Minimizing total weighted tardiness for scheduling equal-length jobs on a single machine

In this paper, we consider the problem of minimizing total weighted tardiness for equal-length jobs with arbitrary release dates on a single machine. This problem is mentioned as a minimal open problem, see http://www2.informatik.uni-osnabrueck.de/knust/class/dateien/classes/ein_ma/ein_ma, i.e., its complexity status is still open. The latest results on this problem were presented in the years 2000 and 2005, namely solution algorithms for special cases. We present some properties of this problem and discuss possible ways for future research.