Résumé : Saccharomyces cerevisiae, also known as Baker or brewer yeast, is an important microorganism which transforms carbon sources into CO2 aerobically (respiration) or ethanol anaerobically (fermentation). However, the yeast is also able of producing ethanol under high fluxes of glucose uptake or Crabtree effect in a phenomenon called overflow metabolism. An additional important feature of S. cerevisiae is that it is capable of consuming ethanol in a strategy known as 'produce-accumulate-consume'. These characteristics have been exploited in the bioprocess industry for the production of high concentrations of biomass and the consumption of undesirable metabolites products. In this sense, mathematical models are a powerful tool that allows the control, design, monitoring and optimization of bioprocesses. In this thesis, a microscopic model based on Flux balance analysis of fed-batch cultures of S. cerevisiae is proposed. The model relies on a metabolic network which contains the necessary internal fluxes for reproducing respiratory, respiro-fermentative, nitrogen and amino acids metabolisms, and a biomass reaction which accounts for the necessary fractions of metabolic precursors and macromolecules and energetic requirements for its production. A flux balance analysis is solve based on: i) an objective cost function which classically accounts for biomass growth maximization, ii) inequalities constraints which link the fluxes to models of substrate uptake rates iii) additional linear constraints for reproducing overflow metabolism phenomena, and iv) conditional equality constraints to account for variable biomass composition (based on protein mass fraction identification with or without ammonium feeding). The FBA is inserted in a set a mass balances aiming at predicting extracellular species concentration time profiles. The uptake rates are modeled considering the dynamics of an intracellular metabolite. The model is identified and validated with experimental data of fed-batch yeast cultures and successfully predicts the dynamics of substrate consumption (glucose and ammonium), biomass growth, ethanol production and the intracellular alpha-ketoglutarate. One of the major objectives to develop a mathematical model is its use for process optimization. In this case study, the optimal time profiles of glucose and nitrogen feeding flow rates have been determined for maximization of the final biomass concentration through a control vector parametrization (CVP) approach.