A general scheme for solving a large set of scheduling problems with rejection in FPT time

Danny Hermelin (), Dvir Shabtay (), Chen Zelig () and Michael Pinedo ()
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Danny Hermelin: Ben-Gurion University of the Negev
Dvir Shabtay: Ben-Gurion University of the Negev
Chen Zelig: Ben-Gurion University of the Negev
Michael Pinedo: New York University

Journal of Scheduling, 2022, vol. 25, issue 2, No 6, 229-255

Abstract: Abstract Mnich and Wiese (Math Program 154:533–562, 2015) proved that the $$\mathcal {NP}$$ NP -hard single-machine scheduling problem with rejection and the total weighted completion time plus total rejection cost as objective is fixed parameter tractable with respect to the number of different processing times and weights in the instance. This result is obtained by reducing the problem to an integer convex programming problem where the number of variables depends solely on the parameter (number of different processing times and weights). We show that this method can be incorporated into a more general scheme for solving a large set of scheduling problems with rejection which share common properties. These problems include various different machine environments, namely single machine, identical machines in parallel, and flow-shops.

Keywords: Scheduling with rejection; Fixed parameter tractable; Single machine; Parallel machines; Flow-shop; $$\mathcal {NP}$$ NP -hard (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10951-022-00731-z

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