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Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

Author

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  • Malgorzata Sterna

    (Poznan University of Technology)

  • Kateryna Czerniachowska

    (Poznan University of Technology)

Abstract

We study the scheduling problem with a common due date on two parallel identical machines and the total early work criterion. The problem is known to be NP-hard. We prove a few dominance properties of optimal solutions of this problem. Their proposal was inspired by the results of some auxiliary computational experiments. Test were performed with the dynamic programming algorithm and list algorithms. Then, we propose the polynomial time approximation scheme, based on structuring problem input. Moreover, we discuss the relationship between the early work criterion and the related late work criterion. We compare the computational complexity and approximability of scheduling problems with both mentioned objective functions.

Suggested Citation

  • Malgorzata Sterna & Kateryna Czerniachowska, 2017. "Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 927-944, September.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1147-7
    DOI: 10.1007/s10957-017-1147-7
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    References listed on IDEAS

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    1. M. Y. Kovalyov & C. N. Potts & L. N. van Wassenhove, 1994. "A Fully Polynomial Approximation Scheme for Scheduling a Single Machine to Minimize Total Weighted Late Work," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 86-93, February.
    2. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    3. C. N. Potts & L. N. Van Wassenhove, 1992. "Single Machine Scheduling to Minimize Total Late Work," Operations Research, INFORMS, vol. 40(3), pages 586-595, June.
    4. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    5. Blazewicz, Jacek & Pesch, Erwin & Sterna, Malgorzata & Werner, Frank, 2005. "The two-machine flow-shop problem with weighted late work criterion and common due date," European Journal of Operational Research, Elsevier, vol. 165(2), pages 408-415, September.
    6. A. M. A. Hariri & C. N. Potts & L. N. Van Wassenhove, 1995. "Single Machine Scheduling to Minimize Total Weighted Late Work," INFORMS Journal on Computing, INFORMS, vol. 7(2), pages 232-242, May.
    7. Jacek Błażewicz & Klaus H. Ecker & Erwin Pesch & Günter Schmidt & Jan Węglarz, 2007. "Handbook on Scheduling," International Handbooks on Information Systems, Springer, number 978-3-540-32220-7, December.
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    Cited by:

    1. Yi-Chun Wang & Ji-Bo Wang, 2023. "Study on Convex Resource Allocation Scheduling with a Time-Dependent Learning Effect," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    2. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    3. Xiaofei Liu & Yajie Li & Weidong Li & Jinhua Yang, 2023. "Combinatorial approximation algorithms for the maximum bounded connected bipartition problem," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.
    4. Chen, Xin & Miao, Qian & Lin, Bertrand M.T. & Sterna, Malgorzata & Blazewicz, Jacek, 2022. "Two-machine flow shop scheduling with a common due date to maximize total early work," European Journal of Operational Research, Elsevier, vol. 300(2), pages 504-511.
    5. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    6. Chen, Xin & Liang, Yage & Sterna, Małgorzata & Wang, Wen & Błażewicz, Jacek, 2020. "Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date," European Journal of Operational Research, Elsevier, vol. 284(1), pages 67-74.
    7. Györgyi, Péter & Kis, Tamás, 2020. "A common approximation framework for early work, late work, and resource leveling problems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 129-137.
    8. Shi-Sheng Li & Jin-Jiang Yuan, 2020. "Single-machine scheduling with multi-agents to minimize total weighted late work," Journal of Scheduling, Springer, vol. 23(4), pages 497-512, August.
    9. Yunhong Min & Byung-Cheon Choi & Myoung-Ju Park & Kyung Min Kim, 2023. "A parallel-machine scheduling problem with an antithetical property to maximize total weighted early work," 4OR, Springer, vol. 21(3), pages 421-437, September.

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