RESOLUTION METHOD FOR MIXED INTEGER LINEAR MULTIPLICATIVE-LINEAR BILEVEL PROBLEMS BASED ON DECOMPOSITION TECHNIQUE

Subject Areas : International Journal of Mathematical Modelling & Computations

Habibe Sadeghi ¹ , Leila Karimi ²

1 - Iran, Islamic Republic of
2 -

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

Keywords: Mixed integer linear programming, Bilevel programming, Benders decomposition, Multiplicative programming,

Abstract :

In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose the initial probleminto two subproblems to names RMP and SP. The lower and upper bound providedfrom the RMP and SP are updated in each iteration. The algorithm converges whenthe dierence between the upper and lower bound is less than an arbitrary tolerance.Finally, we give some numerical examples are presented in order to show the eciencyof algorithm.