Unary NP-hardness of minimizing total weighted tardiness with generalized due dates

In the scheduling with generalized due dates, the due dates are sequenced in the EDD order and assigned to the jobs by the increasing order of their completion times such that the iith completed job receives the iith due date. The exact complexity of the single machine scheduling of minimizing total weighted tardiness with generalized due dates is a long standing open problem. We show in this paper that this problem is unary NP-hard.