which depends on two thresholds. The expression of these thresholds and of the optimal cost are also included in the report.