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Parallel Machine Scheduling: Impact of Adding Extra Machines

Author

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  • Kabir Rustogi

    (School of Computing and Mathematical Sciences, Old Royal Naval College, University of Greenwich, London SE10 9LS, United Kingdom)

  • Vitaly A. Strusevich

    (School of Computing and Mathematical Sciences, Old Royal Naval College, University of Greenwich, London SE10 9LS, United Kingdom)

Abstract

We consider the classical scheduling problems of processing jobs on identical parallel machines to minimize (i) the makespan (the maximum completion time) or (ii) the total flow time (the sum of the completion times). The focus of this study is on the impact that additional machines may have, if added to the system. We measure such a machine impact by the ratio of the value of the objective function computed with the original number of machines to the one computed with extra machines. We give tight bounds on the machine impact for the problem of minimizing the makespan, for both the preemptive and non-preemptive versions, as well as for the problem of minimizing the total flow time. We also present polynomial-time exact and approximation algorithms to make a cost-effective choice of the number of machines, provided that each machine incurs a cost and the objective function captures the trade-off between the cost of the used machines and a scheduling objective.

Suggested Citation

  • Kabir Rustogi & Vitaly A. Strusevich, 2013. "Parallel Machine Scheduling: Impact of Adding Extra Machines," Operations Research, INFORMS, vol. 61(5), pages 1243-1257, October.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:5:p:1243-1257
    DOI: 10.1287/opre.2013.1208
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    References listed on IDEAS

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    1. Rustogi, Kabir & Strusevich, Vitaly A., 2012. "Single machine scheduling with general positional deterioration and rate-modifying maintenance," Omega, Elsevier, vol. 40(6), pages 791-804.
    2. Robert McNaughton, 1959. "Scheduling with Deadlines and Loss Functions," Management Science, INFORMS, vol. 6(1), pages 1-12, October.
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    Citations

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    Cited by:

    1. Halman, Nir & Kellerer, Hans & Strusevich, Vitaly A., 2018. "Approximation schemes for non-separable non-linear boolean programming problems under nested knapsack constraints," European Journal of Operational Research, Elsevier, vol. 270(2), pages 435-447.
    2. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    3. Chen, Jianfu & Chu, Chengbin & Sahli, Abderrahim & Li, Kai, 2024. "A branch-and-price algorithm for unrelated parallel machine scheduling with machine usage costs," European Journal of Operational Research, Elsevier, vol. 316(3), pages 856-872.
    4. Rachid Benmansour & Oliver Braun, 2023. "On the minimum number of resources for a perfect schedule," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 191-204, March.
    5. Kai Li & Fulong Xie & Jianfu Chen & Wei Xiao & Tao Zhou, 2025. "Mathematical models and an effective exact algorithm for unrelated parallel machine scheduling with family setup times and machine cost," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 129-176, March.
    6. Shi Qiang Liu & Erhan Kozan & Mahmoud Masoud & Debiao Li & Kai Luo, 2025. "Multi-stage mine production timetabling with optimising the sizes of mining operations: an application of parallel-machine flow shop scheduling with lot streaming," Annals of Operations Research, Springer, vol. 348(2), pages 1-27, May.
    7. Alan J. Soper & Vitaly A. Strusevich, 2022. "Preemptive and non-preemptive scheduling on two unrelated parallel machines," Journal of Scheduling, Springer, vol. 25(6), pages 659-674, December.
    8. Abdelhak Elidrissi & Rachid Benmansour & Nicolas Zufferey & Mohammed Benbrahim & David Duvivier, 2024. "Minimization of maximum lateness on parallel machines with a single server and job release dates," 4OR, Springer, vol. 22(3), pages 351-385, September.
    9. Alan J. Soper & Vitaly A. Strusevich, 2021. "Parametric analysis of the quality of single preemption schedules on three uniform parallel machines," Annals of Operations Research, Springer, vol. 298(1), pages 469-495, March.

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