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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].
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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

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References

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