  In this paper we study a simple extension of the total weighted flowtime
minimization problem for single and identical parallel machines. While the
standard problem simply defines a set of jobs with their processing times and
weights and assumes that all jobs have release date 0 and have no deadline, we
assume that the release date of each job is a decision variable that is only
constrained by a single global latest arrival deadline. To our knowledge, this
simple yet practically highly relevant extension has never been studied. Our
main contribution is that we show the NP- completeness of the problem even for
the single machine case and provide an exhaustive empirical study of different
typical approaches including genetic algorithms, tree search, and constraint
programming.
