On the parameterized tractability of the just-in-time flow-shop scheduling problem

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Abstract

We study the parameterized complexity of a set of flow-shop scheduling problems in which the objective is to maximize the weighted number of just-in-time jobs. Our analysis focuses on the case where the number of due dates is considerably smaller than the number of jobs and thus can be considered as a parameter. We prove that the two-machine problem is W[1]-hard with respect to this parameter, even if all processing times on the second machine are of unit length, while the problem is in XP when parameterized by the number of machines combined with the number of different due dates. We then move on to study the tractability of the problem when combining the number of different due dates with either the number of different weights or the number of different processing times on the first machine. We prove that in both cases the problem is fixed-parameter tractable for the two-machine case and is W[1]-hard for three or more machines.

Original languageEnglish
Pages (from-to)663-676
Number of pages14
JournalJournal of Scheduling
Volume22
Issue number6
DOIs
StatePublished - 1 Dec 2019

Keywords

  • Fixed-parameter tractability
  • Flow-shop
  • Just-in-time
  • Parameterized complexity
  • Scheduling

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