In this paper nearly time-optimal control policies are derived for a class of linear time-invariant models of production-inventory systems which comprise a cascade of basic production-inventory subsystems with bounded input. The sub-optimal control policies are obtained by constructing the sampled-data model of the production-inventory system where the sampling period is chosen to give the maximum control input for the given shipping rate. The theory is illustrated by the presentation of the results of simulation studies which show the transient behaviour of two production-inventory subsystems in cascade.