The growing diversity in media clients calls for content providers to adapt media content to adhere to their various needs. It is desirable to serve these heterogeneous users in a fast and efficient manner. Scalable media, such as H.264/MPEG-4 SVC, helps make this possible. To account for various viewing capabilities of each user, such as different spatial or temporal resolutions, the Multiple Distortion Measures framework is used [1], [2]. MDM associates multiple distortion values with each packet depending on the user types (low/high resolution viewers, low/high frame rate viewers, etc.) who will consume the media packets. In this paper, we examine how to broadcast media packets with multiple distortion measures to multiple users. The tradeoff between media distortion and delay (in the form of retransmissions) plays an integral role in the scheduling decision. We cast the problem as a stochastic shortest path problem and use Dynamic Programming to find the optimal policy. In the case of statistically static channels, the optimal policy is shown to be a threshold policy where the number of allowable retransmissions is dictated by the importance, in terms of incurred distortion, of each packet. Through experimental results, we show that our policy, which considers multiple distortion measures, achieves up to 8dB gains over conventional approaches. Finally, a policy based on the theoretical results of statistically static channels is empirically shown to have high performance for time-varying channels modeled by a two-state Markov Chain.