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Article Dans Une Revue RAIRO - Operations Research Année : 2001

Minimizing the earliness and tardiness cost of a sequence of tasks on a single machine

Résumé

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 $O(n \log n)$ 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 $O(n^3 \log n)$ 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.

Dates et versions

hal-01185816 , version 1 (21-08-2015)

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Citer

Philippe Chrétienne. Minimizing the earliness and tardiness cost of a sequence of tasks on a single machine. RAIRO - Operations Research, 2001, 35 (2), pp.165-187. ⟨10.1051/ro:2001110⟩. ⟨hal-01185816⟩
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