Automation and Remote Control

, Volume 71, Issue 10, pp 2038–2057 | Cite as

Minimizing total weighted completion time with uncertain data: A stability approach

  • Yu. N. Sotskov
  • N. G. Egorova
  • F. Werner
Scheduling Problems on a Single Machine


A single-machine scheduling problem is investigated provided that the input data are uncertain: The processing time of a job can take any real value from the given segment. The criterion is to minimize the total weighted completion time for the n jobs. As a solution concept to such a scheduling problem with an uncertain input data, it is reasonable to consider a minimal dominant set of job permutations containing an optimal permutation for each possible realization of the job processing times. To find an optimal or approximate permutation to be realized, we look for a permutation with the largest stability box being a subset of the stability region. We develop a branch-and-bound algorithm to construct a permutation with the largest volume of a stability box. If several permutations have the same volume of a stability box, we select one of them due to one of two simple heuristics. The efficiency of the constructed permutations (how close they are to a factually optimal permutation) and the efficiency of the developed software (average CPU-time used for an instance) are demonstrated on a wide set of randomly generated instances with 5 ≤ n ≤ 100.


Schedule Problem Remote Control Completion Time Total Completion Time Optimal Permutation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • Yu. N. Sotskov
    • 1
  • N. G. Egorova
    • 1
  • F. Werner
    • 2
  1. 1.United Institute of Informatics ProblemsBelarussian National Academy of SciencesMinskBelarus
  2. 2.Otto-von-Guericke-UniversityMagdeburgGermany

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