We studied several group testing models with and without
processing times. The objective was to choose an optimal group
size for pooled screening of a contaminated population so as
to collect a prespecified number of good items from it with
minimum testing expenditures. The tested groups that were found
to be contaminated were used as a new sampling population in
later stages of the procedures. Since testing may be
time-consuming, we also considered deadlines to be met for the
testing process. We derived algorithms and exact results for
the underlying distributions, enabling us to find optimal
procedures. Several numerical examples are given.