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Minimizing the total tardiness and job rejection cost in a proportionate flow shop with generalized due dates

Author

Listed:
  • Baruch Mor

    (Ariel University)

  • Gur Mosheiov

    (The Hebrew University)

  • Dvir Shabtay

    (Ben-Gurion University of the Negev)

Abstract

We study a scheduling problem involving both partitioning and scheduling decisions. A solution for our problem is defined by (i) partitioning the set of jobs into a set of accepted and a set of rejected jobs and (ii) scheduling the set of accepted jobs in a proportionate flow shop scheduling system. For a given solution, the jth largest due date is assigned to the job with the jth largest completion time. The quality of a solution is measured by two criteria, one for each set of jobs. The first is the total tardiness of the set of accepted jobs, and the second is the total rejection cost. We study two problems. The goal in the first is to find a solution minimizing the sum of the total tardiness and the rejection cost, while the goal in the second is to find a solution minimizing the total rejection cost, given a bound on the total tardiness. As both problems are $${\mathcal {N}}{\mathcal {P}}$$ N P -hard, we focus on the design of both exact algorithms and approximation schemes.

Suggested Citation

  • Baruch Mor & Gur Mosheiov & Dvir Shabtay, 2021. "Minimizing the total tardiness and job rejection cost in a proportionate flow shop with generalized due dates," Journal of Scheduling, Springer, vol. 24(6), pages 553-567, December.
    • Handle: RePEc:spr:jsched:v:24:y:2021:i:6:d:10.1007_s10951-021-00697-4
    DOI: 10.1007/s10951-021-00697-4
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    References listed on IDEAS

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    1. K. Tanaka & M. Vlach, 1999. "Minimizing maximum absolute lateness and range of lateness under generalizeddue dates on a single machine," Annals of Operations Research, Springer, vol. 86(0), pages 507-526, January.
    2. 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.
    3. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
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    5. C. Sriskandarajah, 1990. "A note on the generalized due dates scheduling problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 587-597, August.
    6. Dvir Shabtay & Nufar Gaspar & Liron Yedidsion, 2012. "A bicriteria approach to scheduling a single machine with job rejection and positional penalties," Journal of Combinatorial Optimization, Springer, vol. 23(4), pages 395-424, May.
    7. Enrique Gerstl & Gur Mosheiov, 2017. "Single machine scheduling problems with generalised due-dates and job-rejection," International Journal of Production Research, Taylor & Francis Journals, vol. 55(11), pages 3164-3172, June.
    8. Hall, Nicholas G. & Sethi, Suresh P. & Sriskandarajah, Chelliah, 1991. "On the complexity of generalized due date scheduling problems," European Journal of Operational Research, Elsevier, vol. 51(1), pages 100-109, March.
    9. Enrique Gerstl & Gur Mosheiov, 2020. "Single machine scheduling to maximize the number of on-time jobs with generalized due-dates," Journal of Scheduling, Springer, vol. 23(3), pages 289-299, June.
    10. 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.
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    Cited by:

    1. Baruch Mor, 2023. "Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection," Operational Research, Springer, vol. 23(1), pages 1-19, March.

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