The best way to describe Barbizet's job? Enforcer. As CEO of the holding company that owns a majority stake in the $35 billion retail conglomerate PPR, it's her job to see that all the companies in PPR's portfolio (including Samsonite, Gucci, and Yves Saint Laurent) are adding to the bottom line. Just ask the folks at Printemps—she dumped PPR's stake in the struggling department-store chain this year.