  We describe an efficient implementation of a recent simplex-type algorithm
for the exact solution of separated continuous linear programs, and compare it
with linear programming approximation of these problems obtained via
discretization of the time horizon. The implementation overcomes many numerical
pitfalls often neglected in theoretical analysis allowing better accuracy or
acceleration up to several orders of magnitude both versus previous
implementation of the simplex-type algorithms and versus a state-of-the-art LP
solver using discretization. Numerical study includes medium, large, and very
large examples of scheduling problems and problems of control of fluid
processing networks. We discuss online and offline optimization settings for
various applications and outline future research directions.
