Two-Stage Linear Recourse Problems under Non-Probabilistic Uncertainty

  • Masahiro Inuiguchi
  • Tetsuzo Tanino
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 73)


In this paper, we apply two-stage recourse programming approach to linear programming problems with uncertain parameters. It is assumed that the set of possible realizations of parameters are known as a polytope. A two-stage recourse problem is formulated in the pessimistic viewpoint. It is shown that this problem is a convex programming problem with respect to the first stage variable vector and a large-scale linear programming problem when all vertices of the polytope representing possible realizations of uncertain parameters are given. A solution algorithm based on a relaxation procedure is proposed. Generally, we need to solve max-min problems or bilinear programming problems during the solution process. Some special cases are discussed in order to solve the max-min problems efficiently.


Feasible Solution Programming Problem Linear Programming Problem Uncertain Parameter Convex Programming Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Masahiro Inuiguchi
    • 1
  • Tetsuzo Tanino
    • 1
  1. 1.Osaka UniversitySuita, OsakaJapan

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