  We consider load scheduling on constrained continuous-time linear dynamical
systems, such as automated irrigation and other distribution networks. The
requested loads are rigid, i.e., the shapes cannot be changed. Hence, it is
only possible to shift the order back-and-forth in time to arrive at a feasible
schedule. We present a numerical algorithm based on using log-barrier functions
to include the state constraints in the social cost function (i.e., an
appropriate function of the scheduling delays). This algorithm requires a
feasible initialization. Further, in another algorithm, we treat the state
constraints as soft constraints and heavily penalize the constraint violations.
This algorithm can even be initialized at an infeasible point. The
applicability of both these numerical algorithms is demonstrated on an
automated irrigation network with two pools and six farms.
