A novel approach to pessimistic bilevel problems. An application to the rank pricing problem with ties

This paper introduces a novel method to address the pessimistic approach to the bilevel problem. It consists of considering a lexicographic biobjective optimization problem at the lower level. To emphasize the significance of this approach, we implement it in the context of the Rank Pricing Problem with Ties. This problem can be formulated as a bilevel problem that inherently demands the use of the pessimistic approach. Considering the properties of the lexicographic biobjective problem involved, we formulate this problem as a single level mixed integer optimization problem, deriving also valid values for the big-Ms involved and valid inequalities for this formulation. The computational experiment carried out confirms the relevance of the proposed method.