Skip to main content
SpringerLink
Log in

Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine

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

Abstract

This paper studies the bounded parallel-batching scheduling problem considering job rejection, deteriorating jobs, setup time, and non-identical job sizes. Each job will be either rejected with a certain penalty cost, or accepted and further processed in batches on a single machine. There is a setup time before processing each batch, and the objective is to minimize the sum of the makespan and the total penalty. Several useful preliminaries for arranging accepted job with identical size are proposed. Based on these preliminaries, we first investigate a special case where all the jobs are considered to have the identical size, and develop a dynamic programming algorithm to solve it. The preliminaries help to reduce the complexity of the dynamic programming algorithm from \( O\left( {n!n^{2} \sum\nolimits_{i = 1}^{n} {w_{j} } } \right) \) to \( O\left( {n^{2} \sum\nolimits_{i = 1}^{n} {w_{j} } } \right) \). For the general problem with non-identical job sizes, we propose a hybrid algorithm combining heuristic with dynamic programming algorithm (H-DP) to obtain satisfactory solutions within reasonable time. Finally, the effectiveness and efficiency of the H-DP algorithm are illustrated by a series of computational 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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. 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 

  2. Zhang, G., Cai, X., Lee, C.Y., et al.: Minimizing makespan on a single batch processing machine with non-identical job sizes. Naval Res. Logist. (NRL) 48(3), 226–240 (2001)

    Article  MATH  Google Scholar 

  3. Pei, J., Liu, X., Pardalos, P.M., Fan, W., Yang, S., Wang, L.: Application of an effective modified gravitational search algorithm for the coordinated scheduling problem in a two-stage supply chain. Int. J. Adv. Manuf. Technol. 70(1–4), 335–348 (2014)

    Article  Google Scholar 

  4. Pei, J., Liu, X., Pardalos, P.M., Fan, W., Wang, L., Yang, S.: Solving a supply chain scheduling problem with non-identical job sizes and release times by applying a novel effective heuristic algorithm. Int. J. Syst. Sci. 47(4), 765–776 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jiang, L., Pei, J., Liu, X., et al.: Uniform parallel batch machines scheduling considering transportation using a hybrid DPSO-GA algorithm. Int. J. Adv. Manuf. Technol. 89(5–8), 1887–1900 (2017)

    Article  Google Scholar 

  6. Suhaimi, N., Nguyen, C., Damodaran, P.: Lagrangian approach to minimize makespan of non-identical parallel batch processing machines. Comput. Ind. Eng. 101, 295–302 (2016)

    Article  Google Scholar 

  7. Malapert, A., Guéret, C., Rousseau, L.M.: A constraint programming approach for a batch processing problem with non-identical job sizes. Eur. J. Oper. Res. 221(3), 533–545 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Al-Salamah, M.: Constrained binary artificial bee colony to minimize the makespan for single machine batch processing with non-identical job sizes. Appl. Soft Comput. 29, 379–385 (2015)

    Article  Google Scholar 

  9. Wu, T., Akartunalı, K., Jans, R., Liang, Z.: Progressive selection method for the coupled lot-sizing and cutting-stock problem. INFORMS J. Comput. 29(3), 523–543 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tan, Y., Carrillo, J.E., Cheng, H.K.: The agency model for digital goods. Decis. Sci. 47(4), 628–660 (2016)

    Article  Google Scholar 

  11. Tan, Y.R., Carrillo, J.E.: Strategic analysis of the agency model for digital goods. Prod. Oper. Manag. 26(4), 724–741 (2017)

    Article  Google Scholar 

  12. Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., et al.: Multiprocessor scheduling with rejection. SIAM J. Discrete Math. 13(1), 64–78 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lu, L., Zhang, L., Yuan, J.: The unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan. Theoret. Comput. Sci. 396(1–3), 283–289 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Feng, H., Liu, H.: Minimizing makespan on an unbounded parallel batch processor with rejection and release times. In: 2009 WRI World Congress on Computer Science and Information Engineering. IEEE, vol. 2, pp. 587–590 (2009)

  15. Zhang, L.Q., Lu, L.F., Ng, C.T.: The unbounded parallel-batch scheduling with rejection. J. Oper. Res. Soc. 63(3), 293–298 (2012)

    Article  Google Scholar 

  16. Zou, J., Miao, C.: Parallel batch scheduling of deteriorating jobs with release dates and rejection. Sci. World J. 16, 3–28 (2014)

    Google Scholar 

  17. Cao, Z., Yang, X.: A PTAS for parallel batch scheduling with rejection and dynamic job arrivals. Theoret. Comput. Sci. 410(27–29), 2732–2745 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lu, L., Cheng, T.C.E., Yuan, J., et al.: Bounded single-machine parallel-batch scheduling with release dates and rejection. Comput. Oper. Res. 36(10), 2748–2751 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Miao, C., Meng, F.: Parallel-batch scheduling with deterioration and rejection on a single machine. AMSE J. AMSE IIETA Publ. 2017 Ser. Adv. A 54(1), 64–74 (2017)

    Google Scholar 

  20. Miao, C., Meng, F., Zou, J., et al.: Batch scheduling with proportional-linear deterioration and outsourcing. Math. Probl. Eng. 2017(4), 1–5 (2017)

    MathSciNet  MATH  Google Scholar 

  21. Ng, C.T., Wang, J.B., Cheng, T.C.E., et al.: A branch-and-bound algorithm for solving a two-machine flow shop problem with deteriorating jobs. Comput. Oper. Res. 37(1), 83–90 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pei, J., Liu, X., Fan, W., Pardalos, P.M., Lu, S.: A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget, and resource constraint in multiple manufacturers. Omega (2017). https://doi.org/10.1016/j.omega.2017.12.003

    Article  Google Scholar 

  23. Pei, J., Cheng, B., Liu, X., Pardalos, P.M., Kong, M.: Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time. Ann. Oper. Res. (2017). https://doi.org/10.1007/s10479-017-2481-8

    Article  MATH  Google Scholar 

  24. Mosheiov, G.: Scheduling jobs with step-deterioration; minimizing makespan on a single-and multi-machine. Comput. Ind. Eng. 28(4), 869–879 (1995)

    Article  MathSciNet  Google Scholar 

  25. Ji, M., He, Y., Cheng, T.C.E.: Scheduling linear deteriorating jobs with an availability constraint on a single machine. Theoret. Comput. Sci. 362(1–3), 115–126 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  26. Kunnathur, A.S., Gupta, S.K.: Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem. Eur. J. Oper. Res. 47(1), 56–64 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  27. Mosheiov, G.: Λ-shaped policies to schedule deteriorating jobs. J. Oper. Res. Soc. 47(9), 1184–1191 (1996)

    Article  MATH  Google Scholar 

  28. Yang, S.J., Lee, H.T., Guo, J.Y.: Multiple common due dates assignment and scheduling problems with resource allocation and general position-dependent deterioration effect. Int. J. Adv. Manuf. Technol. 67(1–4), 181–188 (2013)

    Article  Google Scholar 

  29. Gupta, J.N.D., Gupta, S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14(4), 387–393 (1988)

    Article  Google Scholar 

  30. Zhang, X., Yin, Y., Wu, C.C.: Scheduling with non-decreasing deterioration jobs and variable maintenance activities on a single machine. Eng. Optim. 49(1), 84–97 (2017)

    Article  MathSciNet  Google Scholar 

  31. Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Oper. Res. 38(3), 495–498 (1990)

    Article  MATH  Google Scholar 

  32. Alidaee, B., Womer, N.K.: Scheduling with time dependent processing times: review and extensions. J. Oper. Res. Soc. 50(7), 711–720 (1999)

    Article  MATH  Google Scholar 

  33. Cheng, T.C.E., Ding, Q., Lin, B.M.T.: A concise survey of scheduling with time-dependent processing times. Eur. J. Oper. Res. 152(1), 1–13 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  35. Li, S., Ng, C.T., Cheng, T.C.E., et al.: Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan. Eur. J. Oper. Res. 210(3), 482–488 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  36. Lu, S., Feng, H., Li, X.: Minimizing the makespan on a single parallel batching machine. Theoret. Comput. Sci. 411(7–9), 1140–1145 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71871080, 71231004, 71601065, 71690235, 71501058, 71601060), Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 project), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province, Open Research Fund Program of Key Laboratory of Process Optimization and Intelligent Decision-making (Hefei University of Technology), Ministry of Education.

Author information

Authors and Affiliations

  1. School of Management, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Min Kong, Xinbao Liu, Jun Pei & Zhiping Zhou

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Jun Pei, Zhiping Zhou & Panos M. Pardalos

  3. Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education, Hefei, 230009, People’s Republic of China

    Min Kong, Xinbao Liu & Jun Pei

Authors
  1. Min Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinbao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Pei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhiping Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Min Kong or Jun Pei.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kong, M., Liu, X., Pei, J. et al. Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine. Optim Lett 14, 857–871 (2020). https://doi.org/10.1007/s11590-019-01389-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-019-01389-x

Keywords

Search

Navigation