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      Minimizing weighted mean absolute deviation of job completion times from their weighted mean

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      Author
      Erel, E.
      Ghosh, J. B.
      Date
      2011
      Source Title
      Applied Mathematics and Computation
      Print ISSN
      0096-3003
      Publisher
      Elsevier
      Volume
      217
      Issue
      22
      Pages
      9340 - 9350
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We address a single-machine scheduling problem where the objective is to minimize the weighted mean absolute deviation of job completion times from their weighted mean. This problem and its precursors aim to achieve the maximum admissible level of service equity. It has been shown earlier that the unweighted version of this problem is NP-hard in the ordinary sense. For that version, a pseudo-polynomial time dynamic program and a 2-approximate algorithm are available. However, not much (except for an important solution property) exists for the weighted version. In this paper, we establish the relationship between the optimal solution to the weighted problem and a related one in which the deviations are measured from the weighted median (rather than the mean) of the job completion times; this generalizes the 2-approximation result mentioned above. We proceed to give a pseudo-polynomial time dynamic program, establishing the ordinary NP-hardness of the problem in general. We then present a fully-polynomial time approximation scheme as well. Finally, we report the findings from a limited computational study on the heuristic solution of the general problem. Our results specialize easily to the unweighted case; they also lead to an approximation of the set of schedules that are efficient with respect to both the weighted mean absolute deviation and the weighted mean completion time. © 2011 Elsevier Inc. All rights reserved.
      Keywords
      Approximation scheme
      Dynamic program
      Scheduling
      Approximation scheme
      Computational studies
      Dynamic program
      Heuristic solutions
      Job completion
      Level of service
      NP-hard
      NP-hardness
      Optimal solutions
      Single-machine scheduling
      Solution property
      Time dynamic
      Weighted mean
      Weighted median
      Polynomial approximation
      Permalink
      http://hdl.handle.net/11693/21857
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.amc.2011.04.020
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