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

Danny Hermelin, Dvir Shabtay, Chen Zelig, Michael Pinedo

Research output: Contribution to journalArticlepeer-review

Abstract

Mnich and Wiese (Math Program 154:533–562, 2015) proved that the 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.

Original languageEnglish
Pages (from-to)229-255
Number of pages27
JournalJournal of Scheduling
Volume25
Issue number2
DOIs
StatePublished - 1 Apr 2022

Keywords

  • Fixed parameter tractable
  • Flow-shop
  • NP-hard
  • Parallel machines
  • Scheduling with rejection
  • Single machine

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