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A Lexicographic approach for solving multiobjective bilevel programming problems

Abstract

Multiobjective BLP (MOBLP) problems are the special case of BLP problems which require every feasible solution of upper level multiobjective problem to satisfy the Pareto optimality conditions of a lower level multiobjective problem. For solving single-objective linear BLP problems, Glackin et al. (2009) used the relationship between linear BLP problems and multiple objective linear programming (MOLP) problem along with results for minimizing a linear objective over the efficient set of an MOLP problem. This paper proposes a modification of their methods for solving linear MOBLP problems and finding an efficient solution of these problems by introducing a lexicographic approach. Numerical example is provided to illustrate the approach.

Keywords

Multiobjective Bilevel Programming (MOBLP); Multiple Objective Linear Programming (MOLP); Lexicographic Solution; Efficient Solution.

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