IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v1y1997i2d10.1023_a1009799631608.html
   My bibliography  Save this article

Scheduling Problems in a Practical Allocation Model

Author

Listed:
  • Lisa Hollermann

    (IBM Corporation)

  • Tsan-sheng Hsu

    (Institute of Information Science, Academia Sinica, Nankang)

  • Dian Rae Lopez

    (University of Minnesota)

  • Keith Vertanen

    (Linkvping Universitet)

Abstract

A parallel computational model is defined which addresses I/O contention,latency, and pipe-lined message passing between tasks allocated to differentprocessors. The model can be used for parallel task-allocation on either anetwork of workstations or on a multi-stage inter-connected parallel machine.To study performance bounds more closely, basic properties are developed forwhen the precedence constraints form a directed tree. It is shown that theproblem of optimally scheduling a directed one-level precedence tree on anunlimited number of identical processors in this model is NP-hard. Theproblem of scheduling a directed two-level precedence tree is also shown tobe NP-hard even when the system latency is zero. An approximation algorithm is then presented for scheduling directedone-level task trees on an unlimited number of processors with anapproximation ratio of 3. Simulation results show that this algorithm is, infact, much faster than its worst-case performance bound. Better simulationresults are obtained by improving our approximation algorithm usingheusistics. Restricting the problem to the case of equal task executiontimes, a linear-time algorithm is presented to find an optimal schedule.

Suggested Citation

  • Lisa Hollermann & Tsan-sheng Hsu & Dian Rae Lopez & Keith Vertanen, 1997. "Scheduling Problems in a Practical Allocation Model," Journal of Combinatorial Optimization, Springer, vol. 1(2), pages 129-149, June.
    • Handle: RePEc:spr:jcomop:v:1:y:1997:i:2:d:10.1023_a:1009799631608
    DOI: 10.1023/A:1009799631608
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1009799631608
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1009799631608?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. J. Y. Colin & P. Chrétienne, 1991. "C.P.M. Scheduling with Small Communication Delays and Task Duplication," Operations Research, INFORMS, vol. 39(4), pages 680-684, August.
    2. Cheng, T. C. E. & Sin, C. C. S., 1990. "A state-of-the-art review of parallel-machine scheduling research," European Journal of Operational Research, Elsevier, vol. 47(3), pages 271-292, 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. Guo, Peng & Weidinger, Felix & Boysen, Nils, 2019. "Parallel machine scheduling with job synchronization to enable efficient material flows in hub terminals," Omega, Elsevier, vol. 89(C), pages 110-121.
    2. Yalaoui, F. & Chu, C., 2006. "New exact method to solve the Pm/rj/[summation operator]Cj schedule problem," International Journal of Production Economics, Elsevier, vol. 100(1), pages 168-179, March.
    3. Lin, Hung-Tso & Liao, Ching-Jong, 2003. "A case study in a two-stage hybrid flow shop with setup time and dedicated machines," International Journal of Production Economics, Elsevier, vol. 86(2), pages 133-143, November.
    4. Biber Nurit & Mor Baruch & Schlissel Yitzhak & Shapira Dana, 2023. "Lot scheduling involving completion time problems on identical parallel machines," Operational Research, Springer, vol. 23(1), pages 1-29, March.
    5. Zoltán Varga & Pál Simon, 2014. "Examination Of Scheduling Methods For Production Systems," Advanced Logistic systems, University of Miskolc, Department of Material Handling and Logistics, vol. 8(1), pages 111-120, December.
    6. George L. Vairaktarakis, 2003. "The Value of Resource Flexibility in the Resource-Constrained Job Assignment Problem," Management Science, INFORMS, vol. 49(6), pages 718-732, June.
    7. Anurag Agarwal & Varghese S. Jacob & Hasan Pirkul, 2006. "An Improved Augmented Neural-Network Approach for Scheduling Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 119-128, February.
    8. Hesham K. Alfares, 2022. "Plant shutdown maintenance workforce team assignment and job scheduling," Journal of Scheduling, Springer, vol. 25(3), pages 321-338, June.
    9. Kloster, Konstantin & Moeini, Mahdi & Vigo, Daniele & Wendt, Oliver, 2023. "The multiple traveling salesman problem in presence of drone- and robot-supported packet stations," European Journal of Operational Research, Elsevier, vol. 305(2), pages 630-643.
    10. Lee, Soonhui & Turner, Jonathan & Daskin, Mark S. & Homem-de-Mello, Tito & Smilowitz, Karen, 2012. "Improving fleet utilization for carriers by interval scheduling," European Journal of Operational Research, Elsevier, vol. 218(1), pages 261-269.
    11. Mokotoff, E. & Chretienne, P., 2002. "A cutting plane algorithm for the unrelated parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 141(3), pages 515-525, September.
    12. Henrich, Peter & Land, Martin & Gaalman, Gerard, 2006. "Grouping machines for effective workload control," International Journal of Production Economics, Elsevier, vol. 104(1), pages 125-142, November.
    13. Jun-Ho Lee & Hyun-Jung Kim, 2021. "A heuristic algorithm for identical parallel machine scheduling: splitting jobs, sequence-dependent setup times, and limited setup operators," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 992-1026, December.
    14. Ozdamar, Linet & Birbil, Sevket Ilker, 1998. "Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions," European Journal of Operational Research, Elsevier, vol. 110(3), pages 525-547, November.
    15. D Biskup & M Feldmann, 2006. "Lot streaming with variable sublots: an integer programming formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(3), pages 296-303, March.
    16. Sanjoy K. Baruah, 1998. "The Multiprocessor Scheduling of Precedence-Constrained Task Systems in the Presence of Interprocessor Communication Delays," Operations Research, INFORMS, vol. 46(1), pages 65-72, February.
    17. Daniel Reich & Yuhui Shi & Marina Epelman & Amy Cohn & Ellen Barnes & Kirk Arthurs & Erica Klampfl, 2016. "Scheduling Crash Tests at Ford Motor Company," Interfaces, INFORMS, vol. 46(5), pages 409-423, October.
    18. Shi, Yuhui & Reich, Daniel & Epelman, Marina & Klampfl, Erica & Cohn, Amy, 2017. "An analytical approach to prototype vehicle test scheduling," Omega, Elsevier, vol. 67(C), pages 168-176.
    19. Lagodimos, A. G. & Leopoulos, V., 2000. "Greedy heuristic algorithms for manpower shift planning," International Journal of Production Economics, Elsevier, vol. 68(1), pages 95-106, October.
    20. Ozdamar, Linet & Birbil, Sevket Ilker, 1999. "A hierarchical planning system for energy intensive production environments," International Journal of Production Economics, Elsevier, vol. 58(2), pages 115-129, 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:jcomop:v:1:y:1997:i:2:d:10.1023_a:1009799631608. 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.