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Scheduling parallel machines with inclusive processing set restrictions

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  • Jinwen Ou
  • Joseph Y.‐T. Leung
  • Chung‐Lun Li

Abstract

We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of ${4}\over{3}$ + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Suggested Citation

  • Jinwen Ou & Joseph Y.‐T. Leung & Chung‐Lun Li, 2008. "Scheduling parallel machines with inclusive processing set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 328-338, June.
    • Handle: RePEc:wly:navres:v:55:y:2008:i:4:p:328-338
    DOI: 10.1002/nav.20286
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    References listed on IDEAS

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    1. Celia A. Glass & Hans Kellerer, 2007. "Parallel machine scheduling with job assignment restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(3), pages 250-257, April.
    2. Joseph Y.-T. Leung, 1982. "On Scheduling Independent Tasks with Restricted Execution Times," Operations Research, INFORMS, vol. 30(1), pages 163-171, February.
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    Cited by:

    1. Chuleeporn Kusoncum & Kanchana Sethanan & Richard F. Hartl & Thitipong Jamrus, 2022. "Modified differential evolution and heuristic algorithms for dump tippler machine allocation in a typical sugar mill in Thailand," Operational Research, Springer, vol. 22(5), pages 5863-5895, November.
    2. Hans Kellerer & Joseph Y.‐T. Leung & Chung‐Lun Li, 2011. "Multiple subset sum with inclusive assignment set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 546-563, September.
    3. Shan Wang & Huiqiao Su & Guohua Wan, 2015. "Resource-constrained machine scheduling with machine eligibility restriction and its applications to surgical operations scheduling," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 982-995, November.
    4. Li, Weidong & Ou, Jinwen, 2024. "Approximation algorithms for scheduling parallel machines with an energy constraint in green manufacturing," European Journal of Operational Research, Elsevier, vol. 314(3), pages 882-893.
    5. Kangbok Lee & Joseph Leung & Michael Pinedo, 2013. "Makespan minimization in online scheduling with machine eligibility," Annals of Operations Research, Springer, vol. 204(1), pages 189-222, April.
    6. Mallik Angalakudati & Siddharth Balwani & Jorge Calzada & Bikram Chatterjee & Georgia Perakis & Nicolas Raad & Joline Uichanco, 2014. "Business Analytics for Flexible Resource Allocation Under Random Emergencies," Management Science, INFORMS, vol. 60(6), pages 1552-1573, June.
    7. Dominik Kress & Sebastian Meiswinkel & Erwin Pesch, 2018. "Mechanism design for machine scheduling problems: classification and literature overview," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(3), pages 583-611, July.
    8. Xianglai Qi & Jinjiang Yuan, 2019. "Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-16, February.
    9. André Rossi & Alexis Aubry & Mireille Jacomino, 2011. "A sensitivity analysis to assess the completion time deviation for multi-purpose machines facing demand uncertainty," Annals of Operations Research, Springer, vol. 191(1), pages 219-249, November.
    10. Juntaek Hong & Kangbok Lee & Michael L. Pinedo, 2020. "Scheduling equal length jobs with eligibility restrictions," Annals of Operations Research, Springer, vol. 285(1), pages 295-314, February.
    11. Xianglai Qi & Jinjiang Yuan, 2017. "Semi-online hierarchical scheduling for $$l_p$$ l p -norm load balancing with buffer or rearrangements," 4OR, Springer, vol. 15(3), pages 265-276, September.
    12. Giorgi Tadumadze & Simon Emde & Heiko Diefenbach, 2020. "Exact and heuristic algorithms for scheduling jobs with time windows on unrelated parallel machines," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 461-497, June.
    13. Jinwen Ou & Xueling Zhong & Xiangtong Qi, 2016. "Scheduling parallel machines with inclusive processing set restrictions and job rejection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 667-681, December.
    14. Huiqiao Su & Michael Pinedo & Guohua Wan, 2017. "Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 249-267, April.
    15. Ferreira, Cristiane & Figueira, Gonçalo & Amorim, Pedro, 2021. "Scheduling Human-Robot Teams in collaborative working cells," International Journal of Production Economics, Elsevier, vol. 235(C).

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