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A Mathematical Programming Approach for Online Hierarchical Scheduling

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5573))

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Abstract

This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize makespan. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both algorithm and lower bounds are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m = 4 and 5, respectively.

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Authors and Affiliations

  1. Department of Mathematics, State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310027, China

    Zhiyi Tan & An Zhang

Authors
  1. Zhiyi Tan
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  2. An Zhang
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Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 800 West Campbell Road, TX 75080-3021, Richardson, USA

    Ding-Zhu Du

  2. Chinese Academy of Sciences, Institute of Applied Mathematics, Zhong Guan Cun Dong Lu 55, 100190, Beijing, P. R. China

    Xiaodong Hu

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, FL 32611-6595, Gainesville, USA

    Panos M. Pardalos

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© 2009 Springer-Verlag Berlin Heidelberg

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Tan, Z., Zhang, A. (2009). A Mathematical Programming Approach for Online Hierarchical Scheduling. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_42

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  • DOI: https://doi.org/10.1007/978-3-642-02026-1_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02025-4

  • Online ISBN: 978-3-642-02026-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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