Transformer-based neural networks have achieved state-of-the-art task performance in a number of machine learning domains including natural language processing and computer vision. To further improve their accuracy, recent work has explored the integration of dynamic behavior into these networks in the form of mixture-of-expert (MoE) layers. In this paper, we explore the introduction of such layers to optimize a different metric: inference latency. We introduce a novel system named PLANER that takes an existing Transformer-based network and a user-defined latency target and produces an optimized, sparsely activated version of the original network that tries to meet the latency target while maintaining baseline accuracy. We evaluate PLANER on two real-world language modeling tasks using the Transformer-XL network and achieve inference latency reductions of over 2x at iso-accuracy.