A variant of the classical capacitated facility location problem is fo
rmulated, and some of its relaxations are analyzed. An implementation
of a Lagrangian relaxation of the demand constraints usually yields a
stronger bound than the common Lagrangian relaxation of the capacity c
onstraint. A dual adjustment implementation provides the base for a fa
st optimal enumeration on well-known data sets. Lagrangian decompositi
on can yield an even stronger bound.