IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v37y1990i5p679-694.html
   My bibliography  Save this article

Cyclic sequencing problems in the two‐machine permutation flow shop: Complexity, worst‐case, and average‐case analysis

Author

Listed:
  • Hirofumi Matsuo

Abstract

In this article, we formalize the cyclic sequencing problem in the two‐machine flow shop. When jobs are processed in a repetitive cycle, the size of a scheduling problem is significantly reduced, and the resulting schedule is easy to implement because of its simplicity. Two types of cyclic sequencing problems are considered: the no‐wait problem and the minimum‐wait problem. The no‐wait problem maximizes the throughput rate subject to the condition that there is no buffer space between the two machines. The minimum‐wait problem minimizes the average WIP level subject to the conditions that the maximum throughput rate is maintained and that the FIFO dispatching rule is used in the intermediate buffer space. The no‐wait problem is a well‐known special case of the traveling salesman problem (TSP) and is polynomially solvable. The minimum‐wait problem is shown to be NP‐hard; therefore, we develop a heuristic procedure along with the analysis of its worst‐case and average‐case performance. Here, the average‐case analysis is based on the expected length of the Hamiltonian tour for this special case of the TSP. The average‐case analysis indicates that when the number of jobs in a cycle is small, the derived cyclic schedule yields a low WIP level.

Suggested Citation

  • Hirofumi Matsuo, 1990. "Cyclic sequencing problems in the two‐machine permutation flow shop: Complexity, worst‐case, and average‐case analysis," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 679-694, October.
  • Handle: RePEc:wly:navres:v:37:y:1990:i:5:p:679-694
    DOI: 10.1002/1520-6750(199010)37:53.0.CO;2-Q
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199010)37:53.0.CO;2-Q
    Download Restriction: no

    File URL: https://libkey.io/10.1002/1520-6750(199010)37:53.0.CO;2-Q?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
    ---><---

    References listed on IDEAS

    as
    1. Teofilo Gonzalez & Sartaj Sahni, 1978. "Flowshop and Jobshop Schedules: Complexity and Approximation," Operations Research, INFORMS, vol. 26(1), pages 36-52, February.
    2. Richard M. Karp, 1977. "Probabilistic Analysis of Partitioning Algorithms for the Traveling-Salesman Problem in the Plane," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 209-224, August.
    3. Clyde L. Monma, 1979. "The Two-Machine Maximum Flow Time Problem with Series-Parallel Precedence Constraints: An Algorithm and Extensions," Operations Research, INFORMS, vol. 27(4), pages 792-798, August.
    Full references (including those not matched with items on IDEAS)

    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. Gupta, Jatinder N.D. & Koulamas, Christos & Kyparisis, George J., 2006. "Performance guarantees for flowshop heuristics to minimize makespan," European Journal of Operational Research, Elsevier, vol. 169(3), pages 865-872, March.
    2. Wu, Chin-Chia & Lee, Wen-Chiung, 2006. "Two-machine flowshop scheduling to minimize mean flow time under linear deterioration," International Journal of Production Economics, Elsevier, vol. 103(2), pages 572-584, October.
    3. S.S. Panwalkar & Christos Koulamas, 2015. "Proportionate flow shop: New complexity results and models with due date assignment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 98-106, March.
    4. Lenstra, J. K. & Rinnooy Kan, A. H. G., 1979. "Complexity Of Vehicle Routing And Scheduling Problems," Econometric Institute Archives 272191, Erasmus University Rotterdam.
    5. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    6. T.C.E. Cheng & B.M.T. Lin & A. Toker, 2000. "Makespan minimization in the two‐machine flowshop batch scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(2), pages 128-144, March.
    7. Shoshana Anily, 1996. "The vehicle‐routing problem with delivery and back‐haul options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 415-434, April.
    8. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    9. Guinet, Alain & Legrand, Marie, 1998. "Reduction of job-shop problems to flow-shop problems with precedence constraints," European Journal of Operational Research, Elsevier, vol. 109(1), pages 96-110, August.
    10. Monaci, Marta & Agasucci, Valerio & Grani, Giorgio, 2024. "An actor-critic algorithm with policy gradients to solve the job shop scheduling problem using deep double recurrent agents," European Journal of Operational Research, Elsevier, vol. 312(3), pages 910-926.
    11. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-433, October.
    12. Ji-Bo Wang & Ming-Zheng Wang, 2011. "Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects," Annals of Operations Research, Springer, vol. 191(1), pages 155-169, November.
    13. Li, Gang & Wang, Xiao-Yuan & Wang, Ji-Bo & Sun, Lin-Yan, 2013. "Worst case analysis of flow shop scheduling problems with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 142(1), pages 98-104.
    14. Tamssaouet, Karim & Dauzère-Pérès, Stéphane, 2023. "A general efficient neighborhood structure framework for the job-shop and flexible job-shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 311(2), pages 455-471.
    15. Jansen, Klaus & Mastrolilli, Monaldo & Solis-Oba, Roberto, 2005. "Approximation schemes for job shop scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(2), pages 297-319, December.
    16. 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.
    17. Paul Sutcliffe & Andrew Solomon & Jenny Edwards, 2012. "Computing the variance of tour costs over the solution space of the TSP in polynomial time," Computational Optimization and Applications, Springer, vol. 53(3), pages 711-728, December.
    18. Vairaktarakis, George L. & Cai, Xiaoqiang & Lee, Chung-Yee, 2002. "Workforce planning in synchronous production systems," European Journal of Operational Research, Elsevier, vol. 136(3), pages 551-572, February.
    19. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    20. Lee, Kangbok & Zheng, Feifeng & Pinedo, Michael L., 2019. "Online scheduling of ordered flow shops," European Journal of Operational Research, Elsevier, vol. 272(1), pages 50-60.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:37:y:1990:i:5:p:679-694. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.