IDEAS home Printed from https://ideas.repec.org/a/spr/jsched/v22y2019i1d10.1007_s10951-018-0562-4.html
   My bibliography  Save this article

No-idle, no-wait: when shop scheduling meets dominoes, Eulerian paths and Hamiltonian paths

Author

Listed:
  • J.-C. Billaut

    (Université de Tours)

  • F. Della Croce

    (Politecnico di Torino
    CNR, IEIIT)

  • F. Salassa

    (Politecnico di Torino)

  • V. T’kindt

    (Université de Tours)

Abstract

In shop scheduling, several applications require that some components perform consecutively. We refer to “no-idle schedules” if machines are required to operate with no inserted idle time and to “no-wait schedules” if tasks cannot wait between the end of an operation and the start of the following one. We consider here no-idle/no-wait shop scheduling problems with makespan as the performance measure and determine related complexity results. We first analyse the two-machine no-idle/no-wait flow shop problem and show that it is equivalent to a special version of the game of dominoes which is polynomially solvable by tackling an Eulerian path problem on a directed graph. We present for this problem an O(n) exact algorithm. As a by-product, we show that the Hamiltonian path problem on a digraph G(V, A) with a special structure (where any two vertices i and j either have all successors in common or have no common successors) reduces to the two-machine no-idle/no-wait flow shop problem. Correspondingly, we provide a new polynomially solvable special case of the Hamiltonian path problem. Then, we show that also the m-machine no-idle/no-wait flow shop problem is polynomially solvable and provide an $$O(mn \log n)$$ O ( m n log n ) exact algorithm. Finally, we prove that the decision versions of the two-machine job shop problem and the two-machine open shop problem are NP-complete in the strong sense.

Suggested Citation

  • J.-C. Billaut & F. Della Croce & F. Salassa & V. T’kindt, 2019. "No-idle, no-wait: when shop scheduling meets dominoes, Eulerian paths and Hamiltonian paths," Journal of Scheduling, Springer, vol. 22(1), pages 59-68, February.
  • Handle: RePEc:spr:jsched:v:22:y:2019:i:1:d:10.1007_s10951-018-0562-4
    DOI: 10.1007/s10951-018-0562-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10951-018-0562-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10951-018-0562-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Allahverdi, Ali, 2016. "A survey of scheduling problems with no-wait in process," European Journal of Operational Research, Elsevier, vol. 255(3), pages 665-686.
    2. Kalczynski, Pawel Jan & Kamburowski, Jerzy, 2007. "On no-wait and no-idle flow shops with makespan criterion," European Journal of Operational Research, Elsevier, vol. 178(3), pages 677-685, May.
    3. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
    4. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    5. Nicholas G. Hall & Chelliah Sriskandarajah, 1996. "A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process," Operations Research, INFORMS, vol. 44(3), pages 510-525, June.
    6. I. Adiri & D. Pohoryles, 1982. "Flowshop/no‐idle or no‐wait scheduling to minimize the sum of completion times," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(3), pages 495-504, September.
    7. Giaro, Krzysztof, 2001. "NP-hardness of compact scheduling in simplified open and flow shops," European Journal of Operational Research, Elsevier, vol. 130(1), pages 90-98, April.
    8. Goncharov, Yaroslav & Sevastyanov, Sergey, 2009. "The flow shop problem with no-idle constraints: A review and approximation," European Journal of Operational Research, Elsevier, vol. 196(2), pages 450-456, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Federico Della Croce & Andrea Grosso & Fabio Salassa, 2021. "Minimizing total completion time in the two-machine no-idle no-wait flow shop problem," Journal of Heuristics, Springer, vol. 27(1), pages 159-173, April.
    2. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Federico Della Croce & Andrea Grosso & Fabio Salassa, 2021. "Minimizing total completion time in the two-machine no-idle no-wait flow shop problem," Journal of Heuristics, Springer, vol. 27(1), pages 159-173, April.
    2. S. S. Panwalkar & Christos Koulamas, 2019. "The evolution of schematic representations of flow shop scheduling problems," Journal of Scheduling, Springer, vol. 22(4), pages 379-391, August.
    3. S. S. Panwalkar & Christos Koulamas, 2020. "Three-stage ordered flow shops with either synchronous flow, blocking or no-idle machines," Journal of Scheduling, Springer, vol. 23(1), pages 145-154, February.
    4. Abdennour Azerine & Mourad Boudhar & Djamal Rebaine, 2022. "A two-machine no-wait flow shop problem with two competing agents," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 168-199, January.
    5. Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2020. "Coupled task scheduling with exact delays: Literature review and models," European Journal of Operational Research, Elsevier, vol. 282(1), pages 19-39.
    6. Allahverdi, Ali, 2016. "A survey of scheduling problems with no-wait in process," European Journal of Operational Research, Elsevier, vol. 255(3), pages 665-686.
    7. Levorato, Mario & Figueiredo, Rosa & Frota, Yuri, 2022. "Exact solutions for the two-machine robust flow shop with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 300(1), pages 46-57.
    8. Brammer, Janis & Lutz, Bernhard & Neumann, Dirk, 2022. "Permutation flow shop scheduling with multiple lines and demand plans using reinforcement learning," European Journal of Operational Research, Elsevier, vol. 299(1), pages 75-86.
    9. Byung-Cheon Choi & Joseph Y.-T. Leung & Michael L. Pinedo, 2011. "Minimizing makespan in an ordered flow shop with machine-dependent processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 797-818, November.
    10. Matthias Bultmann & Sigrid Knust & Stefan Waldherr, 2018. "Flow shop scheduling with flexible processing times," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 809-829, July.
    11. Thierry Garaix & Salim Rostami & Xiaolan Xie, 2020. "Daily outpatient chemotherapy appointment scheduling with random deferrals," Flexible Services and Manufacturing Journal, Springer, vol. 32(1), pages 129-153, March.
    12. Li, Wei & Nault, Barrie R. & Ye, Honghan, 2019. "Trade-off balancing in scheduling for flow shop production and perioperative processes," European Journal of Operational Research, Elsevier, vol. 273(3), pages 817-830.
    13. Kravchenko, Svetlana A., 1998. "A polynomial algorithm for a two-machine no-wait job-shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 106(1), pages 101-107, April.
    14. Christoph Hertrich & Christian Weiß & Heiner Ackermann & Sandy Heydrich & Sven O. Krumke, 2020. "Scheduling a proportionate flow shop of batching machines," Journal of Scheduling, Springer, vol. 23(5), pages 575-593, October.
    15. Abdelhakim AitZai & Brahim Benmedjdoub & Mourad Boudhar, 2016. "Branch-and-bound and PSO algorithms for no-wait job shop scheduling," Journal of Intelligent Manufacturing, Springer, vol. 27(3), pages 679-688, June.
    16. Rubén Ruiz & Ali Allahverdi, 2007. "Some effective heuristics for no-wait flowshops with setup times to minimize total completion time," Annals of Operations Research, Springer, vol. 156(1), pages 143-171, December.
    17. Kameng Nip & Zhenbo Wang & Fabrice Talla Nobibon & Roel Leus, 2015. "A combination of flow shop scheduling and the shortest path problem," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 36-52, January.
    18. Wenjie Li & Jinjiang Yuan, 2021. "Single-machine online scheduling of jobs with non-delayed processing constraint," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 830-843, May.
    19. Wu, Xueqi & Che, Ada, 2020. "Energy-efficient no-wait permutation flow shop scheduling by adaptive multi-objective variable neighborhood search," Omega, Elsevier, vol. 94(C).
    20. Zongxu Mu & Minming Li, 2015. "DVS scheduling in a line or a star network of processors," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 16-35, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jsched:v:22:y:2019:i:1:d:10.1007_s10951-018-0562-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.