Advertisement

Optimization Letters

, Volume 12, Issue 4, pp 903–914 | Cite as

An exact algorithm for the bi-objective timing problem

  • Sophie Jacquin
  • Fanny Dufossé
  • Laetitia Jourdan
Original Paper
  • 95 Downloads

Abstract

The timing problem in the bi-objective just-in-time single-machine job-shop scheduling problem (JiT-JSP) is the task to schedule N jobs whose order is fixed, with each job incurring a linear earliness penalty for finishing ahead of its due date and a linear tardiness penalty for finishing after its due date. The goal is to minimize the earliness and tardiness simultaneously. We propose an exact greedy algorithm that finds the entire Pareto front in \(O(N^2)\) time. This algorithm is asymptotically optimal.

Keywords

Just-in-time scheduling Bi-objective Timing problem Exact algorithm 

Notes

Acknowledgements

We acknowledge Dr. Martin Drozdik for proof reading the article and corrected mathematical proofs in the article during the revision phase.

References

  1. 1.
    Aneja, Y.P., Nair, K.P.: Bicriteria transportation problem. Manag. Sci. 25(1), 73–78 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Azizoglu, M., Kondakci, S., Kksalan, M.: Single machine scheduling with maximum earliness and number tardy. Comput. Ind. Eng. 45(2), 257–268 (2003)CrossRefGoogle Scholar
  3. 3.
    Bauman, J., Józefowska, J.: Minimizing the earliness–tardiness costs on a single machine. Comput. Oper. Res. 33(11), 3219–3230 (2006)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dantas, J.D., Varela, L.R.: Scheduling single-machine problem based on just-in-time principles. In: 2014 Sixth World Congress on Nature and Biologically Inspired Computing (NaBIC), pp. 164–169. IEEE (2014)Google Scholar
  5. 5.
    Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2006)zbMATHGoogle Scholar
  6. 6.
    Fang, Y.P., Meng, K., Yang, X.Q.: Piecewise linear multicriteria programs: the continuous case and its discontinuous generalization. Oper. Res. 60(2), 398–409 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Feldmann, M., Biskup, D.: Single-machine scheduling for minimizing earliness and tardiness penalties by meta-heuristic approaches. Comput. Ind. Eng. 44(2), 307–323 (2003)CrossRefGoogle Scholar
  8. 8.
    Hendel, Y., Runge, N., Sourd, F.: The one-machine just-in-time scheduling problem with preemption. Discrete Optim. 6(1), 10–22 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hendel, Y., Sourd, F.: An improved earliness–tardiness timing algorithm. Comput. Oper. Res. 34(10), 2931–2938 (2007)CrossRefzbMATHGoogle Scholar
  10. 10.
    Jacquin, S., Allart, E., Dufossé, F., Jourdan, L.: Decoder-based evolutionary algorithm for bi-objective just-in-time single-machine job-shop. In: IEEE Symposium Series on Computational Intelligence, SSCI, pp. 1–8 (2016)Google Scholar
  11. 11.
    Liu, L., Zhou, H.: Hybridization of harmony search with variable neighborhood search for restrictive single-machine earliness/tardiness problem. Inf. Sci. 226, 68–92 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Mahnam, M., Moslehi, G., Ghomi, S.M.T.F.: Single machine scheduling with unequal release times and idle insert for minimizing the sum of maximum earliness and tardiness. Math. Comput, Model. 57(9), 2549–2563 (2013)CrossRefzbMATHGoogle Scholar
  13. 13.
    Qin, T., Peng, B., Benlic, U., Cheng, T., Wang, Y., Lü, Z.: Iterated local search based on multi-type perturbation for single-machine earliness/tardiness scheduling. COR 61, 81–88 (2015)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Rahimi-Vahed, A., Dangchi, M., Rafiei, H., Salimi, E.: A novel hybrid multi-objective shuffled frog-leaping algorithm for a bi-criteria permutation flow shop scheduling problem. Int. J. Adv. Manuf. Technol. 41(11–12), 1227–1239 (2009)CrossRefGoogle Scholar
  15. 15.
    Rahimi-Vahed, A., Mirzaei, A.H.: Solving a bi-criteria permutation flow-shop problem using shuffled frog-leaping algorithm. Soft Comput. 12(5), 435–452 (2008)CrossRefzbMATHGoogle Scholar
  16. 16.
    Sourd, F., Kedad-Sidhoum, S.: An efficient algorithm for the earliness–tardiness scheduling problem. Optim. Online 1205 (2005)Google Scholar
  17. 17.
    Tanaka, S., Fujikuma, S.: A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time. J. Sched. 15(3), 347–361 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Vidal, T., Crainic, T.G., Gendreau, M., Prins, C.: A unifying view on timing problems and algorithms. CIRRELT-2011-43, Montréal, QC, Canada (2011)Google Scholar
  19. 19.
    Vincent, T.: Multicriteria models for just-in-time scheduling. Int. J. Prod. Res. 49(11), 3191–3209 (2011)CrossRefzbMATHGoogle Scholar
  20. 20.
    Wan, G., Yen, B.P.C.: Single machine scheduling to minimize total weighted earliness subject to minimal number of tardy jobs. Eur. J. Oper. Res. 195(1), 89–97 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Inria Lille - Nord Europe, ORKAD, CRIStALUniversity of Lille 1Villeneuve d’AscqFrance

Personalised recommendations