Oleaginous yeasts have been seen as a feasible alternative to produce the precursors of biodiesel due to their capacity to accumulate lipids as triacylglycerol having profiles with high content of unsaturated fatty acids. The yeast Yarrowia lipolytica is a promising microorganism that can produce lipids under nitrogen depletion conditions and excess of the carbon source. However, under these conditions, this yeast also produces citric acid (overflow metabolism) decreasing lipid productivity. This work presents two mathematical models for lipid production by Y. lipolytica from glucose. The first model is based on Monod and inhibition kinetics, and the second one is based on the Droop quota model approach, which is extended to yeast. The two models showed good agreements with the experimental data used for calibration and validation. The quota based model presented a better description of the dynamics of nitrogen and glucose dynamics leading to a good management of N/C ratio which makes this model interesting for control purposes. Then, quota model was used to evaluate, by means of simulation, a scenario for optimizing lipid productivity and lipid content. For that, a control strategy was designed by approximating the flow rates of glucose and nitrogen with piecewise linear functions. Simulation results achieved productivity of 0.95 g L-1 hr(-1) and lipid content fraction of 0.23 g g(-1), which indicates that this strategy is a promising alternative for the optimization of lipid production.