The modified due date function in single machine total tardiness problem

In this paper the modified due date (MDD) is regarded as a function of time. A globally valid theorem is established by investigating the properties of this function on certain time intervals. This theorem can be used to derive known important conclusions concerning the single machine total tardiness (TT) problem in a convenient way. These can explain the efficiency of the commonly used MDD rule very well, and at the same time show that the MDD function can be a fundamental tool for the single machine TT problem.