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 \(\mathrm {P}= \mathrm {NP}\), 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.
Research partially supported by CAPES (Proc. 33002010176P0), CNPq (Proc.302736/2010-7, 308523/2012-1, and 477203/2012-4), FAPESP (Proc. 2009/00387-7 and 2013/03447-6) and Project MaCLinC of NUMEC/USP.
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Fernandes, C.G., Ferreira, C.E., Franco, Á.J.P., Schouery, R.C.S. (2014). The Envy-Free Pricing Problem and Unit-Demand Markets. In: Fouilhoux, P., Gouveia, L., Mahjoub, A., Paschos, V. (eds) Combinatorial Optimization. ISCO 2014. Lecture Notes in Computer Science(), vol 8596. Springer, Cham. https://doi.org/10.1007/978-3-319-09174-7_20
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DOI: https://doi.org/10.1007/978-3-319-09174-7_20
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