A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due date

This paper studies the problem of scheduling a set of n jobs on a single machine to minimize weighted absolute deviation of completion times from a common due date. It is assumed that weights of jobs are proportional to their processing times. It has been shown by other researchers that the problem can be solved efficiently for a sufficiently large due date. In the present paper we solve the problem for any given due date.