A note on a single machine scheduling problem with generalized total tardiness objective function

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered.

► A single machine problem with a generalized objective function is considered.
► For two special cases, pseudopolynomial algorithms and their graphical modifications are presented.
► Computational results are given for problems with up to 50 jobs.