IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v6y2002i2d10.1023_a1013855712183.html
   My bibliography  Save this article

Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time

Author

Listed:
  • Yong He

    (Zhejiang University)

  • Zhiyi Tan

    (Zhejiang University)

Abstract

This paper considers the on-line problem of scheduling nonpreemptively n independent jobs on m > 1 identical and parallel machines with the objective to maximize the minimum machine completion time. It is assumed that the values of the processing times are unknown but the order of the jobs by their processing times is known in advance. We are asked to decide the assignment of all the jobs to some machines at time zero by utilizing only ordinal data rather than the actual magnitudes of jobs. Algorithms to slove the problem are called ordinal algorithms. In this paper, we give lower bounds and ordinal algorithms. We first propose an algorithm MIN which is at most $$(\left\lceil {\sum {_{i = 1}^m {\text{ }}1/} i} \right\rceil + 1)$$ -competitive for any m machine case, while the lower bound is ∑ i=1 m 1/i. Both are on the order of Θ(ln m). Furthermore, for m = 3, we present an optimal algorithm.

Suggested Citation

  • Yong He & Zhiyi Tan, 2002. "Ordinal On-Line Scheduling for Maximizing the Minimum Machine Completion Time," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 199-206, June.
    • Handle: RePEc:spr:jcomop:v:6:y:2002:i:2:d:10.1023_a:1013855712183
    DOI: 10.1023/A:1013855712183
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1013855712183
    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:1013855712183?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. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
    2. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    3. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    4. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    5. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    6. D. K. Friesen & B. L. Deuermeyer, 1981. "Analysis of Greedy Solutions for a Replacement Part Sequencing Problem," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 74-87, February.
    7. N. V. R. Mahadev & Aleksandar Pekeč & Fred S. Roberts, 1998. "On the Meaningfulness of Optimal Solutions to Scheduling Problems: Can an Optimal Solution be Nonoptimal?," Operations Research, INFORMS, vol. 46(3-supplem), pages 120-134, June.
    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. Rico Walter, 2013. "Comparing the minimum completion times of two longest-first scheduling-heuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 125-139, January.
    2. Rico Walter & Martin Wirth & Alexander Lawrinenko, 2017. "Improved approaches to the exact solution of the machine covering problem," Journal of Scheduling, Springer, vol. 20(2), pages 147-164, April.
    3. Leah Epstein, 2023. "Parallel solutions for ordinal scheduling with a small number of machines," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-24, August.
    4. Yiwei Jiang & Zhiyi Tan & Yong He, 2005. "Preemptive Machine Covering on Parallel Machines," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 345-363, December.

    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. Allen C. Goodman & Miron Stano, 2000. "Hmos and Health Externalities: A Local Public Good Perspective," Public Finance Review, , vol. 28(3), pages 247-269, May.
    2. Bettina Campedelli & Andrea Guerrina & Giulia Romano & Chiara Leardini, 2014. "La performance della rete ospedaliera pubblica della regione Veneto. L?impatto delle variabili ambientali e operative sull?efficienza," MECOSAN, FrancoAngeli Editore, vol. 2014(92), pages 119-142.
    3. Penn Loh & Zoë Ackerman & Joceline Fidalgo & Rebecca Tumposky, 2022. "Co-Education/Co-Research Partnership: A Critical Approach to Co-Learning between Dudley Street Neighborhood Initiative and Tufts University," Social Sciences, MDPI, vol. 11(2), pages 1-17, February.
    4. O'Brien, Raymond & Patacchini, Eleonora, 2003. "Testing the exogeneity assumption in panel data models with "non classical" disturbances," Discussion Paper Series In Economics And Econometrics 0302, Economics Division, School of Social Sciences, University of Southampton.
    5. YongSeog Kim & W. Nick Street & Gary J. Russell & Filippo Menczer, 2005. "Customer Targeting: A Neural Network Approach Guided by Genetic Algorithms," Management Science, INFORMS, vol. 51(2), pages 264-276, February.
    6. Yanling Li & Zita Oravecz & Shuai Zhou & Yosef Bodovski & Ian J. Barnett & Guangqing Chi & Yuan Zhou & Naomi P. Friedman & Scott I. Vrieze & Sy-Miin Chow, 2022. "Bayesian Forecasting with a Regime-Switching Zero-Inflated Multilevel Poisson Regression Model: An Application to Adolescent Alcohol Use with Spatial Covariates," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 376-402, June.
    7. Oscar J. Cacho & Robyn L. Hean & Russell M. Wise, 2003. "Carbon‐accounting methods and reforestation incentives," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 47(2), pages 153-179, June.
    8. Walter M. Cadette, 1999. "Financing Long-Term Care: Options for Policy," Economics Working Paper Archive wp_283, Levy Economics Institute.
    9. Eggli, Yves & Halfon, Patricia & Chikhi, Mehdi & Bandi, Till, 2006. "Ambulatory healthcare information system: A conceptual framework," Health Policy, Elsevier, vol. 78(1), pages 26-38, August.
    10. M. A. Noor & E.A. Al-Said, 2002. "Finite-Difference Method for a System of Third-Order Boundary-Value Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 627-637, March.
    11. Henderson, James E. & Dunn, Michael A., 2007. "Investigating the Potential of Fee-Based Recreation on Private Lands in the Lower Mississippi River Delta," 2007 Annual Meeting, February 4-7, 2007, Mobile, Alabama 34822, Southern Agricultural Economics Association.
    12. Eike Quilling & Birgit Babitsch & Kevin Dadaczynski & Stefanie Kruse & Maja Kuchler & Heike Köckler & Janna Leimann & Ulla Walter & Christina Plantz, 2020. "Municipal Health Promotion as Part of Urban Health: A Policy Framework for Action," Sustainability, MDPI, vol. 12(16), pages 1-10, August.
    13. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    14. Alireza Nili & Mary Tate & David Johnstone, 2019. "The process of solving problems with self-service technologies: a study from the user’s perspective," Electronic Commerce Research, Springer, vol. 19(2), pages 373-407, June.
    15. Chein-Shan Liu & Zhuojia Fu & Chung-Lun Kuo, 2017. "Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 112-123, December.
    16. Ali Akgül & Esra Karatas Akgül & Dumitru Baleanu & Mustafa Inc, 2018. "New Numerical Method for Solving Tenth Order Boundary Value Problems," Mathematics, MDPI, vol. 6(11), pages 1-9, November.
    17. Li, Haitao & Womer, Norman K., 2015. "Solving stochastic resource-constrained project scheduling problems by closed-loop approximate dynamic programming," European Journal of Operational Research, Elsevier, vol. 246(1), pages 20-33.
    18. José Sánchez Maldonado & Salvador Gómez Sala, 2006. "The Reform of Indirect Taxation in Spain: VAT and Excise," International Center for Public Policy Working Paper Series, at AYSPS, GSU paper0607, International Center for Public Policy, Andrew Young School of Policy Studies, Georgia State University.
    19. Georgios Marinakos & Sophia Daskalaki, 2017. "Imbalanced customer classification for bank direct marketing," Journal of Marketing Analytics, Palgrave Macmillan, vol. 5(1), pages 14-30, March.
    20. Tohru Morita & Ken-ichi Sato, 2017. "Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Terms of the Green’s Function," Mathematics, MDPI, vol. 5(4), pages 1-24, November.

    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:6:y:2002:i:2:d:10.1023_a:1013855712183. 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.