Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T06:55:47.939Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimizing the Earliness and Tardiness Costof a Sequence of Tasks on a Single Machine

Published online by Cambridge University Press:  15 August 2002

Philippe Chrétienne
Philippe Chrétienne*
Affiliation:
LIP6, Pôle IA, UPMC, 8 rue du Capitaine Scott, 75015 Paris, France; [email protected].
Get access

Abstract

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(nlogn) 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 logn) algorithm based on a strong dominance property that yields to model the scheduling problem as a minimum cost path in a valued directed acyclic graph.

Keywords

Schedulingalgorithmcomplexity.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 2: ROADEF'99 , April 2001 , pp. 165 - 187
Copyright
© EDP Sciences, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Garey, M.R., Tarjan, R.E. and Wilfong, G.T., One-processor scheduling with symmetric earliness and tardiness penalties. Math. Oper. Res. 13 (1988) 330-348. CrossRef
Baker, K.R. and Scudder, G.D., Sequencing with Earliness-Tardiness Penalties: A Review. Oper. Res. 38 (1989) 22-36. CrossRef
V. Gordon, J.M. Proth and C. Chu, A State-of-the-Art Survey of Due Date Assignment and Scheduling Research: Common Due Date. Rapport de recherche INRIA, 3454, Theme 4 (1998).
V. Gordon, J.M. Proth and C. Chu, A State-of-the-Art Survey of Due Date Assignment and Scheduling Research: SLK, TWK and Other Due Date Assignment Models. Rapport de recherche INRIA, 3537, Theme 4 (1998).
Hoogeveen, J.A. and Van de Velde, S.L., A branch-and-Bound Algorithm for Single-Machine Earliness-Tardiness Scheduling with Idle Time. INFORMS J. Comput. 8 (1996) 402-412. CrossRef
Federgruen, A. and Mosheiov, G., Single-Machine Scheduling Problems with General Breakdowns, Earliness and Tardiness Costs. Oper. Res. 45 (1997) 66-71. CrossRef
Federgruen, A. and Mosheiov, G., Greedy Heuristics for Single-Machine Scheduling Problems with General Earliness and Tardiness Costs. Oper. Res. Lett. 16 (1994) 199-208. CrossRef
Hall, N.G., Kubiak, W. and Sethi, S.P., Earliness-Tardiness Scheduling Problems I. Deviation of Completion Times about a Restrictive Common Due Date. Oper. Res. 39 (1991) 102-110.
Hall, N.G., Kubiak, W. and Sethi, S.P., Earliness-Tardiness Scheduling Problems II. Deviation of Completion Times about a Restrictive Common Due Date. Oper. Res. 39 (1991) 102-110.