Single-machine scheduling with machine unavailability periods and resource dependent processing times
•We study a single-machine scheduling problem with a machine-unavailability period.•Processing times are resource-dependent.•The problem is known to be NP-hard.•We focus on the design of pseudo-polynomial time and approximation algorithms.•Extension to the case of a fixed number of unavailability pe...
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| Published in: | European journal of operational research Vol. 296; no. 2; pp. 423 - 439 |
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| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
16.01.2022
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •We study a single-machine scheduling problem with a machine-unavailability period.•Processing times are resource-dependent.•The problem is known to be NP-hard.•We focus on the design of pseudo-polynomial time and approximation algorithms.•Extension to the case of a fixed number of unavailability periods is provided.
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. |
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| AbstractList | •We study a single-machine scheduling problem with a machine-unavailability period.•Processing times are resource-dependent.•The problem is known to be NP-hard.•We focus on the design of pseudo-polynomial time and approximation algorithms.•Extension to the case of a fixed number of unavailability periods is provided.
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. |
| Author | Shabtay, Dvir |
| Author_xml | – sequence: 1 givenname: Dvir surname: Shabtay fullname: Shabtay, Dvir email: dvirs@bgu.ac.il organization: Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel |
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| Keywords | Single-machine scheduling Approximation algorithms Pseudo polynomial time algorithm Machine unavailability period Controllable processing time Resource allocation |
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| SubjectTerms | Approximation algorithms Controllable processing time Machine unavailability period Pseudo polynomial time algorithm Resource allocation Single-machine scheduling |
| Title | Single-machine scheduling with machine unavailability periods and resource dependent processing times |
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