Linear optimal control strategies for production systems with a discrete-event demand pattern

A class of production systems are considered in this paper with the aim of determining closed-loop strategies providing the production effort as functions of the system state. The key feature of the considered class of systems is that the demand and the way it is satisfied are asynchronous sequences of part requests and instantaneous withdrawals, respectively, generated by discrete-event processes, whereas the production process has continuous-time dynamics. The optimization problem, whose objective is to minimize inventory and lateness costs, is restated as an optimal control problem by exploiting some structural properties of the optimal solution. Then, optimal closed-loop strategies are found with dynamic programming techniques.