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

Imed Kacem (1, 2)

1 LOSI - Laboratoire d'Optimisation des Systèmes Industriels
2 LCOMS - Laboratoire de Conception, Optimisation et Modélisation des Systèmes

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

Keywords: Job shop scheduling; Single machine scheduling; Processor scheduling; Systems engineering and theory; Testing; Polynomials; Lagrangian functions; Genetic algorithms; Dynamic programming; scheduling; lower bounds; family setup times; single machine

Domains: Operations Research [cs.RO]

Imed Kacem. Lower Bounds for Tardiness Minimization on a Single Machine with Family Setup Times. Multiconference on "Computational Engineering in Systems Applications, Oct 2006, Beijing, China. pp.1034-1039, ⟨10.1109/CESA.2006.4281799⟩. ⟨hal-02496064⟩