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Dynamic Restructuring Framework for Scheduling with Release Times and Due-Dates

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  • Nodari Vakhania

    (Centro de Investigación en Ciencias, Universidad Autónoma del Estado de Morelos, Morelos 62209, Mexico)

Abstract

Scheduling jobs with release and due dates on a single machine is a classical strongly NP-hard combination optimization problem. It has not only immediate real-life applications but also it is effectively used for the solution of more complex multiprocessor and shop scheduling problems. Here, we propose a general method that can be applied to the scheduling problems with job release times and due-dates. Based on this method, we carry out a detailed study of the single-machine scheduling problem, disclosing its useful structural properties. These properties give us more insight into the complex nature of the problem and its bottleneck feature that makes it intractable. This method also helps us to expose explicit conditions when the problem can be solved in polynomial time. In particular, we establish the complexity status of the special case of the problem in which job processing times are mutually divisible by constructing a polynomial-time algorithm that solves this setting. Apparently, this setting is a maximal polynomially solvable special case of the single-machine scheduling problem with non-arbitrary job processing times.

Suggested Citation

  • Nodari Vakhania, 2019. "Dynamic Restructuring Framework for Scheduling with Release Times and Due-Dates," Mathematics, MDPI, vol. 7(11), pages 1-42, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1104-:d:287022
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    References listed on IDEAS

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    1. Carlier, Jacques, 1982. "The one-machine sequencing problem," European Journal of Operational Research, Elsevier, vol. 11(1), pages 42-47, September.
    2. Graham McMahon & Michael Florian, 1975. "On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness," Operations Research, INFORMS, vol. 23(3), pages 475-482, June.
    3. W. A. Horn, 1974. "Some simple scheduling algorithms," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 21(1), pages 177-185, March.
    4. Nodari Vakhania, 2004. "Single-Machine Scheduling with Release Times and Tails," Annals of Operations Research, Springer, vol. 129(1), pages 253-271, July.
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    Cited by:

    1. Anran Zhao & Peng Liu & Xiyu Gao & Guotai Huang & Xiuguang Yang & Yuan Ma & Zheyu Xie & Yunfeng Li, 2022. "Data-Mining-Based Real-Time Optimization of the Job Shop Scheduling Problem," Mathematics, MDPI, vol. 10(23), pages 1-30, December.

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