Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

Bartłomiej Przybylski ()
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Bartłomiej Przybylski: Adam Mickiewicz University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 1, No 10, 207-222

Abstract: Abstract We consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.

Keywords: Parallel-machine scheduling; Variable processing times; Position-dependent processing times; Makespan; Total completion time; Polynomial algorithms (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00821-2

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