One of the main concerns in management and economic planning is to sell the right product to the right customer for the right price. Companies in retail and manufacturing employ pricing strategies to maximize their revenues. The Rank Pricing Problem aims at maximizing the revenue of a company by setting the prices of their products, taking into account the customers' preferences and the amount of money they are willing to pay. In this paper, we model the problem as a non linear bilevel program with multiple independent followers and also present a straightforward non linear single level formulation bearing in mind the aim of the problem. Two different linearizations of the models are carried out and two families of valid inequalities are obtained which, embedded in the formulations by implementing a branch-and-cut algorithm, allow us to tighten the upper bound given by the linear relaxation of the models. We also study the polyhedral structure of the models, taking advantage of the fact that a subset of their constraints constitutes a special case of the Set Packing Problem, and characterize all the clique facets. Besides, we develop a preprocessing procedure to reduce the size of the instances. Finally, we show the efficiency of the formulations, the branch-and-cut algorithms and the preprocessing through an extensive computational study.