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International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making

IUKM 2022: Integrated Uncertainty in Knowledge Modelling and Decision Making pp 130–142Cite as

An Analysis to Treat the Degeneracy of a Basic Feasible Solution in Interval Linear Programming

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13199))

Abstract

When coefficients in the objective function cannot be precisely determined, the optimal solution is fluctuated by the realisation of coefficients. Therefore, analysing the stability of an optimal solution becomes essential. Although the robustness analysis of an optimal basic solution has been developed successfully so far, it becomes complex when the solution contains degeneracy. This study is devoted to overcoming the difficulty caused by the degeneracy in a linear programming problem with interval objective coefficients. We focus on the tangent cone of a degenerate basic feasible solution since the belongingness of the objective coefficient vector to its associated normal cone assures the solution’s optimality. We decompose the normal cone by its associated tangent cone to a direct union of subspaces. Several propositions related to the proposed approach are given. To demonstrate the significance of the decomposition, we consider the case where the dimension of the subspace is one. We examine the obtained propositions by numerical examples with comparisons to the conventional techniques.

This work was supported by JSPS KAKENHI Grant Number JP18H01658.

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Authors and Affiliations

  1. Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Zhenzhong Gao & Masahiro Inuiguchi

Authors
  1. Zhenzhong Gao
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  2. Masahiro Inuiguchi
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Corresponding authors

Correspondence to Zhenzhong Gao or Masahiro Inuiguchi .

Editor information

Editors and Affiliations

  1. Osaka Prefecture University, Sakai, Osaka, Japan

    Katsuhiro Honda

  2. University of Hyogo, Kobe, Japan

    Tomoe Entani

  3. Osaka Prefecture University, Sakai, Japan

    Seiki Ubukata

  4. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Van-Nam Huynh

  5. Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

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Gao, Z., Inuiguchi, M. (2022). An Analysis to Treat the Degeneracy of a Basic Feasible Solution in Interval Linear Programming. In: Honda, K., Entani, T., Ubukata, S., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2022. Lecture Notes in Computer Science(), vol 13199. Springer, Cham. https://doi.org/10.1007/978-3-030-98018-4_11

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  • DOI: https://doi.org/10.1007/978-3-030-98018-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-98017-7

  • Online ISBN: 978-3-030-98018-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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