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

Author

Listed:
  • 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. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    2. Steve Seiden, 1999. "Randomized Online Scheduling with Delivery Times," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 399-416, December.
    3. Leslie A. Hall & David B. Shmoys, 1992. "Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 22-35, February.
    4. 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.
    5. 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.
    6. 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.
    7. Mohamed Haouari & Anis Gharbi, 2004. "Lower Bounds for Scheduling on Identical Parallel Machines with Heads and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 187-204, July.
    8. Carlier, Jacques, 1987. "Scheduling jobs with release dates and tails on identical machines to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 29(3), pages 298-306, June.
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    Cited by:

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    3. Ji Tian & Yan Zhou & Ruyan Fu, 2020. "An improved semi-online algorithm for scheduling on a single machine with unexpected breakdown," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 170-180, July.

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