Scheduling under the due date criterion with varying penalties for lateness

The problem of scheduling jobs in a single machine, with due dates being assigned using the CON and SLK due date determination methods, is examined. Different penalties for the early and tardy jobs are assumed. The penalties are job-dependent, proportional to the processing times of jobs raised to an integer, non-unit, positive power. The objective function is the total weighted lateness. Two algorithms providing the optimal sequences are presented and examples illustrating the use of the algorithms are given.