On scheduling an unbounded batch machine

Zhaohui Liu, Jinjiang Yuan, Edwin Tai Chiu Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

36 Citations (Scopus)


A batch machine is a machine that can process up to c jobs simultaneously as a batch, and the processing time of the batch is equal to the longest processing time of the jobs assigned to it. In this paper, we deal with the complexity of scheduling an unbounded batch machine, i.e., c = +∞. We prove that minimizing total tardiness is binary NP-hard, which has been an open problem in the literature. Also, we establish the pseudopolynomial solvability of the unbounded batch machine scheduling problem with job release dates and any regular objective. This is distinct from the bounded batch machine and the classical single machine scheduling problems, most of which with different release dates are unary NP-hard. Combined with the existing results, this paper provides a nearly complete mapping of the complexity of scheduling an unbounded batch machine.
Original languageEnglish
Pages (from-to)42-48
Number of pages7
JournalOperations Research Letters
Issue number1
Publication statusPublished - 1 Jan 2003


  • Batch processing
  • Complexity
  • Scheduling

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Modelling and Simulation

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