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Mixed-integer formulations for the Capacitated Rank Pricing Problem with envy

Concepción Domínguez 1 Martine Labbé 1 Alfredo Marín 2
1 INOCS - Integrated Optimization with Complex Structure
ULB - Université libre de Bruxelles, Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03477171
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Submitted on : Monday, December 13, 2021 - 12:43:45 PM
Last modification on : Thursday, March 24, 2022 - 3:42:42 AM
Long-term archiving on: : Monday, March 14, 2022 - 6:54:23 PM

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Concepción Domínguez, Martine Labbé, Alfredo Marín. Mixed-integer formulations for the Capacitated Rank Pricing Problem with envy. 2021. ⟨hal-03477171⟩

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