Optimal control of inventory-production systems in presence of perturbations on the inventory level

A set of optimal control strategies is determined in this paper for a class of inventory-production systems, in order to optimize the production process in presence of perturbations on the inventory level. The inventory-production system has to satisfy a time-varying external demand, which is assumed to be a piecewise constant function of time; the optimization involves both production speed and the time instants at which the speed is changed. The inventory level, which is the state of the system, is supposed to be subject to some perturbations such that, at some time instants, it can be lower or higher than expected. Starting from the optimal (open-loop) solution found by the authors in a previous work, in this paper the optimal production speed is determined as an optimal (closed-loop) control strategy, which is a function of the system state. Such strategy minimizes the extra-cost that is paid by the system in consequence of a perturbation.