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Some basics on tolerances

Author

Listed:
  • Molitor, P.
  • Jäger, G.
  • Goldengorin, B.

    (Groningen University)

Abstract

In this note we deal with sensitivity analysis of combinatorial optimization problems and its fundamental term, the tolerance. For three classes of objective functions (?, ?, MAX) we prove some basic properties on upper and lower tolerances. We show that the upper tolerance of an element is well defined, how to compute the upper tolerance of an element, and give equivalent formulations when the upper tolerance is +? or > 0. Analogous results are proven for the lower tolerance and some results on the relationship between lower and upper tolerances are given.

Suggested Citation

  • Molitor, P. & Jäger, G. & Goldengorin, B., 2005. "Some basics on tolerances," Research Report 05A13, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    • Handle: RePEc:gro:rugsom:05a13
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    File URL: http://irs.ub.rug.nl/ppn/291398219
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    References listed on IDEAS

    as
    1. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    2. Katta G. Murty, 1968. "Letter to the Editor—An Algorithm for Ranking all the Assignments in Order of Increasing Cost," Operations Research, INFORMS, vol. 16(3), pages 682-687, June.
    3. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
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