Problema da Precificação Livre de Inveja: uma proposta de modelos matemáticos para a variante de consumidores decididos

Abstract

Given a set of consumers, a set of products, a valuation assigned to each product by each consumer, and maximum supply of products, the Envy-free Pricing Problem is to determine an envy-free pricing and allocation, which means that, once the prices of the products are set, each consumer must be at least as satisfied with their product allocation as with any other possible allocation. Starting from a detailed review of several variants of the problem, this work focus on the case of sigle-minded consumers, where each consumer is willing to buy only a specific subset (package) of products. The work considers the unlimited supply version, where it is assumed product avaliability superior to its demand, as well as the limited supply version, still unexplored in the literature. For the unlimited supply case, two Mixed Integer Linear Programming formulations are proposed and computationally evaluated, as well as comparisons among them and an existing formulation in the literature are presented. In the case of limited supply, a quadratic formulation and two linearizations for it are proposed. New instances are generated for this variant, from instances in the literature for the unlimited supply case, which are then used to evaluate the computational performance of the proposed formulations.