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Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers

Author

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  • Abay Molla Kassa

    (University of Bergen)

  • Semu Mitiku Kassa

    (Addis Ababa University
    Botswana International University of Science and Technology (BIUST))

Abstract

In this paper we investigate multilevel programming problems with multiple followers in each hierarchical decision level. It is known that such type of problems are highly non-convex and hard to solve. A solution algorithm have been proposed by reformulating the given multilevel program with multiple followers at each level that share common resources into its equivalent multilevel program having single follower at each decision level. Even though, the reformulated multilevel optimization problem may contain non-convex terms at the objective functions at each level of the decision hierarchy, we applied multi-parametric branch-and-bound algorithm to solve the resulting problem that has polyhedral constraints. The solution procedure is implemented and tested for a variety of illustrative examples.

Suggested Citation

  • Abay Molla Kassa & Semu Mitiku Kassa, 2017. "Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers," Journal of Global Optimization, Springer, vol. 68(4), pages 729-747, August.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:4:d:10.1007_s10898-017-0502-4
    DOI: 10.1007/s10898-017-0502-4
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    References listed on IDEAS

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    1. T. Başar & R. Srikant, 2002. "A Stackelberg Network Game with a Large Number of Followers," Journal of Optimization Theory and Applications, Springer, vol. 115(3), pages 479-490, December.
    2. R. G. Cassidy & M. J. L. Kirby & W. M. Raike, 1971. "Efficient Distribution of Resources Through Three Levels of Government," Management Science, INFORMS, vol. 17(8), pages 462-473, April.
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    Cited by:

    1. Seyfe Belete Worku & Birilew Belayneh Tsegaw & Semu Mitiku Kassa, 2023. "Existence and computations of best affine strategies for multilevel reverse Stackelberg games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 339-366, June.
    2. Addis Belete Zewde & Semu Mitiku Kassa, 2021. "Multilevel multi-leader multiple-follower games with nonseparable objectives and shared constraints," Computational Management Science, Springer, vol. 18(4), pages 455-475, October.
    3. Natnael Nigussie Goshu & Semu Mitiku Kassa, 2024. "A solution method for stochastic multilevel programming problems. A systematic sampling evolutionary approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(1), pages 149-174.
    4. Seyfe Belete Worku & Birilew Belayneh Tsegaw & Semu Mitiku Kassa, 2023. "Multilevel Reverse Stackelberg Differential Games: Existence and Solution Approach for Affine Strategies," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 617-640, February.

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