A note on single-machine scheduling problems with position-dependent processing times

Julien Moncel (1) , Gerd Finke (2) , Vincent Jost (3)

1 LAAS-MOGISA
2 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
3 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

The purpose of this note is two-fold. First, it answers an open prob- lem about a single-machine scheduling problem with exponential position-dependent processing times de ned in [V. S. Gordon, C. N. Potts, V. A.Strusevich, J. D. Whitehead, Single machine scheduling models with deterioration and learning: Handling precedence constraints via priority generation, Journal of Scheduling 11 (2008), 357{370]. In this problem, the processing time of job i when scheduled in rank r is equal to p(i; r) = pir-1,with a positive constant. Gordon et al show in the above-mentioned paper with priority-generating techniques that the problem of minimizing the total ow-time on one machine admits an O(n log n) algorithm when 2]0; 1[[[2;+1[, and leave the case 2 [1; 2[ open. We show that the problem admits an O(n log n) algorithm also for 2 [1; 2[. The second purpose of this note is to provide a simple and general insight on why and when position-dependent scheduling problems on one machine can be solved in time O(n log n).

Mots clés: learning effects; deteriorating jobs; position-dependent processing times; Single-machine scheduling

Domaines: Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Julien Moncel, Gerd Finke, Vincent Jost. A note on single-machine scheduling problems with position-dependent processing times. 2011. ⟨hal-00647789⟩