Optimal Production and Maintenance Control Under a Time Variant Demand

In this paper, optimal production and maintenance planning of a flexible manufacturing system under a time variant demand is considered. There is a preventive maintenance plan to reduce the failure rate of the machine. It is assumed that the failure rate of the machine is a function of its age and its maintenance rate. It is, also, assumed that the demand of the manufacturing product is time dependent and its rate depends on the ievel of the advertisement on that product. The objective is to maximize the expected discounted total profit of the firm over an infinite time horizon. To solve this optimization problem, first, an optimal control is characterized by a set of Hamilton-Jacobi-Bellman partial differential equations. Then, since this set of equations cannot be solved analytically, this stochastic optimal control model is approximated by a deterministic optimal control problem. By solving this new deterministic problem under practical assumptions, a set of suboptimal controls can be found.