Journal
DISCRETE OPTIMIZATION
Volume 22, Issue -, Pages 141-161Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.disopt.2015.09.003
Keywords
Pricing problems; Envy-free allocations; Unit-demand auctions
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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, in which one considers that every consumer buys an 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 is a practical and interesting problem which is, unfortunately, not in APX unless P = NP, We present two new MIP formulations for this problem and experimentally compare them to previous ones 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 one of our MIP formulations can sometimes lead to better results than the previous ones from the literature. We also consider a variant of the network pricing problem in which one has to price toll arcs in a highway, and prove that it is as hard to approximate as the envy-free pricing problem. (C) 2015 Elsevier B.V. All rights reserved.
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