A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines

Chi To Ng, Edwin Tai Chiu Cheng, Andrei M. Bandalouski, Mikhail Y. Kovalyov, Sze Sing Lam

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)


We study the problem of scheduling n non-preemptive jobs on m unrelated parallel machines. Each machine can process a specified subset of the jobs. If a job is assigned to a machine, then it occupies a specified time interval on the machine. Each assignment of a job to a machine yields a value. The objective is to find a subset of the jobs and their feasible assignments to the machines such that the total value is maximized. The problem is NP-hard in the strong sense. We reduce the problem to finding a maximum weight clique in a graph and survey available solution methods. Furthermore, based on the peculiar properties of graphs, we propose an exact solution algorithm and five heuristics. We conduct computer experiments to assess the performance of our and other existing heuristics. The computational results show that our heuristics outperform the existing heuristics.
Original languageEnglish
Pages (from-to)1571-1579
Number of pages9
JournalJournal of the Operational Research Society
Issue number10
Publication statusPublished - 1 Jan 2014


  • cargo loading/unloading
  • fixed interval scheduling
  • interval graph
  • maximum weight clique

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Management Information Systems
  • Marketing
  • Strategy and Management


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