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On the solution of highly degenerate linear programmes

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Abstract

The solution of scheduling problems often gives rise to highly degenerate linear programmes which cause significant computational difficulties for the revised simplex method. Wolfe's highly effective “ad hoc” method for overcoming the cycling or stalling problems associated with degeneracy is described. Here it is given a geometric interpretation in terms of finding a direction of recession for a reduced problem which is fundamental to a full understanding of the procedure. An example of an aircrew scheduling problem is used to illustrate the effectiveness of the method.

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Authors and Affiliations

  1. Department of Theoretical and Applied Mechanics, University of Auckland, Private Bag, Auckland, New Zealand

    D. M. Ryan

  2. Department of Statistics, Institute of Advanced Studies, Australian National University, PO Box 4, 2601, Canberra, ACT, Australia

    M. R. Osborne

Authors
  1. D. M. Ryan
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  2. M. R. Osborne
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Ryan, D.M., Osborne, M.R. On the solution of highly degenerate linear programmes. Mathematical Programming 41, 385–392 (1988). https://doi.org/10.1007/BF01580776

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  • DOI: https://doi.org/10.1007/BF01580776

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