Single machine serial-batching scheduling with independent setup time and deteriorating job processing times

Abstract

This paper investigates the scheduling problems of a single serial-batching machine with independent setup time and deteriorating job processing times. With the assumption of deteriorating jobs, the job processing times are described by an increasing function of their starting times. All the jobs are first partitioned into serial batches and then processed on a single serial-batching machine. Before each batch is processed, an independent constant setup time is required. Two optimization algorithms are proposed to solve the problems of minimizing the makespan and the total number of tardy jobs, respectively. Specifically, for the problem of minimizing the total completion time, two special cases with the smallest and the largest number of batches are studied, and an optimization algorithm is also presented for the special case without setup time.

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

References

  1. 1.

    Gupta, J.N.D., Gupta, S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14, 387–393 (1988)

    Google Scholar 

  2. 2.

    Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Oper. Res. 38, 495–498 (1990)

    Article  MATH  Google Scholar 

  3. 3.

    Qi, X.L., Zhou, S.G., Yuan, J.J.: Single machine parallel-batch scheduling with deteriorating jobs. Theor. Comput. Sci. 410, 830–836 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. 4.

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

    Article  MathSciNet  MATH  Google Scholar 

  5. 5.

    Miao, C.X., Zhang, Y.Z., Cao, Z.G.: Bounded parallel-batch scheduling on single and multi machines for deteriorating jobs. Inf. Process. Lett. 111, 798–803 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. 6.

    Miao, C.X., Zhang, Y.Z., Wu, C.L.: Scheduling of deteriorating jobs with release dates to minimize the maximum lateness. Theor. Comput. Sci. 462, 80–87 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. 7.

    Wu, C.C., Shiau, Y.R., Lee, W.C.: Single-machine group scheduling problems with deterioration consideration. Comput. Oper. Res. 35, 1652–1659 (2008)

    Article  MATH  Google Scholar 

  8. 8.

    Wu, C.C., Lee, W.C.: Single-machine group-scheduling problems with deteriorating setup times and job-processing times. Int. J. Prod. Econ. 115, 128–133 (2008)

    Article  Google Scholar 

  9. 9.

    Wang, J.B., Lin, L., Shan, F.: Single-machine group scheduling problems with deteriorating jobs. Int. J. Adv. Manuf. Technol. 39, 808–812 (2008)

    Article  Google Scholar 

  10. 10.

    Wang, J.B., Gao, W.J., Wang, L.Y., Wang, D.: Single machine group scheduling with general linear deterioration to minimize the makespan. Int. J. Adv. Manuf. Technol. 43, 146–150 (2009)

    Article  Google Scholar 

  11. 11.

    Zhang, X.G., Yan, G.L.: Single-machine group scheduling problems with deteriorated and learning effect. Appl. Math. Comput. 216, 1259–1266 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. 12.

    Yang, S.J., Yang, D.L.: Single-machine group scheduling problems under the effects of deterioration and learning. Comput. Ind. Eng. 58, 754–758 (2010)

    Article  Google Scholar 

  13. 13.

    Wang, J.B., Sun, L.Y.: Single-machine group scheduling with linearly decreasing time-dependent setup times and job processing times. Int. J. Adv. Manuf. Technol. 49, 765–772 (2010)

    Article  Google Scholar 

  14. 14.

    Wei, C.M., Wang, J.B.: Single machine quadratic penalty function scheduling with deteriorating jobs and group technology. Appl. Math. Model. 34, 3642–3647 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. 15.

    Huang, X., Wang, M.Z., Wang, J.B.: Single-machine group scheduling with both learning effects and deteriorating jobs. Comput. Ind. Eng. 60, 750–754 (2011)

    Article  Google Scholar 

  16. 16.

    Yang, S.J.: Group scheduling problems with simultaneous considerations of learning and deterioration effects on a single-machine. Appl. Math. Model. 35, 4008–4016 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. 17.

    Bai, J., Li, Z.R., Huang, X.: Single-machine group scheduling with general deterioration and learning effects. Appl. Math. Model. 36, 1267–1274 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. 18.

    Lee, W.C., Lu, Z.S.: Group scheduling with deteriorating jobs to minimize the total weighted number of late jobs. Appl. Math. Comput. 218, 8750–8757 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. 19.

    Wang, J.B., Huang, X., Wu, Y.B., Ji, P.: Group scheduling with independent setup times, ready times, and deteriorating job processing times. Int. J. Adv. Manuf. Technol. 60, 643–649 (2012)

    Article  Google Scholar 

  20. 20.

    Wang, D., Huo, Y.Z., Ji, P.: Single-machine group scheduling with deteriorating jobs and allotted resource. Optim. Lett. (2012). doi:10.1007/s11590-012-0577-2

  21. 21.

    Xuan, H., Tang, L.X.: Scheduling a hybrid flowshop with batch production at the last stage. Comput. Oper. Res. 34, 2718–2733 (2007)

    Article  MATH  Google Scholar 

  22. 22.

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We would like to thank the editors and referees for their valuable comments and suggestions. This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71171071, 71131002), and LATNA laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jun Pei.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Pei, J., Liu, X., Pardalos, P.M. et al. Single machine serial-batching scheduling with independent setup time and deteriorating job processing times. Optim Lett 9, 91–104 (2015). https://doi.org/10.1007/s11590-014-0740-z

Download citation

Keywords

  • Serial-batching scheduling
  • Deteriorating jobs
  • Single machine
  • Setup time