A note on the complexity of the problem of two-agent scheduling on a single machine

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128 Citations (Scopus)


We consider a two-agent scheduling problem on a single machine where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agent's objective is to minimize the total weighted completion time we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.
Original languageEnglish
Pages (from-to)386-393
Number of pages8
JournalJournal of Combinatorial Optimization
Issue number4
Publication statusPublished - 1 Dec 2006


  • Cooperative sequencing
  • Games/group decisions
  • Multi-agent deterministic sequencing
  • Production/scheduling

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

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