Women are under-represented in academic staff in universities worldwide. Our work builds on other studies of 'demographic inertia'. We find that time will not bridge the gender representation gap in academia, and echo others in saying bold actions are required to reach parity. Our work then uses New Zealand's unique system of scoring individual research performance to test empirically which levers universities should pull, and in which combinations. We combine individual research performance scores with 20 years of data from one university to parametrize a rank-structured mathematical model using Leslie matrices. Our model compares three key levers of change at universities' disposal - hiring, promotion and attrition. We apply the model to a bifurcated population of university staff - those with high research activity, and those who are moderately active - based on their national research quality score. We then test levers in various combinations that management could pull to improve gender representation. We find that the solutions are different for the high versus moderate research performers. For individuals with high research activity, universities should concentrate on equitable hiring practices. For those with more moderate research activity, more equitable promotion practices hold the key.