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An Investigation of the Optimistic Solution to the Linear Trilevel Programming Problem

Author

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  • Maryam Esmaeili

    (Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz 61357-83151, Iran)

  • Habibe Sadeghi

    (Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz 61357-83151, Iran)

Abstract

In this paper, we consider a general version of a linear trilevel programming problem. Three different types of optimistic optimal solutions for a special trilevel programming problem have formerly been suggested. This paper presents the mathematical formulation of all of the three types of optimistic optimal solutions for the given linear trilevel programming problem. Moreover, some properties of the inducible region (the feasible region for the trilevel programming problem) corresponding to each optimistic optimal solution are investigated. Finally, a numerical example is presented to compare the different types of optimistic optimal solutions.

Suggested Citation

  • Maryam Esmaeili & Habibe Sadeghi, 2018. "An Investigation of the Optimistic Solution to the Linear Trilevel Programming Problem," Mathematics, MDPI, vol. 6(10), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:179-:d:172422
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    References listed on IDEAS

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    1. Florensa, Carlos & Garcia-Herreros, Pablo & Misra, Pratik & Arslan, Erdem & Mehta, Sanjay & Grossmann, Ignacio E., 2017. "Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches," European Journal of Operational Research, Elsevier, vol. 262(2), pages 449-463.
    2. Masatoshi Sakawa & Ichiro Nishizaki, 2012. "Interactive fuzzy programming for multi-level programming problems: a review," International Journal of Multicriteria Decision Making, Inderscience Enterprises Ltd, vol. 2(3), pages 241-266.
    3. Stephan Dempe & Maria Pilecka, 2015. "Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming," Journal of Global Optimization, Springer, vol. 61(4), pages 769-788, April.
    4. Nuno Faísca & Pedro Saraiva & Berç Rustem & Efstratios Pistikopoulos, 2009. "A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems," Computational Management Science, Springer, vol. 6(4), pages 377-397, October.
    5. Ke, Ginger Y. & Bookbinder, James H., 2018. "Coordinating the discount policies for retailer, wholesaler, and less-than-truckload carrier under price-sensitive demand: A tri-level optimization approach," International Journal of Production Economics, Elsevier, vol. 196(C), pages 82-100.
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