Single-machine scheduling with time window-dependent processing times

Chams Lahlou (1) , Stéphane Dauzère-Pérès (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 CMP-ENSMSE - Centre Microélectronique de Provence - Site Georges Charpak (CMP-GC)

In the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coefficient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models considered in previous papers on scheduling problems with time-dependent processing times. Various computational complexity results are presented for the makespan criterion, which show that the problem is NP-hard, even with two time windows. Solving procedures are also proposed for some special cases.

Mots clés: scheduling; one-machine; time-dependent processing time; time windows; computational complexity

Domaines: Recherche opérationnelle [math.OC]; Complexité [cs.CC]

Chams Lahlou, Stéphane Dauzère-Pérès. Single-machine scheduling with time window-dependent processing times. Journal of the Operational Research Society, 2006, 57 (2), pp.133-139. ⟨10.1057/palgrave.jors.2601931⟩. ⟨hal-00363040⟩