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Minimizing the maximum lateness for scheduling with release times and job rejection

Author

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  • Imed Kacem

    (Université de Lorraine)

  • Hans Kellerer

    (Universität Graz)

Abstract

We study scheduling problems with release times and rejection costs with the objective function of minimizing the maximum lateness. Our main result is a PTAS for the single machine problem with an upper bound on the rejection costs. This result is extended to parallel, identical machines. The corresponding problem of minimizing the rejection costs with an upper bound on the lateness is also examined. We show how to compute a PTAS for determining an approximation of the Pareto frontier on both objective functions on parallel, identical machines. Moreover, we present an FPTAS with strongly polynomial time for the maximum lateness problem without release times on identical machines when the number of machines is constant. Finally, we extend this FPTAS to the case of unrelated machines.

Suggested Citation

  • Imed Kacem & Hans Kellerer, 2024. "Minimizing the maximum lateness for scheduling with release times and job rejection," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-22, October.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:3:d:10.1007_s10878-024-01205-y
    DOI: 10.1007/s10878-024-01205-y
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    References listed on IDEAS

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    1. Hermelin, Danny & Pinedo, Michael & Shabtay, Dvir & Talmon, Nimrod, 2019. "On the parameterized tractability of single machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 273(1), pages 67-73.
    2. Leslie A. Hall & David B. Shmoys, 1992. "Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 22-35, February.
    3. Imed Kacem & Hans Kellerer & Maryam Seifaddini, 2016. "Efficient approximation schemes for the maximum lateness minimization on a single machine with a fixed operator or machine non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 970-981, October.
    4. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    5. Cheng He & Joseph Y.-T. Leung & Kangbok Lee & Michael L. Pinedo, 2016. "Improved algorithms for single machine scheduling with release dates and rejections," 4OR, Springer, vol. 14(1), pages 41-55, March.
    6. 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.
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