IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v54y2006i3p464-474.html
   My bibliography  Save this article

On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions

Author

Listed:
  • Mabel C. Chou

    (Department of Decision Sciences, National University of Singapore, 117591 Singapore)

  • Hui Liu

    (Verizon Laboratories, Boston, Massachusetts)

  • Maurice Queyranne

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia, Canada)

  • David Simchi-Levi

    (Engineering Systems Division and the Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We consider the stochastic single-machine problem, when the objective is to minimize the expected total weighted completion time of a set of jobs that are released over time. We assume that the existence and the parameters of each job including its release date, weight, and expected processing times are not known until its release date. The actual processing times are not known until processing is completed. We analyze the performance of the on-line nonpreemptive weighted shortest expected processing time among available jobs (WSEPTA) heuristic. When a scheduling decision needs to be made, this heuristic assigns, among the jobs that have arrived but not yet processed, one with the largest ratio of its weight to its expected processing time. We prove that when the job weights and processing times are bounded and job processing times are mutually independent random variables, WSEPTA is asymptotically optimal for the single-machine problem. This implies that WSEPTA generates a solution whose relative error approaches zero as the number of jobs increases. This result can be extended to the stochastic flow shop and open shop problems, as well as models with stochastic job weights.

Suggested Citation

  • Mabel C. Chou & Hui Liu & Maurice Queyranne & David Simchi-Levi, 2006. "On the Asymptotic Optimality of a Simple On-Line Algorithm for the Stochastic Single-Machine Weighted Completion Time Problem and Its Extensions," Operations Research, INFORMS, vol. 54(3), pages 464-474, June.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:3:p:464-474
    DOI: 10.1287/opre.1060.0270
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1060.0270
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1060.0270?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. Michael H. Rothkopf, 1966. "Scheduling with Random Service Times," Management Science, INFORMS, vol. 12(9), pages 707-713, May.
    2. Philip Kaminsky & David Simchi-Levi, 1998. "Probabilistic Analysis and Practical Algorithms for the Flow Shop Weighted Completion Time Problem," Operations Research, INFORMS, vol. 46(6), pages 872-882, December.
    3. Cathy H. Xia & George J. Shanthikumar & Peter W. Glynn, 2000. "On the Asymptotic Optimality of the SPT Rule for the Flow Shop Average Completion Time Problem," Operations Research, INFORMS, vol. 48(4), pages 615-622, August.
    4. Dimitris Bertsimas & David Gamarnik & Jay Sethuraman, 2003. "From Fluid Relaxations to Practical Algorithms for High-Multiplicity Job-Shop Scheduling: The Holding Cost Objective," Operations Research, INFORMS, vol. 51(5), pages 798-813, October.
    5. Cheng-Shang Chang & David D. Yao, 1993. "Rearrangement, Majorization and Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 658-684, August.
    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. Manzhan Gu & Xiwen Lu & Jinwei Gu, 2017. "An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 473-495, February.
    2. Manzhan Gu & Xiwen Lu, 2011. "Asymptotical optimality of WSEPT for stochastic online scheduling on uniform machines," Annals of Operations Research, Springer, vol. 191(1), pages 97-113, November.
    3. Huiqiao Su & Guohua Wan & Shan Wang, 2019. "Online scheduling for outpatient services with heterogeneous patients and physicians," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 123-149, January.
    4. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 2022. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1796-1811, October.
    5. Martin Skutella & Maxim Sviridenko & Marc Uetz, 2016. "Unrelated Machine Scheduling with Stochastic Processing Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 851-864, August.
    6. Shen, Zuo-Jun Max & Xie, Jingui & Zheng, Zhichao & Zhou, Han, 2023. "Dynamic scheduling with uncertain job types," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1047-1060.
    7. Nicole Megow & Tjark Vredeveld, 2014. "A Tight 2-Approximation for Preemptive Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1297-1310, November.
    8. Megow, N. & Vredeveld, T., 2009. "Approximating preemptive stochastic scheduling," Research Memorandum 054, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Xiaoyan Zhang & Ran Ma & Jian Sun & Zan-Bo Zhang, 0. "Randomized selection algorithm for online stochastic unrelated machines scheduling," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    10. Vredeveld, T., 2009. "Stochastic Online Scheduling," Research Memorandum 052, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. Megow, N. & Vredeveld, T., 2006. "Approximation results for preemptive stochastic online scheduling," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. Nicole Megow & Marc Uetz & Tjark Vredeveld, 2006. "Models and Algorithms for Stochastic Online Scheduling," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 513-525, August.
    13. Rowan Wang & Oualid Jouini & Saif Benjaafar, 2014. "Service Systems with Finite and Heterogeneous Customer Arrivals," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 365-380, July.

    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. Philip Kaminsky & Onur Kaya, 2008. "Scheduling and due‐date quotation in a make‐to‐order supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(5), pages 444-458, August.
    2. Hui Liu & Maurice Queyranne & David Simchi‐Levi, 2005. "On the asymptotic optimality of algorithms for the flow shop problem with release dates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 232-242, April.
    3. Kaminsky, Philip & Kaya, Onur, 2008. "Inventory positioning, scheduling and lead-time quotation in supply chains," International Journal of Production Economics, Elsevier, vol. 114(1), pages 276-293, July.
    4. Susan H. Xu & Haijun Li, 2000. "Majorization of Weighted Trees: A New Tool to Study Correlated Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 298-323, May.
    5. Bertsimas, Dimitris., 1995. "The achievable region method in the optimal control of queueing systems : formulations, bounds and policies," Working papers 3837-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. Martin Skutella & Maxim Sviridenko & Marc Uetz, 2016. "Unrelated Machine Scheduling with Stochastic Processing Times," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 851-864, August.
    7. Brian C. Dean & Michel X. Goemans & Jan Vondrák, 2008. "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 945-964, November.
    8. Mandelbaum, Marvin & Hlynka, Myron, 2003. "Job sequencing using an expert," International Journal of Production Economics, Elsevier, vol. 85(3), pages 389-401, September.
    9. Diabat, Ali & Bianchessi, Nicola & Archetti, Claudia, 2024. "On the zero-inventory-ordering policy in the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1024-1038.
    10. V. Rattini, 2016. "Managing the Workload: an Experiment on Individual Decision Making and Performance," Working Papers wp1080, Dipartimento Scienze Economiche, Universita' di Bologna.
    11. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2002. "The Stochastic Inventory Routing Problem with Direct Deliveries," Transportation Science, INFORMS, vol. 36(1), pages 94-118, February.
    12. Manzhan Gu & Xiwen Lu & Jinwei Gu, 2017. "An asymptotically optimal algorithm for large-scale mixed job shop scheduling to minimize the makespan," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 473-495, February.
    13. Philip Kaminsky & David Simchi-Levi, 2001. "The Asymptotic Optimality of the SPT Rule for the Flow Shop Mean Completion Time Problem," Operations Research, INFORMS, vol. 49(2), pages 293-304, April.
    14. Varun Gupta & Benjamin Moseley & Marc Uetz & Qiaomin Xie, 2020. "Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 497-516, May.
    15. Marbán Sebastián & Rutten Cyriel & Vredeveld Tjark, 2010. "Asymptotic optimality of SEPT in Bayesian Scheduling," Research Memorandum 051, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    16. José Niño-Mora, 2000. "Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs," Economics Working Papers 514, Department of Economics and Business, Universitat Pompeu Fabra.
    17. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    18. Lisa Fleischer & Jay Sethuraman, 2005. "Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 916-938, November.
    19. Zhuang, Weifen & Li, Michael Z.F., 2012. "Monotone optimal control for a class of Markov decision processes," European Journal of Operational Research, Elsevier, vol. 217(2), pages 342-350.
    20. Arthur Charpentier & Lariosse Kouakou & Matthias Lowe & Philipp Ratz & Franck Vermet, 2021. "Collaborative Insurance Sustainability and Network Structure," Papers 2107.02764, arXiv.org, revised Sep 2022.

    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:inm:oropre:v:54:y:2006:i:3:p:464-474. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.