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An improved heuristic for parallel machine scheduling with rejection

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  • Ou, Jinwen
  • Zhong, Xueling
  • Wang, Guoqing

Abstract

In this paper we study a classical parallel machine scheduling model with m machines and n jobs, where each job is either accepted and then processed by one of the machines, or rejected and then a rejection penalty is paid. The objective is to minimize the completion time of the last accepted job plus the total penalty of all rejected jobs. The scheduling problem is known to be NP-hard in the strong sense. We find some new optimal properties and develop an O(nlog n + n/ε) heuristic to solve the problem with a worst-case bound of 1.5 + ε, where ε > 0 can be any small given constant. This improves upon the worst-case bound 2−1m of the heuristic presented by Bartal et al. (Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., & Stougie, L. (2000). Multiprocessor scheduling with rejection. SIAM Journal on Discrete Mathematics, 13, 64–78) in the scheduling literature.

Suggested Citation

  • Ou, Jinwen & Zhong, Xueling & Wang, Guoqing, 2015. "An improved heuristic for parallel machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 241(3), pages 653-661.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:653-661
    DOI: 10.1016/j.ejor.2014.09.028
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    References listed on IDEAS

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    1. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    2. Lee, Ik Sun & Sung, C.S., 2008. "Minimizing due date related measures for a single machine scheduling problem with outsourcing allowed," European Journal of Operational Research, Elsevier, vol. 186(3), pages 931-952, May.
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    4. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
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    6. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
    7. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
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    Cited by:

    1. Lingfa Lu & Liqi Zhang & Jie Zhang & Lili Zuo, 2020. "Single Machine Scheduling with Outsourcing Under Different Fill Rates or Quantity Discount Rates," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-15, January.
    2. Ou, Jinwen & Zhong, Xueling, 2017. "Bicriteria order acceptance and scheduling with consideration of fill rate," European Journal of Operational Research, Elsevier, vol. 262(3), pages 904-907.
    3. Peihai Liu & Xiwen Lu, 2020. "New approximation algorithms for machine scheduling with rejection on single and parallel machine," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 929-952, November.
    4. Xiaofei Liu & Peiyin Xing & Weidong Li, 2020. "Approximation Algorithms for the Submodular Load Balancing with Submodular Penalties," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    5. 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.
    6. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    7. Baruch Mor & Gur Mosheiov, 2021. "A note: flowshop scheduling with linear deterioration and job-rejection," 4OR, Springer, vol. 19(1), pages 103-111, March.
    8. Baruch Mor & Gur Mosheiov & Dana Shapira, 2020. "Flowshop scheduling with learning effect and job rejection," Journal of Scheduling, Springer, vol. 23(6), pages 631-641, December.
    9. Wencheng Wang & Xiaofei Liu, 2021. "A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties," Mathematics, MDPI, vol. 10(1), pages 1-10, December.
    10. Baruch Mor & Gur Mosheiov, 2016. "Minimizing maximum cost on a single machine with two competing agents and job rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1524-1531, December.
    11. Mohamadreza Dabiri & Mehdi Yazdani & Bahman Naderi & Hassan Haleh, 2022. "Modeling and solution methods for hybrid flow shop scheduling problem with job rejection," Operational Research, Springer, vol. 22(3), pages 2721-2765, July.
    12. Xueling Zhong & Jinwen Ou, 2017. "Improved approximation algorithms for parallel machine scheduling with release dates and job rejection," 4OR, Springer, vol. 15(4), pages 387-406, December.
    13. Xiaofei Liu & Man Xiao & Weidong Li & Yaoyu Zhu & Lei Ma, 2023. "Algorithms for single machine scheduling problem with release dates and submodular penalties," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-18, May.
    14. Zhong, Xueling & Fan, Jie & Ou, Jinwen, 2022. "Coordinated scheduling of the outsourcing, in-house production and distribution operations," European Journal of Operational Research, Elsevier, vol. 302(2), pages 427-437.
    15. Gur Mosheiov & Assaf Sarig & Vitaly Strusevich, 2020. "Minmax scheduling and due-window assignment with position-dependent processing times and job rejection," 4OR, Springer, vol. 18(4), pages 439-456, December.
    16. Xiaofei Liu & Weidong Li, 2020. "Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    17. Hanane Krim & Nicolas Zufferey & Jean-Yves Potvin & Rachid Benmansour & David Duvivier, 2022. "Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times," Journal of Scheduling, Springer, vol. 25(1), pages 89-105, February.
    18. Baruch Mor & Gur Mosheiov, 2018. "A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection," Annals of Operations Research, Springer, vol. 271(2), pages 1079-1085, December.
    19. Ren-Xia Chen & Shi-Sheng Li, 2020. "Minimizing maximum delivery completion time for order scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1044-1064, November.
    20. R. Micale & C. M. La Fata & M. Enea & G. La Scalia, 2021. "Regenerative scheduling problem in engineer to order manufacturing: an economic assessment," Journal of Intelligent Manufacturing, Springer, vol. 32(7), pages 1913-1925, October.
    21. Tarhan, İstenç & Oğuz, Ceyda, 2022. "A matheuristic for the generalized order acceptance and scheduling problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 87-103.
    22. 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.
    23. Weidong Li & Qianna Cui, 2018. "Vector scheduling with rejection on a single machine," 4OR, Springer, vol. 16(1), pages 95-104, March.
    24. Xiaofei Liu & Weidong Li & Yaoyu Zhu, 2021. "Single Machine Vector Scheduling with General Penalties," Mathematics, MDPI, vol. 9(16), pages 1-16, August.
    25. Joonyup Eun & Chang Sup Sung & Eun-Seok Kim, 2017. "Maximizing total job value on a single machine with job selection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(9), pages 998-1005, September.

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