The single-machine total tardiness scheduling problem: Review and extensions

We review the latest theoretical developments for the single-machine total tardiness 1//T¯ scheduling problem and propose extensions to some of them. We also review (and in some cases extend) exact algorithms, fully polynomial time approximation schemes, heuristic algorithms, special cases and generalizations of the 1//T¯ problem. Our findings indicate that the 1//T¯ problem continues to attract significant research interest from both a theoretical and a practical perspective. Even though the problem is ordinary NP-hard, the current state-of-the-art algorithms are capable of solving problems with up to 500 jobs.