Skip to main content
Springer Nature Link
Log in

Common due window assignment and single machine scheduling with delivery time, resource allocation, and job-dependent learning effect

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

A single machine scheduling problem takes into account a common due window assignment, including delivery time, resource allocation and learning effect. The basic processing time, position and allotted resources are all linked to the actual processing time. We take into consideration three goal functions, which minimize the costs of earliness, tardiness, start time of window, window size, resource allocation and makespan. The aim is to find the optimal sequence and distribution of resources. Polynomial time algorithms are provided for each of the three issues. The algorithms have \(O(n^3)\) levels of complexity, where n is the number of jobs. Special cases with the same learning rates are also considered. Polynomial time algorithms are also provided for each of the special cases. The algorithms have \(O(n\textrm{log}n)\) levels of complexity.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Algorithm 1
Algorithm 2
Algorithm 3
Algorithm 4

Similar content being viewed by others

References

  1. Wang, J.-B., Wang, J.-J.: Research on scheduling with job-dependent learning effect and convex resource dependent processing times. Int. J. Prod. Res. 53(19), 5826–5836 (2015)

    Google Scholar 

  2. Wang, J.-B., Liu, F., Wang, J.-J.: Research on m-machine flow shop scheduling with truncated learning effects. Int. Trans. Oper. Res. 26(3), 1135–1151 (2019)

    MathSciNet  Google Scholar 

  3. Geng, X.-N., Wang, J.-B., Bai, D.: Common due date assignment scheduling for a no-wait flowshop with convex resource allocation and learning effect. Eng. Optim. 51(8), 1301–1323 (2019)

    MathSciNet  Google Scholar 

  4. Liang, X.-X., Zhang, B., Wang, J.-B., Yin, N., Huang, X.: Study on flow shop scheduling with sum-of-logarithm-processing-times-based learning effects. J. Appl. Math. Comput. 61, 373–388 (2019)

    MathSciNet  Google Scholar 

  5. Wang, J.-B., Gao, M., Wang, J.-J., Liu, L., He, H.: Scheduling with a position-weighted learning effect and job release dates. Eng. Optim. 52(9), 1475–1493 (2020)

    MathSciNet  Google Scholar 

  6. Sun, X., Geng, X.-N., Liu, F.: Flow shop scheduling with general position weighted learning effects to minimise total weighted completion time. J. Oper. Res. Soc. 72(12), 2674–2689 (2021)

    Google Scholar 

  7. Qian, J., Zhan, Y.: Single-machine group scheduling model with position-dependent and job-dependent DeJong’s learning effect. Mathematics 10(14), 2454 (2022)

    Google Scholar 

  8. Wang, J.-B., Zhang, L.-H., Lv, Z.-G., Lv, D.-Y., Geng, X.-N., Sun, X.: Heuristic and exact algorithms for single-machine scheduling problems with general truncated learning effects. Comput. Appl. Math. 41, 417 (2022)

    MathSciNet  Google Scholar 

  9. Gao, J., Zou, J., Zhang, Y.: Single-machine scheduling with a deteriorating maintenance activity and De Jong’s learning effect. Int. J. Found. Comput. S. https://doi.org/10.1142/S0129054122460030 (2022)

  10. Ferraro, A., Rossit, D.A., Toncovich, A.: Flow shop scheduling problem with non-linear learning effects: A linear approximation scheme for non-technical users. J. Comput. Appl. Math. 424(1), 114983 (2023)

    MathSciNet  Google Scholar 

  11. Qian, J.: Note on single machine common flow allowance group scheduling with learning effect and resource allocation. Comput. Ind. Eng. 186, 109750 (2023)

    Google Scholar 

  12. Xin, X., Jiang, Q., Li, C., Li, S., Chen, K.: Permutation flow shop energy-efficient scheduling with a position-based learning effect. Int. J. Prod. Res. 61(2), 382–409 (2023)

    Google Scholar 

  13. Pei, J., Zhou, Y., Yan, P., Pardalos, P.M.: A concise guide to scheduling with learning and deteriorating effects. Int. J. Prod. Res. 61(6), 2010–2031 (2023)

    Google Scholar 

  14. Li, M.-H., Lv, D.-Y., Lu, Y.-Y., Wang, J.-B.: Scheduling with group technology, resource allocation, and learning effect simultaneously. Mathematics 12(7), 1029 (2024)

    Google Scholar 

  15. Sun, L., Zhang, X.H., Ning, L.: Results of parallel-machine scheduling model with maintenance activity considering time-dependent deterioration, delivery times, and resource allocation. Math. Probl. Eng. 2021, 8826345 (2021)

    Google Scholar 

  16. Qian, J., Zhan, Y.: The due date assignment scheduling problem with delivery times and truncated sum-of-processing-times-based learning effect. Mathematics 9(23), 3085 (2021)

    Google Scholar 

  17. Qian, J., Han, H.: The due date assignment scheduling problem with the deteriorating jobs and delivery time. J Appl. Math. Comput. 68, 2173–2186 (2022)

    MathSciNet  Google Scholar 

  18. Qian, J., Chang, G.: A note on study on proportionate flowshop scheduling with due-date assignment and position-dependent weights. Optim. Lett. 16, 2645–2648 (2022)

    MathSciNet  Google Scholar 

  19. Qian, J., Chang, G., Zhang, X.: Single-machine common due-window assignment and scheduling with position-dependent weights, delivery time, learning effect and resource allocations. J Appl. Math. Comput. https://doi.org/10.1007/s12190-024-02023-5 (2024)

  20. Wang, J.-B., Xue, J., Cui, B., Gao, M.: Single-machine scheduling problems with variable processing yimes and past-sequence-dependent delivery times. Asia-Pacific J. Oper. Res. 39(2), 2150013 (2022)

    Google Scholar 

  21. Zhang, C., Li, Y., Cao, J., Yang, Z., Coelho, L.C.: Exact and matheuristic methods for the parallel machine scheduling and location problem with delivery time and due date. Comput. Oper. Res. 147, 105936 (2022)

    MathSciNet  Google Scholar 

  22. Qian, J., Zhan, Y.: The due window assignment problems with deteriorating job and delivery time. Mathematics 10(10), 2454 (2022)

    Google Scholar 

  23. Qian, J., Han, H.Y.: Improved algorithms for proportionate flow shop scheduling with due-window assignment. Ann. Oper. Res. 309, 249–258 (2022)

    MathSciNet  Google Scholar 

  24. Wang, S.-H., Lv, D.-Y., Wang, J.-B.: Research on position-dependent weights scheduling with delivery times and truncated sum-of-processing-times-based learning effect. J. Ind. Manag. Optim. 19(4), 2824–2837 (2023)

    MathSciNet  Google Scholar 

  25. Ren, N., Lv, D.-Y., Wang, J.-B., Wang, X.-Y.: Solution algorithms for single-machine scheduling with learning effects and exponential past-sequence-dependent delivery times. J. Ind. Manag. Optim. 19(11), 8429–8450 (2023)

    MathSciNet  Google Scholar 

  26. Ren, N., Wang, J.-B., Wang, E.: Research on delivery times scheduling with truncated learning effects. Comput. Appl. Math. 42, 243 (2023)

    MathSciNet  Google Scholar 

  27. Mao, R.-R., Wang, Y.-C., Lv, D.-Y., Wang, J.-B., Lu, Y.-Y.: Delivery times scheduling with deterioration effects in due window assignment environments. Mathematics 11(18), 3983 (2023)

    Google Scholar 

  28. Mao, R.-R., Lv, D.-Y., Ren, N., Wang, J.-B.: Supply chain scheduling with deteriorating jobs and delivery times. J. Appl. Math. Comput. https://doi.org/10.1007/s12190-024-02052-0 (2024)

  29. Wang, Y.-C., Wang, J.-B.: Study on convex resource allocation scheduling with a time-dependent learning effect. Mathematics 11(14), 3179 (2023)

    Google Scholar 

  30. Yan, J.-X., Ren, N., Bei, H.-B., Bao, H., Wang, J.-B.: Study on resource allocation scheduling problem with learning factors and group technology. J. Ind. Manag. Optim. 19(5), 3419–3435 (2023)

    MathSciNet  Google Scholar 

  31. Chen, Y., Ma, X.L., Zhang, G.Q., Cheng, Y.X.: On optimal due date assignment without restriction and resource allocation in group technology scheduling. J. Comb. Optim. 45(2), 64 (2023)

    MathSciNet  Google Scholar 

  32. Sun, X., Geng, X.-N., Wang, J.-B., Liu, F.: Convex resource allocation scheduling in the no-wait flowshop with common flow allowance and learning effect. Int. J. Prod. Res. 57(6), 1873–1897 (2019)

    Google Scholar 

  33. Liu, W., Jiang, C.: Due-date assignment scheduling involving job-dependent learning effects and convex resource allocation. Eng. Optimiz. 52(1), 74–89 (2020)

    MathSciNet  Google Scholar 

  34. Sun, L., Yu, A.J., Wu, B.: Single machine common flow allowance group scheduling with learning effect and resource allocation. Comput. Ind. Eng. 139, 106126 (2020)

    Google Scholar 

  35. Koulamas, C., Kyparisis, G.J.: Single-machine scheduling problems with past-sequence-dependent delivery times. Int. J. Prod. Econ. 126(2), 264–266 (2010)

    Google Scholar 

  36. Janiak, A., Janiak, W.A., Krysiak, T., Kwiatkowski, T.: A survey on scheduling problems with due windows. Eur. J. Oper. Res. 242(2), 347–357 (2015)

    MathSciNet  Google Scholar 

  37. Rolim, G.A., Nagano, M.S.: Structural properties and algorithms for earliness and tardiness scheduling against common due dates and windows: A review. Comput. Ind. Eng. 149, 106803 (2020)

    Google Scholar 

  38. Huang, X., Yin, N., Liu, W.-W., Wang, J.-B.: Common due window assignment scheduling with proportional linear deterioration effects. Asia-Pacific J. Oper. Res. 37(1), 1950031 (2020)

    MathSciNet  Google Scholar 

  39. Wang, J.-B., Zhang, B., Li, L., Bai, D., Feng, Y.-B.: Due window assignment scheduling problems with position-dependent weights on a single machine. Optim. Lett. 52(2), 185–193 (2020)

    MathSciNet  Google Scholar 

  40. 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. Dis. Math. 5, 287–326 (1979)

    MathSciNet  Google Scholar 

  41. Wang, J.-B., Li, L.: Machine scheduling with deteriorating jobs and modifying maintenance activities. Comput. J. 61(1), 47–53 (2018)

    MathSciNet  Google Scholar 

  42. He, H., Hu, Y., Liu, W.-W.: Scheduling with deteriorating effect and maintenance activities under parallel processors. Eng. Optimiz. 53(12), 2070–2087 (2021)

    Google Scholar 

  43. Sun, X., Liu, T., Geng, X.-N., Hu, Y., Xu, J.-X.: Optimization of scheduling problems with deterioration effects and an optional maintenance activity. J. Sched. 26, 251–266 (2023)

    MathSciNet  Google Scholar 

  44. Oron, D.: Scheduling controllable processing time jobs in a deteriorating environment. J. Oper. Res. Soc. 64, 49–56 (2014)

    Google Scholar 

  45. Lv, Z.-G., Zhang, L.-H., Wang, X.-Y., Wang, J.-B.: Single machine scheduling proportionally deteriorating jobs with ready times subject to the total weighted completion time minimization. Mathematics 12(4), 610 (2024)

    Google Scholar 

  46. Zhang, L.-H., Geng, X.-N., Xue, J., Wang, J.-B.: Single machine slack due window assignment and deteriorating jobs. J. Ind. Manag. Optim. 20(4), 1593–1614 (2024)

    MathSciNet  Google Scholar 

  47. Wang, J.-B., Wang, Y.-C., Wan, C., Lv, D.-Y., Zhang, L.: Controllable processing time scheduling with total weighted completion time objective and deteriorating jobs. Asia-Pacific J. Oper. Res. 2350026, https://doi.org/10.1142/S0217595923500264 (2024)

  48. Lv, D.-Y., Wang, J.-B.: No-idle flow shop scheduling with deteriorating jobs and common due date under dominating machines. Asia-Pacific J. Oper. Res. 2450003, https://doi.org/10.1142/S021759592450003 (2024)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Northeastern University, Shenyang, 110819, People’s Republic of China

    Jin Qian & Zhiyuan Guo

Authors
  1. Jin Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiyuan Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin Qian.

Ethics declarations

Conflict of interest

The authors declare no Conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qian, J., Guo, Z. Common due window assignment and single machine scheduling with delivery time, resource allocation, and job-dependent learning effect. J. Appl. Math. Comput. 70, 4441–4471 (2024). https://doi.org/10.1007/s12190-024-02090-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-024-02090-8

Keywords

Mathematics Subject Classification