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We discuss the main results of the author’s PhD thesis (Canon 2005) presented in December 2005 at the Université François-Rabelais de Tours and supervised by J.-C. Billaut and J.-L. Bouquard. This thesis is written in French and is available from the author upon request. It deals with three different problems arising in the call center industry: the problem of dimensioning a call center, the annualisation...
In this paper, we survey some results, conjectures and open problems dealing with the combinatorial and algorithmic aspects of the linear ordering problem. This problem consists in finding a linear order which is at minimum distance from a (weighted or not) tournament. We show how it can be used to model an aggregation problem consisting of going from individual preferences defined on a set of candidates...
Dial-a-Ride is an emerging transport system, in which a fleet of vehicles, without fixed routes and schedules, carries people from the desired pickup point to the desired delivery point, during a pre-specified time interval. It can be modeled as an $$\mathcal{NP}$$ -hard routing and scheduling problem, with a suitable mixed integer programming formulation. Exact approaches to this problem are too...
This paper summarizes the main results presented by the author in his PhD thesis (Montoya-Torres 2005), supervised by Stéphane Dauzèere-Pérés, Jean-Pierre Campagne and Hélène Marian, and defended on 29 November 2005 at the École des Mines de Saint-Étienne and Université Jean-Monnet. The thesis is written in French and is available upon request from the author. This work deals with a real-life transportation...
We give a complete characterization of constant quadratic functions over an affine variety. This result is used to convexify the objective function of a general quadratic programming problem (Pb) which contains linear equality constraints. Thanks to this convexification, we show that one can express as a semidefinite program the dual of the partial Lagrangian relaxation of (Pb) where the linear constraints...
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