In this paper we establish a theoretical framework for a class of production and maintenance planning problems. Results obtained in this paper include local Lipschitz property of the optimal cost function, existence of the optimal control policies, and necessary and sufficient conditions for optimality. The maintenance considered involves activities such as lubrication, routine adjustments etc. The effect of the maintenance is modelled as control constraints. By using the concept of viscosity solutions we are able to relax some restrictive smooth assumptions on the optimal cost functions.