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

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