Time-optimal control policies for cascaded production-inventory systems with control and state constraints

Abstract

In this paper time-optimal control policies are derived for models of production-inventory systems consisting of a cascade of basic production- inventory systems with control and state constraints. The analytic solution is due to a decoupling of the complete system into its subsystems by a recursive definition of the cascaded system. It is shown that there is at least one bang-bang controlled subsystem. For the "other" subsystems singular control policies are obtained. Introducing a pseudo-bang-bang control for these systems it is demonstrated that by strengthening the constraints there is a continuous transition from a singular to a bang-bang control.