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

Philippe Chrétienne

RAIRO - Operations Research (2010)

  • Volume: 35, Issue: 2, page 165-187
  • ISSN: 0399-0559

Abstract

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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(n3logn) 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.

How to cite

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Chrétienne, Philippe. "Minimizing the Earliness and Tardiness Cost of a Sequence of Tasks on a Single Machine." RAIRO - Operations Research 35.2 (2010): 165-187. <http://eudml.org/doc/197824>.

@article{Chrétienne2010,
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(n3logn) 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. },
author = {Chrétienne, Philippe},
journal = {RAIRO - Operations Research},
keywords = { Scheduling; algorithm; complexity.; scheduling; complexity},
language = {eng},
month = {3},
number = {2},
pages = {165-187},
publisher = {EDP Sciences},
title = {Minimizing the Earliness and Tardiness Cost of a Sequence of Tasks on a Single Machine},
url = {http://eudml.org/doc/197824},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Chrétienne, Philippe
TI - Minimizing the Earliness and Tardiness Cost of a Sequence of Tasks on a Single Machine
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 165
EP - 187
AB - 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(n3logn) 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.
LA - eng
KW - Scheduling; algorithm; complexity.; scheduling; complexity
UR - http://eudml.org/doc/197824
ER -

References

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  1. M.R. Garey, R.E. Tarjan and G.T. Wilfong, One-processor scheduling with symmetric earliness and tardiness penalties. Math. Oper. Res.13 (1988) 330-348.  Zbl0671.90033
  2. K.R. Baker and G.D. Scudder, Sequencing with Earliness-Tardiness Penalties: A Review. Oper. Res.38 (1989) 22-36.  Zbl0699.90052
  3. 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).  Zbl1009.90054
  4. 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).  Zbl1009.90054
  5. J.A. Hoogeveen and S.L. Van de Velde, A branch-and-Bound Algorithm for Single-Machine Earliness-Tardiness Scheduling with Idle Time. INFORMS J. Comput.8 (1996) 402-412.  Zbl0884.90102
  6. A. Federgruen and G. Mosheiov, Single-Machine Scheduling Problems with General Breakdowns, Earliness and Tardiness Costs. Oper. Res.45 (1997) 66-71.  Zbl0892.90100
  7. A. Federgruen and G. Mosheiov, Greedy Heuristics for Single-Machine Scheduling Problems with General Earliness and Tardiness Costs. Oper. Res. Lett.16 (1994) 199-208.  Zbl0823.90060
  8. N.G. Hall, W. Kubiak and S.P. Sethi, Earliness-Tardiness Scheduling Problems I. Deviation of Completion Times about a Restrictive Common Due Date. Oper. Res.39 (1991) 102-110.  Zbl0762.90037
  9. N.G. Hall, W. Kubiak and S.P. Sethi, Earliness-Tardiness Scheduling Problems II. Deviation of Completion Times about a Restrictive Common Due Date. Oper. Res.39 (1991) 102-110.  Zbl0762.90037

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