Skip to main content
SpringerLink
Log in

Efficient algorithms for machine scheduling problems with earliness and tardiness penalties

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Balakrishnan, N., Kanet, J. J., & Sridharan, S. V. (1998). Early/tardy scheduling with sequence dependent setups on uniform parallel machines. Computers and Operations Research, 26, 127–141.

    Article  Google Scholar 

  • Cheng, R., Gen, M., & Tosawa, T. (1995). Minmax earliness/tardiness scheduling in identical parallel machine system using genetic algorithm. Computers and Industrial Engineering, 29(1-4), 513–517.

    Article  Google Scholar 

  • cnet.com (2001). http://news.cnet.com/news/0-1004-200-5867112.html.

  • Davis, J. S., & Kanet, J. J. (1993). Single-machine scheduling with early and tardy completion costs. Naval Research Logistics, 40, 85–101.

    Article  Google Scholar 

  • Garey, M. R., Tarjan, R. E., & Wilfong, G. T. (1988). One-processor scheduling with symmetric earliness and tardiness penalties. Mathematics of Operations Research, 13, 330–348.

    Google Scholar 

  • Herrmann, J. W., & Lee, C.-Y. (1995). Solving a class scheduling problem with a genetic algorithm. ORSA Journal of Computing, 7(4), 443–452.

    Google Scholar 

  • James, R., & Buchanan, J. (1997). A neighbourhood scheme with a compressed solution space for the early/tardy scheduling problem. European Journal of Operational Research, 102(3), 513–527.

    Article  Google Scholar 

  • Joslin, D., & Clements, D. (1999). Squeaky wheel optimization. Journal of Artificial Intelligence Research, 10, 353–373.

    Google Scholar 

  • Kanet, J. J., & Sridharan, V. (2000). Scheduling with inserted idle time: problem taxonomy and literature review. Operations Research, 48(1), 99–110.

    Article  Google Scholar 

  • Kim, D. W., Kim, K.-H., Jang, W., & Chen, F. F. (2002). Unrelated parallel machine scheduling with setup times using simulated annealing. Robotics and Computer Integrated Manufacturing, 18, 223–231.

    Article  Google Scholar 

  • Lawler, E. L. (1977). A “pseudopolynomial” algorithm for sequencing jobs to minimize total tardiness. Annals of Discrete Mathematics, 1, 331–342.

    Article  Google Scholar 

  • Radhakrishnan, S., & Ventura, J. A. (2000). Simulated annealing for parallel machine scheduling with earliness-tardiness penalties and sequence-dependent set-up times. International Journal of Production Research, 38(10), 2233–2252.

    Article  Google Scholar 

  • Storer, R. H., Wu, S., & Vaccari, R. (1992). New search spaces for sequencing problems with application to job shop scheduling. Operations Research, 39(10), 1495–1509.

    Google Scholar 

  • Szwarc, W., & Mukhopadhyay, S. K. (1995). Optimal timing schedules in earliness-tardiness single machine sequencing. Naval Research Logistics, 42(7), 1109–1114.

    Article  Google Scholar 

  • Tarjan, R. E. (1983). Data structures and network algorithms. Philadelphia: Society for Industrial and Applied Mathematics.

    Google Scholar 

  • Zhu, Z., & Heady, R. B. (2000). Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach. Computers and Industrial Engineering, 38, 297–305.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ILOG (S) Pte Ltd, 77 Science Park Drive, Singapore, 118256, Singapore

    Guang Feng

  2. School of Information Systems, Singapore Management University, 80 Stamford Road, Singapore, 178902, Singapore

    Hoong Chuin Lau

Authors
  1. Guang Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hoong Chuin Lau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hoong Chuin Lau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, G., Lau, H.C. Efficient algorithms for machine scheduling problems with earliness and tardiness penalties. Ann Oper Res 159, 83–95 (2008). https://doi.org/10.1007/s10479-007-0284-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-007-0284-z

Keywords

Search

Navigation