Optimal Control of Manufacturing Flow and Preventive Maintenance

In this paper, we address the optimal control issues corresponding to the planning of the production rate and maintenance rate of a failure prone manufacturing system. The discounted cost of our optimization problem is assumed to be a function of the inventory and the maintenance rate, where certain cost rates are specified for positive and negative inventories and maintenance, and there is a constant demand rate for the commodity produced. The objective of this paper is to choose the rates of production and maintenance to minimize a discounted cost over infinite horizon and to partially characterize the optimal solution. In the case where the maximum maintenance rate is equal to a constant coefficient times the maximum production rate , we obtain a solution and show that the optimal solution is characterized by a critical surface, namely "hedging surface". Its description is also given.