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This is a summary of the author’s PhD thesis supervised by Andrea Lodi and defended on 16 April 2009 at the University of Bologna. The thesis is written in English and available for download at http://www.or.deis.unibo.it/staff_pages/dambrosio/Phd_Th_DAmbrosio.tar.gz . The main topic of the thesis is Mixed Integer Non-Linear Programming, with focus on non-convex problems (i.e., problems for which...
This is a summary of the author’s PhD thesis supervised by Pr. Olivier Hudry and defended on 7th June 2010 at Télécom ParisTech. The thesis is written in French (introduction and overview of results) and English (articles, which contain the proofs) and is available from the author upon request or from http://www.lri.fr/~dauger/ . It deals in a first part with algorithmic and combinatorial properties...
We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties.
A customer would like to buy a given set of products in a given set of Internet shops. For each Internet shop, standard prices for the products are known as well as a concave increasing discounting function of total standard and delivery price. The problem is to buy all the required products at the minimum total discounted price. Computational complexity of various special cases is established. Properties...
In Blazewich et al. (4OR-Q J Oper Res 12(1):35–48, 2014), an Internet shopping problem with price-sensitive discounts was introduced, in which a customer wants to buy a given set of products in a given set of Internet shops. This problem is an extension of the original Internet shopping optimization problem (ISOP) presented in Blazewich et al. (Int J Appl Math Comput Sci 20(2):385–390, 2010). For...
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