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Efficient algorithms for machine scheduling problems with earliness and tardiness penalties

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  • Guang Feng
  • Hoong Lau

Abstract

In this paper, we study the multi-machine scheduling problem with earliness and tardiness penalties and sequence dependent setup times. This problem can be decomposed into two subproblems—sequencing and timetabling. Sequencing focuses on assigning each job to a fixed machine and determine the job sequence on each machine. We call such assignment a semi-schedule. Timetabling focuses on finding an executable schedule from the semi-schedule via idle-time insertion. Sequencing is strongly NP-hard in general. Although timetabling is polynomial-time solvable, it can become a computational bottleneck if the procedure is executed many times within a larger framework. This paper makes two contributions. We first propose a quantum improvement to the computational efficiency of the timetabling algorithm. We then apply it within a squeaky wheel optimization framework to solve the sequencing and overall problem. Finally, we demonstrate the strength of our proposed algorithms by experiments. Copyright Springer Science+Business Media, LLC 2008

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  • Guang Feng & Hoong Lau, 2008. "Efficient algorithms for machine scheduling problems with earliness and tardiness penalties," Annals of Operations Research, Springer, vol. 159(1), pages 83-95, March.
    • Handle: RePEc:spr:annopr:v:159:y:2008:i:1:p:83-95:10.1007/s10479-007-0284-z
    DOI: 10.1007/s10479-007-0284-z
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    References listed on IDEAS

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    1. Wlodzimierz Szwarc & Samar K. Mukhopadhyay, 1995. "Optimal timing schedules in earliness‐tardiness single machine sequencing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(7), pages 1109-1114, October.
    2. Michael R. Garey & Robert E. Tarjan & Gordon T. Wilfong, 1988. "One-Processor Scheduling with Symmetric Earliness and Tardiness Penalties," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 330-348, May.
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    5. John J. Kanet & V. Sridharan, 2000. "Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review," Operations Research, INFORMS, vol. 48(1), pages 99-110, February.
    6. Robert H. Storer & S. David Wu & Renzo Vaccari, 1992. "New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling," Management Science, INFORMS, vol. 38(10), pages 1495-1509, October.
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    Cited by:

    1. F. Rodriguez & C. Blum & C. García-Martínez & M. Lozano, 2012. "GRASP with path-relinking for the non-identical parallel machine scheduling problem with minimising total weighted completion times," Annals of Operations Research, Springer, vol. 201(1), pages 383-401, December.
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    3. Arthur Kramer & Anand Subramanian, 2019. "A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems," Journal of Scheduling, Springer, vol. 22(1), pages 21-57, February.
    4. Ivo Blöchliger & Nicolas Zufferey, 2013. "Multi-coloring and job-scheduling with assignment and incompatibility costs," Annals of Operations Research, Springer, vol. 211(1), pages 83-101, December.

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