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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Vydané v:	European journal of operational research Ročník 296; číslo 2; s. 423 - 439
Hlavný autor:	Shabtay, Dvir
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 16.01.2022
Predmet:	Approximation algorithms Controllable processing time Machine unavailability period Pseudo polynomial time algorithm Resource allocation Single-machine scheduling Single-machine scheduling Approximation algorithms Pseudo polynomial time algorithm Machine unavailability period Controllable processing time Resource allocation
ISSN:	0377-2217, 1872-6860
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Popis
Shrnutí:	•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.
ISSN:	0377-2217 1872-6860
DOI:	10.1016/j.ejor.2021.03.034