Advertisement

Two-Machine Flow Shop with a Dynamic Storage Space and UET Operations

  • Joanna Berlińska
  • Alexander Kononov
  • Yakov ZinderEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

The paper establishes the NP-hardness in the strong sense of a two-machine flow shop scheduling problem with unit execution time (UET) operations, dynamic storage availability, job dependent storage requirements, and the objective to minimise the time required for the completion of all jobs, i.e. to minimise the makespan. Each job seizes the required storage space for the entire period from the start of its processing on the first machine till the completion of its processing on the second machine. The considered scheduling problem has several applications, including star data gathering networks and certain supply chains and manufacturing systems. The NP-hardness result is complemented by a polynomial-time approximation scheme (PTAS) and several heuristics. The presented heuristics are compared by means of computational experiments.

Keywords

Two-machine flow shop Makespan Dynamic storage Computational complexity Polynomial-time approximation scheme 

References

  1. 1.
    Berlińska, J.: Scheduling for data gathering networks with data compression: Berlińska. J. Eur. J. Oper. Res. 246, 744–749 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berlińska, J.: Scheduling data gathering with maximum lateness objective. In: Wyrzykowski, R. et al. (eds.) PPAM 2017, Part II. LNCS, vol. 10778, pp. 135–144. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78054-2_13CrossRefGoogle Scholar
  3. 3.
    Berlińska, J.: Heuristics for scheduling data gathering with limited base station memory. Ann. Oper. Res. (2019).  https://doi.org/10.1007/s10479-019-03185-3. In pressCrossRefGoogle Scholar
  4. 4.
    Błażewicz, J., Kubiak, W., Szwarcfiter, J.: Scheduling unit-time tasks on flow-shops under resource constraints. Ann. Oper. Res. 16, 255–266 (1988)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Błażewicz J., Lenstra, J.K., Rinnooy Kan, A.H.G.: Scheduling subject to resource constraints: classification and complexity. Discret. Appl. Math. 5, 11–24 (1983)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Fernandez de la Vega, W., Lueker, G.S.: Bin packing can be solved within \(1+ \varepsilon \) in linear time. Combinatorica 1(4), 349–355 (1981)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Fung, J., Zinder, Y.: Permutation schedules for a two-machine flow shop with storage. Oper. Res. Lett. 44(2), 153–157 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco (1979)Google Scholar
  9. 9.
    Gu, H., Memar, J., Kononov, A., Zinder, Y.: Efficient Lagrangian heuristics for the two-stage flow shop with job dependent buffer requirements. J. Discret. Algorithms 52–53, 143–155 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Luo, W., Xu, Y., Gu, B., Tong, W., Goebel, R., Lin, G.: Algorithms for communication scheduling in data gathering network with data compression. Algorithmica 80(11), 3158–3176 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Röck, H.: Some new results in no-wait flow shop scheduling. Z. Oper. Res. 28(1), 1–16 (1984)MathSciNetGoogle Scholar
  12. 12.
    Süral, H., Kondakci, S., Erkip, N.: Scheduling unit-time tasks in renewable resource constrained flowshops. Z. Oper. Res. 36(6), 497–516 (1992)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.School of Mathematical and Physical SciencesUniversity of Technology SydneyUltimoAustralia

Personalised recommendations