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Minimizing maximum absolute lateness and range of lateness under generalizeddue dates on a single machine

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  • K. Tanaka
  • M. Vlach

Abstract

We investigate the problems of minimizing the maximum absolute lateness and range oflateness under generalized due dates on a single machine. In contrast to the traditional duedate cases, we show that these problems are unary NP‐hard. Furthermore, we present simpleapproximation algorithms for these problems, and show that they achieve the performanceratios of n for the problem of minimizing the maximum absolute lateness and of [ n/2 ] forthe problem of minimizing the range of lateness, where [ x ] is the smallest integer no lessthan x. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:86:y:1999:i:0:p:507-526:10.1023/a:1018987625819
    DOI: 10.1023/A:1018987625819
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    Cited by:

    1. 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.
    2. Barketau, M.S. & Cheng, T.C.E. & Kovalyov, M.Y., 2008. "Batch scheduling of deteriorating reworkables," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1317-1326, September.
    3. 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.
    4. Alexander Lazarev & Nikolay Pravdivets & Egor Barashov, 2024. "Approximation of the Objective Function of Single-Machine Scheduling Problem," Mathematics, MDPI, vol. 12(5), pages 1-16, February.
    5. 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.
    6. Gur Mosheiov & Daniel Oron & Dvir Shabtay, 2022. "On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates," Journal of Scheduling, Springer, vol. 25(5), pages 577-587, October.
    7. Wang, Du-Juan & Yin, Yunqiang & Xu, Jianyou & Wu, Wen-Hsiang & Cheng, Shuenn-Ren & Wu, Chin-Chia, 2015. "Some due date determination scheduling problems with two agents on a single machine," International Journal of Production Economics, Elsevier, vol. 168(C), pages 81-90.
    8. Inderfurth, Karl & Kovalyov, Mikhail Y. & Ng, C.T. & Werner, Frank, 2007. "Cost minimizing scheduling of work and rework processes on a single facility under deterioration of reworkables," International Journal of Production Economics, Elsevier, vol. 105(2), pages 345-356, February.

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