Group divisible designs are building blocks of numerous constructions in
the design theory. Here we consider a natural generalization of GDDs to
coverings and packings, which have the same structure as GDDs with the difference that any pair of
points which is not a subset of a group is contained in at most (at least) one block.
In this talk, we discuss generalizations of the Sch\"{o}nheim and Johnson bounds
on the size of group divisible packing designs. Then we
construct an optimal family of group divisible packing designs with blocks of
size three from a family of optimal coverings.