Aided by scalable video coding, multirate multicast has become a promising technique of providing differentiated quality of experience (QoE) for massive numbers of video subscribers operating in heterogeneous channel conditions. Nevertheless, due to the time-varying nature of wireless channels and the subscribers' diverse requirements, it is challenging to dynamically control the video rate in the light of the available radio resource to achieve the best QoE. To elaborate a little further, the time scale of resource scheduling is of short-term nature, which determines the short-term video quality variation, but from a service provider's perspective the design objective is to optimize the long-term QoE for all subscribers. Despite its importance, this problem has not been considered before. Explicitly, we formulated this problem as a time-averaged stochastic optimization problem which avoids the impact of both the shortterm channel quality fluctuation and that of the video bitrates, whilst maintaining both inter-and intra-group fairness. The stratified structure of the problem inspires us to decompose it into a two-phase optimization: coarse grained assignment for each user group and fine grained assignment for each subgroup. We propose an adaptive multicast algorithm based on Lyapunov's optimization theory for solving this problem, by striking a compelling trade-off between the system's utility and its queue stability. We quantify the achievable performance of our proposed solution based on realistic video traces.