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Comparing the minimum completion times of two longest-first scheduling-heuristics


  • Rico Walter

    () (Faculty of Economics and Business Administration, Friedrich Schiller University Jena)


For the basic problem of non-preemptively scheduling n independent jobs on m identical parallel machines so that the minimum (or earliest) machine completion time is maximized, we compare the performance relationship between two well-known longest-first heuristics - the LPT- (longest processing time) and the RLPT-heuristic (restricted LPT). We provide insights into the solution structure of these two sequencing heuristics and prove that the minimum completion time of the LPT-schedule is at least as long as the minimum completion time of the RLPT-schedule. Furthermore, we show that the minimum completion time of the RLPT-heuristic always remains within a factor of 1/m of the optimal minimum completion time. The paper finishes with a comprehensive experimental study of the probabilistic behavior of RLPT-schedules compared to LPT-schedules in the two-machine case.

Suggested Citation

  • Rico Walter, 2017. "Comparing the minimum completion times of two longest-first scheduling-heuristics," Jena Research Papers in Business and Economics - Working and Discussion Papers (Expired!) 13/2010, Friedrich-Schiller-University Jena, School of Economics and Business Administration.
  • Handle: RePEc:jen:jenjbe:2010-13

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    Scheduling - Identical parallel machines - Heuristics - Minimum completion time - Worst-case analysis;

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