LIP6 1999/007

• Reports «Minimisation du coût de l'avance et du retard d'une séquence de tâches sur une machine»
• Ph. Chrétienne
• 27 pages - 04/06/1999 - document en - http://www.lip6.fr/lip6/reports/1999/lip6.1999.007.ps.gz 91 Ko
• Contact Philippe.Chretienne (at) nulllip6.fr
• Ancien Thème : SYSDEF
Assume that n tasks must be processed by one machine in a fixed sequence. The processing time, the preferred starting time and the earliness and tardiness costs per time unit are known for each task. The problem is to allocate each task a starting time such that the total cost incurred by the early and tardy tasks is minimum. Garey et al. have proposed a nice O(nlog n) algorithm for the special case of symmetric and task-independent costs. In this paper we first extend that algorithm to the case of asymmetric and task-independent cost without increasing its worst-case complexity. For the general case of asymmetric and task-dependent costs, we propose an O(n3 log n) algorithm based on a strong dominance property that yields to efficiently model the scheduling problem as a minimum cost path in a valued directed acyclic graph.