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.
Keywords
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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Aggarwal, G., Feder, T., Motwani, R., Zhu, A.: Algorithms for multi-product pricing. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 72–83. Springer, Heidelberg (2004)
Barabãsi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Briest, P.: Uniform budgets and the envy-free pricing problem. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 808–819. Springer, Heidelberg (2008)
Chen, N., Deng, X.: Envy-free pricing in multi-item markets. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010, Part II. LNCS, vol. 6199, pp. 418–429. Springer, Heidelberg (2010)
Cramton, P., Shoham, Y., Steinberg, R. (eds.): Combinatorial Auctions. MIT Press, Cambridge (2006)
Gilbert, E.N.: Random plane networks. J. Soc. Ind. Appl. Math. 9(4), 533–543 (1961)
Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1164–1173 (2005)
Heilporn, G., Labbé, M., Marcotte, P., Savard, G.: A polyhedral study of the network pricing problem with connected toll arcs. Networks 55(3), 234–246 (2010)
Leyton-Brown, K., Pearson, M., Shoham, Y.: Towards a universal test suite for combinatorial auction algorithms. In: Proceedings of the 2nd ACM Conference on Electronic Commerce, pp. 66–76 (2000)
Myklebust, T.G.J., Sharpe, M.A., Tunçel, L.: Efficient heuristic algorithms for maximum utility product pricing problems. Research report, Department of Combinatorics and Optimization, University of Waterloo, November 2012
Oren, S., Smith, S., Wilson, R.: Product line pricing. J. Bus. 57(1), S73–S79 (1984)
Rusmevichientong, P., Roy, B.V., Glynn, P.W.: A nonparametric approach to multiproduct pricing. Oper. Res. 54(1), 82–98 (2006)
Sen, S.: Issues in optimal product design. In: Analytic Approaches to Product and Marketing Planning: The Second Conference, pp. 265–274 (1982)
Shioda, R., Tunçel, L., Myklebust, T.G.: Maximum utility product pricing models and algorithms based on reservation price. Comput. Optim. Appl. 48(2), 157–198 (2011)
Smith, S.A.: New product pricing in quality sensitive markets. Mark. Sci. 5(1), 70–87 (1986)
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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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