Optimal control of a production system with periodic maintenance

In this paper the authors consider a production system consisting of one machine for which maintenance is perfromed on a periodic basis. When the machine is undergoing maintenance, the system is shut down and cannot produce. One part-type is produced and the demand rate is assumed to be constant. In order to make on-time delivery, the objective is to produce following the demand as closely as possible. However, the maintenance disruptions make the production deviate from the demand. The authors formulate the production flow control problem as an optimal control model and use Pontryagin’s minimum principle to solve the special case of one up-down cycle. They then solve the general N-cycle problem based on the one-cycle solution.