Advertisement

Journal of Scheduling

, Volume 13, Issue 6, pp 629–638 | Cite as

On the complexity of bi-criteria scheduling on a single batch processing machine

  • L. L. Liu
  • C. T. Ng
  • T. C. E. Cheng
Article

Abstract

This paper considers hierarchical bi-criteria scheduling on a single batch processing machine where the primary criterion is the makespan. We show that the problem where the secondary criterion is the total completion time can be solved in polynomial time for a given machine capacity and the problem where the secondary criterion is the (weighted) number of late jobs is (strongly) NP-hard.

Keywords

Scheduling Batch processing Bi-criteria Complexity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Brucker, P., Gladky, A., Hoogevreen, H., Kovalyov, M. Y., Potts, C. N., Tautenhahn, T., & Van de Velde, S. (1998). Scheduling a batching machine. Journal of Scheduling, 1, 31–54. CrossRefGoogle Scholar
  2. Chandru, V., Lee, C. Y., & Uzsoy, R. (1993). Minimizing total completion time on batch processing machine. International Journal of Production Research, 31, 2097–2122. CrossRefGoogle Scholar
  3. Chen, C. L., & Bulfin, R. L. (1993). Complexity of single machine, multi-criteria scheduling problems. European Journal of Operational Research, 70, 115–125. CrossRefGoogle Scholar
  4. Cheng, T. C. E., Liu, Z. H., & Yu, W. C. (2001). Scheduling jobs with release dates and deadlines on a batch processing machine. IIE Transactions, 33, 685–690. Google Scholar
  5. Jolai, F. (2005). Minimizing number of tardy jobs on a batch processing machine with incompatible job families. European Journal of Operational Research, 162, 184–190. CrossRefGoogle Scholar
  6. Karp, R. M. (1972). Reducibility among combinatorial problems. In R. E., Miller, & J. W., Thatcher (Eds.), Complexity of computer computations (pp. 85–103). New York: Plenum. Google Scholar
  7. Lee, C. Y., & Uzsoy, R. (1999). Minimizing makespan on a single batch processing machine with dynamic job arrivals. International Journal of Production Research, 37, 219–236. CrossRefGoogle Scholar
  8. Lee, C. Y., & Vairaktarakis, G. L. (1993). Complexity of single machine hierarchical scheduling: A survey. Complexity in Numerical Optimization, 19, 269–298. Google Scholar
  9. Liu, Z. H., Yuan, J. J., & Cheng, T. C. E. (2003). On scheduling an unbounded batch machine. Operations Research Letters, 31, 42–48. CrossRefGoogle Scholar
  10. Mehta, S. V., & Uzsoy, R. (1998). Minimizing total tardiness on a batch processing machine with incompatible job families. IIE Transactions, 30, 165–178. CrossRefGoogle Scholar
  11. Moore, J. M. (1968). An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15, 102–109. CrossRefGoogle Scholar
  12. Nagar, A., Haddock, J., & Heragu, S. (1995). Multiple and bicriteria scheduling: A literature survey. European Journal of Operational Research, 81, 88–104. CrossRefGoogle Scholar
  13. Perez, I. C., Fowler, J. W., & Carlyle, W. M. (2005). Minimizing total weighted tardiness on a single batch process machine with incompatible job families. Computers and Operations Research, 32, 327–341. Google Scholar
  14. Smith, W. E. (1956). Various optimizers for single stage production. Naval Research Logistics Quarterly, 3, 59–66. CrossRefGoogle Scholar
  15. Uzsoy, R. (1995). Scheduling batch processing machines with incompatible job families. International Journal of Production Research, 33, 2685–2708. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of ScienceShanghai Second Polytechnic UniversityPudongChina
  2. 2.Department of Logistics and Maritime StudiesThe Hong Kong Polytechnic UniversityHung HomHong Kong

Personalised recommendations