  The motivation for this work stems from the problem of scheduling requests
for flow at supply points along an automated network of open-water channels.
The off-take flows are rigid-profile inputs to the system dynamics. In
particular, the channel operator can only shift orders in time to satisfy
constraints on the automatic response to changes in the load. This leads to a
non-convex semi-infinite programming problem, with sum-separable cost that
encodes the collective sensitivity of end users to scheduling delays. The
constraints encode the linear time-invariant continuous-time dynamics and
limits on the state across a \al{continuous} scheduling horizon. Discretization
is used to arrive at a more manageable approximation of the semi-infinite
program. A method for parsimoniously refining the discretization is applied to
ensure continuous-time feasibility for solutions of the approximate problem. It
is then shown how to improve cost without loss of feasibility. Supporting
analysis is provided, along with simulation results for a realistic irrigation
channel setup to illustrate the approach.
