Lower Bounds for Tardiness Minimization on a Single Machine with Family Setup Times

In this paper, we consider the scheduling of N jobs on a single machine with family setup times in order to minimize the total tardiness. The set of jobs is divided into F families. Between two jobs of the same family, we have not to stop the machine. However, when switching from family to another, a setup is required. Each family is characterized by a setup time independent of the sequence. We propose a set of approaches to compute lower bounds for the tardiness criterion. These approaches are analyzed and tested on a large set of numerical experiments in order to identify the dominant lower bounds