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Pricing under a consumer choice model has been extensively studied in economics and revenue management. In this paper, we tackle a generalization of the Rank Pricing Problem (RPP), a multi-product pricing problem with unit-demand customers and a ranking-based consumer choice model. We generalize the RPP assuming that each product has a limited amount of copies for sale, and we call this extension the Capacitated Rank Pricing Problem (CRPP). We compare the envy-free allocation of the products (a fairness criterion requiring that customers receive their highest-ranked product given the pricing) with the envy version of the problem. Next, we focus on the CRPP with envy. We introduce two integer linear formulations for the CRPP and derive valid inequalities leveraging the structure of the problem. Afterwards, we develop separation procedures for the families of valid inequalities of greater size. The performance of the formulations and the resolution algorithms developed is tested by means of extensive computational experiments.

International audience; 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 considers a unit-demand model with unlimited supply and uniform budgets in which customers have a rank-buying behavior. Under these assumptions, the problem is first analyzed from the perspective of bilevel pricing models and formulated as a non linear bilevel program with multiple independent followers. We also present a direct 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 extensive computational experiments.

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., info:eu-repo/semantics/nonPublished