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Single-machine scheduling with machine unavailability periods and resource dependent processing times

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  • Shabtay, Dvir

Abstract

We study a single-machine scheduling problem, where each of the job processing times is a bounded linear decreasing function of the amount of resource allocated to its processing operation, and there is a single and fixed machine-unavailability interval that begins at time T. A solution is given by (i) partitioning the jobs into two sets, corresponding to the set of jobs to be processed before and after the unavailability period; and (ii) defining the amount of resource allocated to the processing operation of each of the jobs. A solution is feasible if the total processing time of all jobs assigned to be processed before the unavailability period does not exceed T. Our aim is to find a feasible solution that minimizes the makespan plus the total resource consumption cost. As the problem is known to be NP-hard even for constant processing times, we focus on the design of pseudo-polynomial time and approximation algorithms. Extension to the case of a fixed number of unavailability intervals is also provided.

Suggested Citation

  • Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    • Handle: RePEc:eee:ejores:v:296:y:2022:i:2:p:423-439
    DOI: 10.1016/j.ejor.2021.03.034
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    Cited by:

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    2. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.

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