Assortment optimization is an important problem that arises in many\nindustries such as retailing and online advertising where the goal is to find a\nsubset of products from a universe of substitutable products which maximize\nseller's expected revenue. One of the key challenges in this problem is to\nmodel the customer substitution behavior. Many parametric random utility\nmaximization (RUM) based choice models have been considered in the literature.\nHowever, in all these models, probability of purchase increases as we include\nmore products to an assortment. This is not true in general and in many\nsettings more choices hurt sales. This is commonly referred to as the choice\noverload. In this paper we attempt to address this limitation in RUM through a\ngeneralization of the Markov chain based choice model considered in Blanchet et\nal. (2016). As a special case, we show that our model reduces to a\ngeneralization of MNL with no-purchase attractions dependent on the assortment\nS and strictly increasing with the size of assortment S. While we show that the\nassortment optimization under this model is NP-hard, we present fully\npolynomial-time approximation scheme (FPTAS) under reasonable assumptions.\n