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Online interval scheduling on two related machines: the power of lookahead

Author

Listed:
  • Nicolas Pinson

    (ENS-Lyon)

  • Frits C. R. Spieksma

    (Eindhoven University of Technology)

Abstract

We consider an online interval scheduling problem on two related machines. If one machine is at least as twice as fast as the other machine, we say the machines are distinct; otherwise the machines are said to be similar. Each job $$j \in J$$ j ∈ J is characterized by a length $$p_j$$ p j , and an arrival time $$t_j$$ t j ; the question is to determine whether there exists a feasible schedule such that each job starts processing at its arrival time. For the case of unit-length jobs, we prove that when the two machines are distinct, there is an amount of lookahead allowing an online algorithm to solve the problem. When the two machines are similar, we show that no finite amount of lookahead is sufficient to solve the problem in an online fashion. We extend these results to jobs having arbitrary lengths, and consider an extension focused on minimizing total waiting time.

Suggested Citation

  • Nicolas Pinson & Frits C. R. Spieksma, 2019. "Online interval scheduling on two related machines: the power of lookahead," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 224-253, July.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:1:d:10.1007_s10878-019-00381-6
    DOI: 10.1007/s10878-019-00381-6
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    References listed on IDEAS

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    1. Douglas Smith, L. & Nauss, Robert M. & Mattfeld, Dirk Christian & Li, Jian & Ehmke, Jan F. & Reindl, M., 2011. "Scheduling operations at system choke points with sequence-dependent delays and processing times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 669-680, September.
    2. Passchyn, Ward & Briskorn, Dirk & Spieksma, Frits C.R., 2016. "Mathematical programming models for lock scheduling with an emission objective," European Journal of Operational Research, Elsevier, vol. 248(3), pages 802-814.
    3. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    4. Passchyn, Ward & Coene, Sofie & Briskorn, Dirk & Hurink, Johann L. & Spieksma, Frits C.R. & Vanden Berghe, Greet, 2016. "The lockmaster’s problem," European Journal of Operational Research, Elsevier, vol. 251(2), pages 432-441.
    5. Stanley P. Y. Fung & Chung Keung Poon & Feifeng Zheng, 2008. "Online interval scheduling: randomized and multiprocessor cases," Journal of Combinatorial Optimization, Springer, vol. 16(3), pages 248-262, October.
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