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Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function

Author

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  • Puchit Sariddichainunta

    (Osaka University)

  • Masahiro Inuiguchi

    (Osaka University)

Abstract

A bilevel linear programming problem with ambiguous lower-level objective function is a sequential decision making under uncertainty of rational reaction. The ambiguous lower-level objective function is assumed that the coefficient vector of the follower lies in a convex polytope. We apply the maximin solution approach and formulate it as a special kind of three-level programming problem. Since an optimal solution exists at a vertex of feasible region, we adopt k-th best method to search an optimal solution. At each iteration of the k-th best method, we check rationality, local optimality and global optimality of the candidate solution. In this study, we propose a global optimality test based on an inner approximation method and compare its computational efficiency to other test methods based on vertex enumeration. We also extensively utilize the history of rationality tests to verify the rationality of the solution in the follower’s problem. Numerical experiments show the advantages of the proposed methods.

Suggested Citation

  • Puchit Sariddichainunta & Masahiro Inuiguchi, 2017. "Global optimality test for maximin solution of bilevel linear programming with ambiguous lower-level objective function," Annals of Operations Research, Springer, vol. 256(2), pages 285-304, September.
  • Handle: RePEc:spr:annopr:v:256:y:2017:i:2:d:10.1007_s10479-016-2293-2
    DOI: 10.1007/s10479-016-2293-2
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    References listed on IDEAS

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    4. Masahiro Inuiguchi & Puchit Sariddichainunta, 2016. "Bilevel linear programming with ambiguous objective function of the follower," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 415-434, December.
    5. LeBlanc, Larry J. & Boyce, David E., 1986. "A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows," Transportation Research Part B: Methodological, Elsevier, vol. 20(3), pages 259-265, June.
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    Cited by:

    1. Martin Weibelzahl & Alexandra Märtz, 2020. "Optimal storage and transmission investments in a bilevel electricity market model," Annals of Operations Research, Springer, vol. 287(2), pages 911-940, April.
    2. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    3. Christoph Buchheim & Dorothee Henke, 2022. "The robust bilevel continuous knapsack problem with uncertain coefficients in the follower’s objective," Journal of Global Optimization, Springer, vol. 83(4), pages 803-824, August.

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