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A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates

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  • Kailiang Xu
  • Zuren Feng
  • Liangjun Ke

Abstract

In most deterministic scheduling problems, job-processing times are regarded as constant and known in advance. However, in many realistic environments, job-processing times can be controlled by the allocation of a common resource to jobs. In this paper, we consider the problem of scheduling jobs with arbitrary release dates and due dates on a single machine, where job-processing times are controllable and are modeled by a non-linear convex resource consumption function. The objective is to determine simultaneously an optimal processing permutation as well as an optimal resource allocation, such that no job is completed later than its due date, and the total resource consumption is minimized. The problem is strongly $\mathcal{NP}$ -hard. A branch and bound algorithm is presented to solve the problem. The computational experiments show that the algorithm can provide optimal solution for small-sized problems, and near-optimal solution for medium-sized problems in acceptable computing time. Copyright Springer Science+Business Media, LLC 2010

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  • Kailiang Xu & Zuren Feng & Liangjun Ke, 2010. "A branch and bound algorithm for scheduling jobs with controllable processing times on a single machine to meet due dates," Annals of Operations Research, Springer, vol. 181(1), pages 303-324, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:303-324:10.1007/s10479-010-0746-6
    DOI: 10.1007/s10479-010-0746-6
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    Cited by:

    1. Kailiang Xu & Zuren Feng & Liangjun Ke, 2011. "Single machine scheduling with total tardiness criterion and convex controllable processing times," Annals of Operations Research, Springer, vol. 186(1), pages 383-391, June.
    2. Fateme Akhoondi & M.M. Lotfi, 2016. "A heuristic algorithm for master production scheduling problem with controllable processing times and scenario-based demands," International Journal of Production Research, Taylor & Francis Journals, vol. 54(12), pages 3659-3676, June.
    3. Radosław Rudek, 2012. "Scheduling problems with position dependent job processing times: computational complexity results," Annals of Operations Research, Springer, vol. 196(1), pages 491-516, July.
    4. Yim, Seho & Hong, Sung-Pil & Park, Myoung-Ju & Chung, Yerim, 2022. "Inverse interval scheduling via reduction on a single machine," European Journal of Operational Research, Elsevier, vol. 303(2), pages 541-549.

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