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. In this paper, we present a bilevel and a non linear single level formulation of the problem, carry out two different linearisations of the models and develop some preprocessing techniques. We also study the polyhedral structure of the model, taking advantage of the fact that a subset of its constraints constitutes a special case of the Set Packing Problem, and characterize all the clique inequalities. Besides, we obtain two families of valid inequalities which, embedded in the formulation by implementing a branch-and-cut algorithm, allow us to tighten the upper bound given by the linear relaxation of the models. Finally, we show the efficiency of the formulations, the preprocessing and the branch-and-cut algorithm through an extensive computational study.