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Penalty Function Approach to Linear Trilevel Programming

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  • D. J. White

    (University of Manchester)

Abstract

In this paper, we study a trilevel decision-making situation in which decisionmaker 1 selects an action, within a specified constraint set, then decisionmaker 2 selects an action within a constraint set determined by the action of decisionmaker 2, and finally decisionmaker 3 selects an action within a constraint set determined by the actions of decisionmakers 1 and 2. Each decisionmaker has an objective function to be optimized within the imposed constraint set. Bard (Ref. 1) presents a five-step algorithm for solving this problem. This paper presents an alternative approach to the key first step of that algorithm, which has some qualitative advantages over it.

Suggested Citation

  • D. J. White, 1997. "Penalty Function Approach to Linear Trilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 183-197, April.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:1:d:10.1023_a:1022610103712
    DOI: 10.1023/A:1022610103712
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    Cited by:

    1. G. Z. Ruan & S. Y. Wang & Y. Yamamoto & S. S. Zhu, 2004. "Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 409-429, November.
    2. Fakhry, Ramy & Hassini, Elkafi & Ezzeldin, Mohamed & El-Dakhakhni, Wael, 2022. "Tri-level mixed-binary linear programming: Solution approaches and application in defending critical infrastructure," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1114-1131.
    3. Tilahun, Surafel Luleseged, 2019. "Feasibility reduction approach for hierarchical decision making with multiple objectives," Operations Research Perspectives, Elsevier, vol. 6(C).
    4. Styliani Avraamidou & Efstratios N. Pistikopoulos, 2019. "Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems," Journal of Global Optimization, Springer, vol. 74(3), pages 443-465, July.

    More about this item

    Keywords

    Trilevel programming; penalty functions;

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