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Zbl 1049.90022
Chrétienne, Philippe
Minimizing the earliness and tardiness cost of a sequence of tasks on a single machine. (English)
[J] RAIRO, Oper. Res. 35, No. 2, 165-187 (2001). ISSN 0399-0559; ISSN 1290-3868/e

Summary: 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.

MSC 2000:: *90B35 Scheduling theory
90C90 Appl. of mathematical programming

Keywords: scheduling; algorithm; complexity

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