Skip to main content
SpringerLink
Log in

A note on the algorithm LPT-FF for a flowshop scheduling with two batch-processing machines

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

A flowshop scheduling problem with two batch-processing machines is investigated in this paper, with the optimization goal to minimize the makespan. When the job processing times on the two machines are positively correlated, a \(4\)-approximation algorithm for this NP-hard problem was previously proposed. We show that this algorithm has a worst-case performance guarantee of \(2\).

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

Fig. 1

Similar content being viewed by others

References

  1. Cheng, B., Yang, S., Hu, X., Chen, B.: Minimizing makespan and total completion time for parallel batch processing machines with non-identical job sizes. Appl. Math. Model. 36, 3161–3167 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cheng, B., Yang, S., Hu, X., Li, K.: Scheduling algorithm for flow shop with two batch-processing machines and arbitrary job sizes. Int. J. Syst. Sci. 45, 571–578 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dupont, L., Flipo, C.D.: Minimizing the makespan on a batch machine with arbitrary job sizes: an exact procedure. Comput. Oper. Res. 29, 807–819 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and Company, San Francisco (1979)

    MATH  Google Scholar 

  5. Graham, R.L., Lawler, E.L., Lenstra, J.K., Kan, R.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ikura, Y., Gimple, M.: Scheduling algorithms for a single batching processing machine. Oper. Res. Lett. 5, 61–65 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ji, M., Cheng, T.C.E.: Batch scheduling simple linear deterioration jobs on a single machine to minimize makespan. Eur. J. Oper. Res. 202, 90–98 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  8. Johnson, S.M.: Optimal two- and three-machine production schedules with setup times included. Naval Res. Logist. 1, 61–68 (1954)

    Article  Google Scholar 

  9. Kashan, A.H., Karimi, B., Ghomi, F.: A note minimizing makespan on a single batch processing machine with nonidentical job sizes. Theor. Comput. Sci. 410, 2754–2758 (2009)

    Article  MATH  Google Scholar 

  10. Kashan, A.H., Karimi, B., Jenabi, M.: A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes. Comput. Oper. Res. 35, 1084–1098 (2008)

    Article  MATH  Google Scholar 

  11. Kashan, A.H., Karimi, B., Jolai, F.: Minimizing makespan on a single batch processing machine with non-identical job sizes: A hybrid genetic approach. In: Proceedings of the 6th European Conference on Evolutionary Computation in Combinatorial Optimization (EvoCOP 2006), LNCS 3906. pp 135–146 (2006)

  12. Lee, C.-Y., Uzsoy, R., Martin, L.A.: Efficient algorithms for scheduling semiconductor burn-in operations. Oper. Res. 40, 764–775 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, C.L., Lee, C.-Y.: Scheduling with agreeable release times and due dates on a batch processing machine. Eur. J. Oper. Res. 96, 564–569 (1997)

    Article  MATH  Google Scholar 

  14. Li, S., Li, G., Wang, X., Liu, Q.: Minimizing makespan on a single batch processing machine with release times and arbitrary job sizes. Oper. Res. Lett. 33, 157–164 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Li, S., Ng, C.T., Cheng, T.C.E., Yuan, J.: Parallel batch scheduling of deteriorating jobs with release times to minimize the makespan. Eur. J. Oper. Res. 210, 482–488 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  16. Méndez, C.A., Cerdá, J., Grossmann, I.E., Harjunkoski, I., Fahl, M.: State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comput. Chem. Eng. 30, 913–946 (2006)

    Article  Google Scholar 

  17. Rajaram, K., Karmarkar, U.S.: Campaign planning and scheduling for multiproduct batch operations with applications to the food-processing industry. Manuf. Serv. Oper. Manag. 6, 253–269 (2004)

    Google Scholar 

  18. Tang, L., Liu, P.: Minimizing makespan in a two-machine flowshop scheduling with batching and release time. Math. Comput. Model. 49, 1071–1077 (2009)

    Article  MATH  Google Scholar 

  19. Tang, L., Zhang, Y.: A new Lagrangian relaxation algorithm for scheduling dissimilar parallel machines with release dates. Int. J. Syst. Sci. 42, 1133–1141 (2011)

    Article  MATH  Google Scholar 

  20. Uzsoy, R.: Scheduling a single batch processing machine with non-identical job sizes. Int. J. Prod. Res. 32, 1615–1635 (1994)

    Article  MATH  Google Scholar 

  21. Xia, B., Tan, Z.: Tighter bounds of the first fit algorithm for the bin-packing problem. Discrete Appl. Math. 158, 1668–1675 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Zhang, G., Cai, X., Lee, C.-Y., Wong, C.K.: Minimizing makespan on a single batch processing machine with nonidentical job sizes. Naval Res. Logist. 48, 226–240 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

Dong is supported by the Zhejiang Provincial Natural Science Foundation Grants No. LY13A010015 and the Science Foundation of Zhejiang Sci-Tech University (ZSTU) Grants No. 13062171-Y; Hu is supported by the National Natural Science Foundation of China Grants No. 11271324 and 11471286; Lin is supported by NSERC and the Science Foundation of Zhejiang Sci-Tech University (ZSTU) Grants No. 14062170-Y. Lin’s work was mostly done during his sabbatical leave at the ZSTU.

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, Zhejiang, China

    Jianming Dong, Jueliang Hu & Guohui Lin

  2. Department of Computing Science, University of Alberta, Edmonton, AB, T6G 2E8, Canada

    Guohui Lin

Authors
  1. Jianming Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jueliang Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guohui Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guohui Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dong, J., Hu, J. & Lin, G. A note on the algorithm LPT-FF for a flowshop scheduling with two batch-processing machines. Optim Lett 10, 109–118 (2016). https://doi.org/10.1007/s11590-015-0859-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-015-0859-6

Keywords

Search

Navigation