Skip to main content
SpringerLink
Log in

A no-delay single machine scheduling problem to minimize total weighted early and late work

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

A Correction to this article was published on 03 March 2022

This article has been updated

Abstract

This paper investigates the no-delay single machine scheduling problem to minimize the total weighted early and late work. This criterion is one of the most important objectives in practice but has not been studied so far in the literature. First, we formulate the problem as a 0–1 integer programming formulation. Since the complexity of the problem is proven to be NP-hard, we propose two metaheuristics, namely General Variable Neighborhood Search and hybrid GRASP-VND, based on new neighborhood structures. The results demonstrate that all proposed methods can solve optimally instances up to 30 jobs. However, extensive computational experimentation, on large-sized instances, show that the quality of the solutions given by GVNS is better than that obtained by hybrid GRASP-VND algorithm.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Change history

References

  1. Ben-Yehoshua, Y., Mosheiov, G.: A single machine scheduling problem to minimize total early work. Comput. Oper. Res. 73, 115–118 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  2. Błażewicz, J., Pesch, E., Sterna, M., Werner, F.: Open shop scheduling problems with late work criteria. Discrete Appl. Math. 134(1–3), 1–24 (2004).

  3. Boese, K.D., Kahng, A.B., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Oper. Res. Lett. 16(2), 101–113 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, X., Kovalev, S., Liu, Y., Sterna, M., Chalamon, I., Błażewicz, J.: Semi-online scheduling on two identical machines with a common due date to maximize total early work. Discrete Appl. Math. 290, 71–78 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, X., Kovalev, S., Sterna, M., Błażewicz, J.: Mirror scheduling problems with early work and late work criteria. J. Sched. pp 1–5 (2020)

  6. Chen, X., Wang, Z., Pesch, E., Sterna, M., Błażewicz, J.: Two-machine flow-shop scheduling to minimize total late work: revisited. Eng. Optim. 51(7), 1268–1278 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  7. Gendreau, M., Hertz, A., Laporte, G.: New insertion and postoptimization procedures for the traveling salesman problem. Oper. Res. 40(6), 1086–1094 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  8. Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423–454 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  9. Hariri, A.M., Potts, C.N., Van Wassenhove, L.N.: Single machine scheduling to minimize total weighted late work. ORSA J. Comput. 7(2), 232–242 (1995).

    Article  MATH  Google Scholar 

  10. He, D.W., Kusiak, A., Artiba, A.: A scheduling problem in glass manufacturing. IIE Trans. 28(2), 129–139 (1996).

    Article  Google Scholar 

  11. Kethley, R.B., Alidaee, B.: Single machine scheduling to minimize total weighted late work: a comparison of scheduling rules and search algorithms. Comput. Ind. Eng. 43(3), 509–528 (2002).

    Article  Google Scholar 

  12. Li, S.S., Yuan, J.J.: Single-machine scheduling with multi-agents to minimize total weighted late work. J. Sched. pp 1–16 (2020)

  13. Mosheiov, G., Oron, D., Shabtay, D.: Minimizing total late work on a single machine with generalized due-dates. Eur. J. Oper. Res. (2021)

  14. Potts, C.N., Van Wassenhove, L.N.: Approximation algorithms for scheduling a single machine to minimize total late work. Oper. Res. Lett. 11(5), 261–266 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  15. Potts, C.N., Van Wassenhove, L.N.: Single machine scheduling to minimize total late work. Oper. Res. 40(3), 586–595 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  16. Resende, M.G., Ribeiro, C.C.: Grasp: Greedy randomized adaptive search procedures. In: Search methodologies, pp. 287–312. Springer (2014)

  17. Ronald, S.: More distance functions for order-based encodings. In: 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360), pp. 558–563. IEEE (1998)

  18. Sterna, M.: A survey of scheduling problems with late work criteria. Omega 39(2), 120–129 (2011).

    Article  Google Scholar 

  19. Sterna, M.: Late and early work scheduling: a survey. Omega p. 102453 (2021)

  20. Wu, C.C., Yin, Y., Wu, W.H., Chen, H.M., Cheng, S.R.: Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem. Soft Comput. 20(4), 1329–1339 (2016).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Engineering, Abu Dhabi University, Abu Dhabi, UAE

    Issam Krimi

  2. SI2M Laboratory, National Institute of Statistics and Applied Economics (INSEA), Rabat, Morocco

    Rachid Benmansour

  3. LAMIH, CNRS, UMR 8201, Université Polytechnique Hauts-de-France, F-59313, Valenciennes, France

    Raca Todosijević & Mustapha Ratli

  4. INSA Hauts-de-France, F-59313, Valenciennes, France

    Raca Todosijević & Mustapha Ratli

  5. Khalifa University, PO Box 127788, Abu Dhabi, United Arab Emirates

    Nenad Mladenovic

Authors
  1. Issam Krimi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rachid Benmansour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raca Todosijević
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nenad Mladenovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mustapha Ratli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Issam Krimi.

Additional information

Publisher's Note

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

The original online version of this article was revised: “The affiliation of coauthors has been incorrectly published. This has been updated in original version.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krimi, I., Benmansour, R., Todosijević, R. et al. A no-delay single machine scheduling problem to minimize total weighted early and late work. Optim Lett 17, 2113–2131 (2023). https://doi.org/10.1007/s11590-022-01849-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-022-01849-x

Keywords

Search

Navigation