Traditional scheduling and due-date determination models assume that the pr
oduction system is operating in a static and deterministic environment and
that the system carries no workload at each scheduling epoch. In this resea
rch we consider a due-date determination model where the scheduler wishes t
o update the existing schedule when some new jobs have arrived into the sys
tem. In this model, jobs are categorized as either "old'' or "new'' jobs, w
here the due-dates of the old jobs are treated as given parameters and thos
e of the new jobs are decision variables. The objective is to minimize the
maximum weighted tardiness penalty and the due-date assignment cost. The co
mputational complexity of this model is analyzed, and an efficient algorith
m is developed for an important special case.