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Online scheduling on two parallel machines with release dates and delivery times

Author

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  • Peihai Liu

    (East China University of Science and Technology)

  • Xiwen Lu

    (East China University of Science and Technology)

Abstract

We consider an online scheduling problem where jobs arrive over time. A set of independent jobs has to be scheduled on two parallel machines, where preemption is not allowed and the number of jobs is unknown in advance. The characteristics of each job, i.e., processing time and delivery time, become known at its release date. Each job is delivered to the destination independently and immediately at its completion time on the machines. The objective is to minimize the time by which all jobs have been delivered. We present an online algorithm which has a competitive ratio of $$(1+\sqrt{5})/2\approx 1.618$$ ( 1 + 5 ) / 2 ≈ 1.618 . Finally, our experimental results show that, in practice, the worst case error ratio is much better than the theoretical bound.

Suggested Citation

  • Peihai Liu & Xiwen Lu, 2015. "Online scheduling on two parallel machines with release dates and delivery times," Journal of Combinatorial Optimization, Springer, vol. 30(2), pages 347-359, August.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9760-y
    DOI: 10.1007/s10878-014-9760-y
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    References listed on IDEAS

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    1. Liu, Ming & Chu, Chengbin & Xu, Yinfeng & Zheng, Feifeng, 2010. "An optimal online algorithm for single machine scheduling with bounded delivery times," European Journal of Operational Research, Elsevier, vol. 201(3), pages 693-700, March.
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    7. Jinjiang Yuan & Shisheng Li & Ji Tian & Ruyan Fu, 2009. "A best on-line algorithm for the single machine parallel-batch scheduling with restricted delivery times," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 206-213, February.
    8. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
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    Cited by:

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