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An enumerative algorithm for computing all possibly optimal solutions to an interval LP

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  • Carla Oliveira

    ()

  • Carlos Antunes

    ()

  • Carlos Barrico

    ()

Abstract

Interval programming techniques are a valuable approach for tackling uncertainty in mathematical programming models, because they only require the knowledge of the feasible range of variation of the model coefficients. Nevertheless, the use of these techniques has some limitations, namely when the number of decision variables with interval coefficients is high since the number of objective functions at stake in the sub-problem for testing the (weak) efficiency of each non-basic variable may be easily out of an acceptable computational effort. A similar problem may arise with the number of sub-problems for testing the multi-parametric optimality of each solution obtained (that is, to check whether the solution is possibly optimal or not) and the multi-parametric optimality of each edge by using the all emanating edges algorithm. An alternative algorithm is suggested that allows obtaining all possibly optimal solutions, which fulfill the formal criteria of optimality in a feasible bounded region. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Carla Oliveira & Carlos Antunes & Carlos Barrico, 2014. "An enumerative algorithm for computing all possibly optimal solutions to an interval LP," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 530-542, July.
  • Handle: RePEc:spr:topjnl:v:22:y:2014:i:2:p:530-542
    DOI: 10.1007/s11750-012-0268-2
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    References listed on IDEAS

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    1. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    2. Inuiguchi, Masahiro & Sakawa, Masatoshi, 1995. "Minimax regret solution to linear programming problems with an interval objective function," European Journal of Operational Research, Elsevier, vol. 86(3), pages 526-536, November.
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    Cited by:

    1. Mingzhi Chen & Sheng-Guo Wang & Paul P. Wang & Xiaoxiang Ye, 2016. "A new equivalent transformation for interval inequality constraints of interval linear programming," Fuzzy Optimization and Decision Making, Springer, vol. 15(2), pages 155-175, June.
    2. Shiang-Tai Liu, 2016. "A mathematical programming approach to sample coefficient of variation with interval-valued observations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-18, April.
    3. Henriques, C.O. & Inuiguchi, M. & Luque, M. & Figueira, J.R., 2020. "New conditions for testing necessarily/possibly efficiency of non-degenerate basic solutions based on the tolerance approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 341-355.

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