Skip to main content
SpringerLink
Log in

A heuristic for single machine common due date assignment problem with different earliness/tardiness weights

  • Theoretical Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

This paper considers the common due date assignment for single machine weighted earliness/tardiness scheduling problem with different earliness and tardiness weights for jobs where the objective is to minimize the cost of the sum of weighted earliness/tardiness and assignment common due date. The single machine common due date assignment problem where all jobs have the same earliness/tardiness weight has a polynomial-time algorithm to solve it optimally. Furthermore, some properties for the problem where the common due date is an input have been revealed by researchers in the literature. This paper proposes a heuristic algorithm for the problem using the revealed properties of similar problems’ optimal solutions such as the V-shaped property and zero-start time of the machine. The experimental study of this paper shows that the proposed heuristic finds better solutions for the problems in a reasonable time than a commercial solver has when the problem size is increased.

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

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Arık, O.A., Schutten, M., Topan, E.: Weighted earliness/tardiness parallel machine scheduling problem with a common due date. Expert Syst. Appl. 187, 115916 (2022). https://doi.org/10.1016/J.ESWA.2021.115916

    Article  Google Scholar 

  2. Panwalkar, S.S., Smith, M.L., Seidmann, A.: Common due date assignment to minimize total penalty for the one machine scheduling problem. Oper. Res. 30, 391–399 (1982). https://doi.org/10.1287/opre.30.2.391

    Article  Google Scholar 

  3. Hall, N.G., Posner, M.E.: Earliness-tardiness scheduling problems, I: weighted deviation of completion times about a common due date. Oper. Res. 39, 836–846 (1991). https://doi.org/10.1287/opre.39.5.836

    Article  Google Scholar 

  4. Kanet, J.J.: Minimizing the average deviation of job completion times about a common, due date. Nav. Res. Logist. Q. 28, 643–651 (1981). https://doi.org/10.1002/nav.3800280411

    Article  Google Scholar 

  5. Raghavachari, M., Zammouri, M.: Single machine scheduling with coefficient of variation minimization. Eur. J. Oper. Res. 62, 302–310 (1992). https://doi.org/10.1016/0377-2217(92)90120-X

    Article  Google Scholar 

  6. Bector, C.R., Gupta, Y.P., Gupta, M.C.: V-shape property of optimal sequence of jobs about a common due date on a single machine. Comput. Oper. Res. 16, 583–588 (1989). https://doi.org/10.1016/0305-0548(89)90043-9

    Article  Google Scholar 

  7. Raghavachari, M.: A V-shape property of optimal schedule of jobs about a common due date. Eur. J. Oper. Res. 23, 401–402 (1986). https://doi.org/10.1016/0377-2217(86)90306-1

    Article  Google Scholar 

  8. Arık, O.A.: Single machine earliness/tardiness scheduling problem with grey processing times and the grey common due date. Grey Syst. Theory Appl. 11, 95–109 (2021). https://doi.org/10.1108/gs-01-2020-0010

    Article  Google Scholar 

  9. Cheng, T.C.E., Gupta, M.C.: Survey of scheduling research involving due date determination decisions. Eur. J. Oper. Res. 38, 156–166 (1989). https://doi.org/10.1016/0377-2217(89)90100-8

    Article  Google Scholar 

  10. Elion, S.: Production scheduling. In: Haley, K.B. (ed.) Operations Research ’78, pp. 237–266. North-Holland Publishing Company, Amsterdam (1979)

    Google Scholar 

  11. Gordon, V., Proth, J.-M., Chu, C.: A survey of the state-of-the-art of common due date assignment and scheduling research. Eur. J. Oper. Res. 139, 1–25 (2002). https://doi.org/10.1016/S0377-2217(01)00181-3

    Article  Google Scholar 

  12. Seidmann, A., Panwalkar, S.S., Smith, M.L.: Optimal assignment of due-dates for a single processor scheduling problem. Int. J. Prod. Res. 19, 393–399 (1981). https://doi.org/10.1080/00207548108956667

    Article  Google Scholar 

  13. Cheng, T.C.E.: An alternative proof of optimality for the common due-date assignment problem. Eur. J. Oper. Res. 37, 250–253 (1988). https://doi.org/10.1016/0377-2217(88)90334-7

    Article  Google Scholar 

  14. Sung, C.S., Min, J.I., Park, C.K.: Heuristic algorithms for a single-machine common due date assignment under earliness/tardiness measure. J. Oper. Res. Soc. Jpn. 36, 121–133 (1993)

    Google Scholar 

  15. Koulamas, C.: Common due date assignment with generalized earliness/tardiness penalties. Comput. Ind. Eng. 109, 79–83 (2017). https://doi.org/10.1016/j.cie.2017.04.040

    Article  Google Scholar 

  16. De, P., Ghosh, J.B., Wells, C.E.: Optimal delivery time quotation and order sequencing. Decis. Sci. 22, 379–390 (1991). https://doi.org/10.1111/J.1540-5915.1991.TB00353.X

    Article  Google Scholar 

  17. Koulamas, C.: A unified solution approach for the due date assignment problem with tardy jobs. Int. J. Prod. Econ. 132, 292–295 (2011). https://doi.org/10.1016/J.IJPE.2011.04.023

    Article  Google Scholar 

  18. Kahlbacher, H.G., Cheng, T.C.E.: Parallel machine scheduling to minimize costs for earliness and number of tardy jobs. Discrete Appl. Math. 47, 139–164 (1993). https://doi.org/10.1016/0166-218X(93)90088-6

    Article  Google Scholar 

  19. Li, S.-S., Chen, R.-X.: Scheduling with common due date assignment to minimize generalized weighted earliness–tardiness penalties. Optim. Lett. 14, 1681–1699 (2020). https://doi.org/10.1007/s11590-019-01462-5

    Article  Google Scholar 

  20. Shabtay, D., Mosheiov, G., Oron, D.: Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work. Eur. J. Oper. Res. (2022). https://doi.org/10.1016/J.EJOR.2022.02.017

    Article  Google Scholar 

  21. Yeung, W.K., Oguz, C., Cheng, T.C.E.: Single-machine scheduling with a common due window. Comput. Oper. Res. 28, 157–175 (2001). https://doi.org/10.1016/S0305-0548(99)00097-0

    Article  Google Scholar 

  22. De, P., Ghosh, J.B., Wells, C.E.: Due-date assignmentand early/tardy scheduling on identical parallel machines. Nav. Res. Logist. 41, 17–32 (1994). https://doi.org/10.1002/1520-6750(199402)41:1<17::AID-NAV3220410103>3.0.CO;2-X

    Article  Google Scholar 

  23. Cheng, T.C., Chen, Z.-L.: Parallel-machine scheduling problems with earliness and tardiness penalties. J. Oper. Res. Soc. 45, 685–695 (1994). https://doi.org/10.1057/jors.1994.106

    Article  Google Scholar 

  24. Diamond, J.E., Cheng, T.C.E.: Error bound for common due date assignment and job scheduling on parallel machines. IIE Trans. Insti. Ind. Eng. 32, 445–448 (2000). https://doi.org/10.1023/A:1007644826949

    Article  Google Scholar 

  25. Mosheiov, G.: A common due-date assignment problem on parallel identical machines. Comput. Oper. Res. 28, 719–732 (2001). https://doi.org/10.1016/S0305-0548(99)00127-6

    Article  Google Scholar 

  26. Xiao, W.-Q., Li, C.-L.: Approximation algorithms for common due date assignment and job scheduling on parallel machines. IIE Trans. Inst. Ind. Eng. 34, 466–477 (2002). https://doi.org/10.1080/07408170208928883

    Article  Google Scholar 

  27. Mosheiov, G., Yovel, U.: Minimizing weighted earliness-tardiness and due-date cost with unit processing-time jobs. Eur. J. Oper. Res. 172, 528–544 (2006). https://doi.org/10.1016/j.ejor.2004.10.021

    Article  Google Scholar 

  28. Min, L., Cheng, W.: Genetic algorithms for the optimal common due date assignment and the optimal scheduling policy in parallel machine earliness/tardiness scheduling problems. Robot Comput. Integr. Manuf. 22, 279–287 (2006). https://doi.org/10.1016/j.rcim.2004.12.005

    Article  Google Scholar 

  29. Drobouchevitch, I.G., Sidney, J.B.: Minimization of earliness, tardiness and due date penalties on uniform parallel machines with identical jobs. Comput. Oper. Res. 39, 1919–1926 (2012). https://doi.org/10.1016/j.cor.2011.05.012

    Article  Google Scholar 

  30. Kim, J.-G., Kim, J.-S., Lee, D.-H.: Fast and meta-heuristics for common due-date assignment and scheduling on parallel machines. Int. J. Prod. Res. 50, 6040–6057 (2012). https://doi.org/10.1080/00207543.2011.644591

    Article  Google Scholar 

  31. Xiong, X., Wang, D., Cheng, E., Wu, T.C., Yin, C.-C.: Single-machine scheduling and common due date assignment with potential machine disruption. Int. J. Prod. Res. 56, 1345–1360 (2018). https://doi.org/10.1080/00207543.2017.1346317

    Article  Google Scholar 

  32. Ng Daniel, C.T.D., Cheng, T.C.E., Kovalyov, M.Y., Lam, S.S.: Single machine scheduling with a variable common due date and resource-dependent processing times. Comput. Oper. Res. 30, 1173–1185 (2003). https://doi.org/10.1016/S0305-0548(02)00066-7

    Article  Google Scholar 

  33. Keha, A.B., Khowala, K., Fowler, J.W.: Mixed integer programming formulations for single machine scheduling problems. Comput. Ind. Eng. 56, 357–367 (2009). https://doi.org/10.1016/J.CIE.2008.06.008

    Article  Google Scholar 

  34. Biskup, D., Feldmann, M.: Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due dates. Comput. Oper. Res. 28, 787–801 (2001). https://doi.org/10.1016/S0305-0548(00)00008-3

    Article  Google Scholar 

Download references

Acknowledgements

Not applicable.

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Industrial Engineering Department, Nuh Naci Yazgan University, Kayseri, 38170, Turkey

    Oğuzhan Ahmet Arik

Authors
  1. Oğuzhan Ahmet Arik
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

OAA designed the investigated problem and he contributed to the design of the proposed algorithm and experimental study in the paper. OAA also edited and wrote the paper. OAA read and approved the final manuscript.

Corresponding author

Correspondence to Oğuzhan Ahmet Arik.

Ethics declarations

Conflict of interest

The author declares that they have no conflict of interest.

Ethical approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

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

Arik, O.A. A heuristic for single machine common due date assignment problem with different earliness/tardiness weights. OPSEARCH 60, 1561–1574 (2023). https://doi.org/10.1007/s12597-023-00652-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-023-00652-1

Keywords

JEL Classification

Search

Navigation