Production and maintenance control for manufacturing systems

This note addresses the production and maintenance control problem of a failure prone manufacturing system consisting of one machine and producing one part type. The machine is assumed to have three working states: good, average and bad, and a failure state. In the three working states, the machine can produce parts and some of these parts are rejected with a rate depending on the machine state. In the failure state, no part is produced. The state transition of the machine is governed by a continuous-time Markov process. The jump rates from average and bad states to the good state are the preventive maintenance rates and the one from failure state to good state is the corrective maintenance rate. The production rate and the maintenance rates are optimized.