The envy-free pricing problem and unit-demand markets

Abstract

A common problem faced in economics is to decide the pricing of products of a company, since poorly chosen prices might lead to low profit. One important model for this is the unit-demand envy-free pricing problem, where one considers that every consumer buys the item that maximizes his own profit, and the goal is to find a pricing of the items that maximizes the expected profit of the seller. This problem is not in APX unless P = NP, but it is still interesting to be solved in practice. So, we present four new MIP formulations for it and experimentally compare them to a previous one from the literature. We describe three models to generate different random instances for general unit-demand auctions, that we designed for the computational experiments. Each model has a nice economic interpretation. Our results show that our MIP formulations are a great improvement both for solving the problem to optimality or in order to obtain solutions with small gap. © 2014 Springer International Publishing.