Lower bounds for earliness-tardiness minimization on a single machine

Maher Rebai (1) , Imed Kacem (2, 3) , Kondo Adjallah (4)

1 LOSI - Laboratoire d'Optimisation des Systèmes Industriels
2 LITA - Laboratoire d'Informatique Théorique et Appliquée
3 LCOMS - Laboratoire de Conception, Optimisation et Modélisation des Systèmes
4 LGIPM - Laboratoire de Génie Informatique, de Production et de Maintenance

In this paper, we propose tow lower bounds for the problem of scheduling N-independent jobs on a single machine to minimize the sum of early and tardy costs. Jobs have distinct due dates and processing times with earliness and tardiness costs. The problem is proved to be NP-hard. A simple local search algorithm is presented in order to derive an upper bound for the problem and tested the proposed lower bounds in a branch and bound algorithm. Computational experiments show that in several cases, where the lower bounds of the literature are weak, our lower bounds are more efficient.

Keywords: Costs; Job shop scheduling; Single machine scheduling; Job production systems; Testing; Processor scheduling; Modems; Assembly; Production facilities; Scheduling problem; Branch and bound; lower bound; upper bound

Domains: Operations Research [cs.RO]

Maher Rebai, Imed Kacem, Kondo Adjallah. Lower bounds for earliness-tardiness minimization on a single machine. Industrial Engineering (CIE39), Jul 2009, Troyes, France. pp.23-27, ⟨10.1109/ICCIE.2009.5223868⟩. ⟨hal-02496043⟩