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Scheduling under linear constraints

Author

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  • Nip, Kameng
  • Wang, Zhenbo
  • Wang, Zizhuo

Abstract

We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with no more than two linear constraints, or both the number of machines and the number of linear constraints are fixed constants, then the problem is polynomial-time solvable via solving a series of linear programming problems. If both the number of machines and the number of constraints are inputs of the problem instance, then the problem is NP-Hard. We further propose several approximation algorithms for the latter case.

Suggested Citation

  • Nip, Kameng & Wang, Zhenbo & Wang, Zizhuo, 2016. "Scheduling under linear constraints," European Journal of Operational Research, Elsevier, vol. 253(2), pages 290-297.
    • Handle: RePEc:eee:ejores:v:253:y:2016:i:2:p:290-297
    DOI: 10.1016/j.ejor.2016.02.028
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    Citations

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    Cited by:

    1. Zhenbo Wang & Kameng Nip, 2017. "Bin packing under linear constraints," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1198-1209, November.
    2. Kameng Nip & Tianning Shi & Zhenbo Wang, 2022. "Some graph optimization problems with weights satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 200-225, January.
    3. Kameng Nip & Zhenbo Wang & Zizhuo Wang, 2017. "Knapsack with variable weights satisfying linear constraints," Journal of Global Optimization, Springer, vol. 69(3), pages 713-725, November.
    4. Siyun Zhang & Kameng Nip & Zhenbo Wang, 0. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-17.
    5. Chen, Lin & Ye, Deshi & Zhang, Guochuan, 2018. "Parallel machine scheduling with speed-up resources," European Journal of Operational Research, Elsevier, vol. 268(1), pages 101-112.
    6. Parhizkar, Tarannom & Mosleh, Ali & Roshandel, Ramin, 2017. "Aging based optimal scheduling framework for power plants using equivalent operating hour approach," Applied Energy, Elsevier, vol. 205(C), pages 1345-1363.
    7. Siyun Zhang & Kameng Nip & Zhenbo Wang, 2022. "Related machine scheduling with machine speeds satisfying linear constraints," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1724-1740, October.

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