We study assortment problems under the Marginal Exponential Model (MEM) with deterministic demand. We show that optimal solutions to such assortment problems can be efficiently determined under some mild conditions, and provide a simple approach that finds near optimal solutions when these conditions fail. Furthermore, we improve the existing MEM parameter estimation method given by Mishra et al. (2014). Our numerical studies show that using MEM to capture choice behavior in assortment optimization leads to better results than using heteroscedastic exponomial choice (HEC) model, a model recently introduced by Alptekinoglu and Semple (2018) to capture heteroscedasticity.