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Online scheduling of malleable parallel jobs with setup times on two identical machines

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  • Guo, Shouwei
  • Kang, Liying

Abstract

In this paper we consider online scheduling of malleable parallel jobs on two identical machines, where jobs arrive over time. Each job Jj has an execution time tj=pj/kj+(kj-1)cj when it is processed on kj machines, where pj>0 and cj>0 are the length and setup time of job Jj. The objective is to minimize the makespan. For the problem with two machines, we present an online algorithm with competitive ratio of 1+[alpha], where . We show that 1+[alpha] is a lower bound on the competitive ratio of any online algorithm for the problem with machines. So our algorithm is optimal for the case of two machines.

Suggested Citation

  • Guo, Shouwei & Kang, Liying, 2010. "Online scheduling of malleable parallel jobs with setup times on two identical machines," European Journal of Operational Research, Elsevier, vol. 206(3), pages 555-561, November.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:3:p:555-561
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    References listed on IDEAS

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    1. Liao, Ching-Jong & Chao, Chien-Wen & Lin, Chien-Hung, 2009. "Minimizing the sum of job completion times on capacitated two-parallel machines," European Journal of Operational Research, Elsevier, vol. 197(2), pages 475-481, September.
    2. Koulamas, Christos & Kyparisis, George J., 2008. "An improved delayed-start LPT algorithm for a partition problem on two identical parallel machines," European Journal of Operational Research, Elsevier, vol. 187(2), pages 660-666, June.
    3. Havill, Jessen T. & Mao, Weizhen, 2008. "Competitive online scheduling of perfectly malleable jobs with setup times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1126-1142, June.
    4. Koulamas, Christos & Kyparisis, George J., 2009. "A modified LPT algorithm for the two uniform parallel machine makespan minimization problem," European Journal of Operational Research, Elsevier, vol. 196(1), pages 61-68, July.
    5. Kedad-Sidhoum, Safia & Solis, Yasmin Rios & Sourd, Francis, 2008. "Lower bounds for the earliness-tardiness scheduling problem on parallel machines with distinct due dates," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1305-1316, September.
    6. Li, Rongheng & Huang, Huei-Chuen, 2007. "Improved algorithm for a generalized on-line scheduling problem on identical machines," European Journal of Operational Research, Elsevier, vol. 176(1), pages 643-652, January.
    7. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    8. Deshi Ye & Xin Han & Guochuan Zhang, 2009. "A note on online strip packing," Journal of Combinatorial Optimization, Springer, vol. 17(4), pages 417-423, May.
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    Cited by:

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    2. Wu, Xiaohu & Loiseau, Patrick, 2023. "Efficient approximation algorithms for scheduling moldable tasks," European Journal of Operational Research, Elsevier, vol. 310(1), pages 71-83.

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