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A Penalty Method For Solving Bilevel Linear Fractional/Linear Programming Problems

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  • HERMINIA I. CALVETE

    (Dpto. de Métodos Estadísticos, Universidad de Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain)

  • CARMEN GALÉ

    (Dpto. de Métodos Estadísticos, Universidad de Zaragoza, Pedro Cerbuna, 12, 50009 Zaragoza, Spain)

Abstract

Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem.

Suggested Citation

  • Herminia I. Calvete & Carmen Galé, 2004. "A Penalty Method For Solving Bilevel Linear Fractional/Linear Programming Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 207-224.
    • Handle: RePEc:wsi:apjorx:v:21:y:2004:i:02:n:s0217595904000205
    DOI: 10.1142/S0217595904000205
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    Cited by:

    1. Ritu Arora & Kavita Gupta, 2018. "Branch and bound algorithm for discrete multi- level linear fractional programming problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 5-21.

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