In recent years, the Galactic Center (GC) region (200 pc in radius) has been studied in detail with spectroscopic stellar data as well as an estimate of the ongoing star formation rate. The aims of this paper are to study the chemical evolution of the GC region by means of a detailed chemical evolution model and to compare the results with high resolution spectroscopic data in order to impose constraints on the GC formation history.The chemical evolution model assumes that the GC region formed by fast infall of gas and then follows the evolution of alpha-elements and Fe. We test different initial mass functions (IMFs), efficiencies of star formation and gas infall timescales. To reproduce the currently observed star formation rate, we assume a late episode of star formation triggered by gas infall/accretion. We find that, in order to reproduce the [alpha/Fe] ratios as well as the metallicity distribution function observed in GC stars, the GC region should have experienced a main early strong burst of star formation, with a star formation efficiency as high as 25 Gyr^{-1}, occurring on a timescale in the range 0.1-0.7 Gyr, in agreement with previous models of the entire bulge. Although the small amount of data prevents us from drawing firm conclusions, we suggest that the best IMF should contain more massive stars than expected in the solar vicinity, and the last episode of star formation, which lasted several hundred million years, should have been triggered by a modest episode of gas infall/accretion, with a star formation efficiency similar to that of the previous main star formation episode. This last episode of star formation produces negligible effects on the abundance patterns and can be due to accretion of gas induced by the bar. Our results exclude an important infall event as a trigger for the last starburst.

10 pages, 8 figures, accepted for publication in MNRAS