This paper describes a Lagrangian relaxation based method to solve the
short-term resource scheduling (STRS) problem with ramp constraints.
Instead of discretizing the generation levels, the ramp rate constrain
ts are relaxed with the system demand constraints using Lagrange multi
pliers. Three kinds of ramp constraints, startup, operating and shutdo
wn ramp constraints are considered. The proposed method has been appli
ed to solve the hydro-thermal generation scheduling problem at PG&E. A
n example along with numerical results is also presented.