Scheduling parallel batching machines in a sequence

Ward Passchyn (Corresponding author), Frits C.R. Spieksma

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
33 Downloads (Pure)


Motivated by the application of scheduling a sequence of locks along a waterway, we consider a scheduling problem where multiple parallel batching machines are arranged in a sequence and process jobs that travel along this sequence. We investigate the computational complexity of this problem. More specifically, we show that minimizing the sum of completion times is strongly NP-hard, even for two identical machines and when all jobs travel in the same direction. A second NP-hardness result is obtained for a different special case where jobs all travel at an identical speed. Additionally, we introduce a class of so-called synchronized schedules and investigate special cases where the existence of an optimum solution which is synchronized can be guaranteed. Finally, we reinforce the claim that bidirectional travel contributes fundamentally to the computational complexity of this problem by describing a polynomial time procedure for a setting with identical machines and where all jobs travel in the same direction at equal speed.

Original languageEnglish
Pages (from-to)335-357
Number of pages23
JournalJournal of Scheduling
Issue number3
Publication statusPublished - 15 Jun 2019


  • Complexity
  • Machine scheduling
  • Machine sequence
  • Parallel batching machine


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