Skip to main content
SpringerLink
Log in

MIP formulations and heuristics for solving parallel batching problems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper addresses the scheduling problem involving batch processing machines, which is also known as parallel batching in the literature. The presented mixed integer programming formulation first provides an elegant model for the problem under study. Furthermore, it enables solutions to the problem instances beyond the capability of exact methods developed so far. In order to alleviate computational burden, the authors propose MIP-based heuristic approaches which balance solution quality and computing time.

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

  1. C. N. Potts and M. Y. Kovalyov, Scheduling with batching: A review, European Journal of Operational Research, 2000, 120: 228–249.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Damodaran, P. K. Manjeshwar, and K. Srihari, Minimizing makespan on a batch processing machine with non-identical job sizes using genetic algorithms, International Journal of Production Economics, 2006, 103: 882–891.

    Article  Google Scholar 

  3. V. Chandru, C. Y. Lee, and R. Uzsoy, Minimizing total completion time on batch processing machines, International Journal of Production Research, 1993, 31: 2097–2121.

    Article  Google Scholar 

  4. C. L. Li and C. Y. Lee, Scheduling with agreeable release times and due dates on a batch processing machine, European Journal of Operational Research, 1997, 96: 564–569.

    Article  MATH  Google Scholar 

  5. C. S. Sung and Y. I. Choung, Minimizing makespan on a single burn-in oven in semiconductor manufacturing, European Journal of Operational Research, 2000, 120: 559–574.

    Article  MATH  Google Scholar 

  6. R. Uzsoy, Scheduling a single batch processing machine with non-identical job sizes, International Journal of Production Research, 1994, 32: 1615–1635.

    Article  MATH  Google Scholar 

  7. Y. Ikura and M. Gimple, Scheduling algorithms for a single batch processing machine, Operations Research Letters, 1986, 5: 61–65.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Brucker, M. Y. Kovalyov, Y. M. Shafransky, and F. Werner, Batch scheduling with deadlines on parallel machines, Annals of Operations Research, 1998, 83: 23–40.

    Article  MATH  MathSciNet  Google Scholar 

  9. S. V. Mehta and R. Uzsoy, Minimizing total tardiness on a batch processing machine with incompatible job families, IIE Transactions, 1998, 30: 165–178.

    Article  Google Scholar 

  10. A. Devpura, J. W. Fowler, M. Carlyle, and I. Perez, Minimizing total weighted tardiness on a single batch processing machine with incompatible job families, in Proceedings of the Symposium on Operations Research, 2000: 366–371.

  11. L. Dupont and C. Dhaenens-Flipo, Minimizing the makespan on a batch processing machine with non-identical job sizes, Computers and Operations Research, 2002, 29: 807–819.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Melouk, P. Damodaran, and P. Y. Chang, Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing, International Journal of Production Economics, 2004, 87: 141–147.

    Article  Google Scholar 

  13. T. C. E. Cheng, B. M. T. Lin, and A. Toker, Makespan minimization in the two-machine flowshop batch scheduling problem, Naval Research Logistics, 2000, 47: 128–144.

    Article  MATH  MathSciNet  Google Scholar 

  14. C. S. Sung, Y. H. Kim, and S. H. Yoon, A problem reduction and decomposition approach for scheduling for a flowshop of batch processing machines, European Journal of Operational Research, 2000, 121: 179–192.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. H. Ahmadi, R. H. Ahmadi, S. Dasu, and C. S. Tang, Batching and scheduling jobs on batch and discrete processors, Operations Research, 1992, 39: 750–763.

    Article  MathSciNet  Google Scholar 

  16. C. N. Potts, V. A. Strusevich, and T. Tautenhahn, Scheduling batches with simultaneous job processing for two-machine shop problems, Journal of Scheduling, 2001, 4: 25–51.

    Article  MATH  MathSciNet  Google Scholar 

  17. P. Damodaran and K. Srihari, Mixed integer formulation to minimize makespan in a flow shop with batch processing machines, Mathematical and Computer Modelling, 2004, 40: 1465–1472.

    Article  MATH  MathSciNet  Google Scholar 

  18. C. Liao and L. Liao, Improved milp models for two-machine flowshop with batch processing machines, Mathematical and Computer Modelling, 2008, 48: 1254–1264.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair of Industrial Management, Department of Business Administration and Economics, Dresden University of Technology (Technische Universitaet Dresden), Dresden, 01062, Germany

    Udo Buscher & Liji Shen

Authors
  1. Udo Buscher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liji Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Udo Buscher.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buscher, U., Shen, L. MIP formulations and heuristics for solving parallel batching problems. J Syst Sci Complex 23, 884–895 (2010). https://doi.org/10.1007/s11424-010-0210-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-010-0210-3

Keywords

Search

Navigation