Scheduling a single machine to minimize earliness penalties subject to the SLK due-date determination method

This paper considers a single machine scheduling problem. There are n jobs to be processed on a single machine. The problem is to minimize total earliness penalties subject to no tardy jobs. The problem is NP-complete if the due-dates are arbitrary. We study the problem when the due-dates are determined by the equal slack (SLK) method. Two special cases of the problem are solved in polynomial time. The first one is the problem with equally weighted monotonous penalty objective function. The second one is the problem with weighted linear penalty objective function.