Robust Assortment Optimization under the Markov Chain Model

Assortment optimization problems arise widely in many practical applications such as retailing and online advertising. In this problem, the goal is to select a subset from a universe of substitutable items to offer to customers in order to maximize the expected revenue. The demand of any item depends on the substitution behavior of the customers that is captured mathematically by a choice model that specifies the probability a random consumer selects a particular item from any given offer set. The objective of the decision maker is to identify an offer set that maximizes expected revenue. Many parametric choice models have extensively been studied in the literature in diverse areas including marketing, transportation, economics, and operations management. The Multinomial logit (MNL) model is by far the most popular model in practice due to its tractability (Talluri and Van Ryzin 2004). However, some of the simplifying assumptions behind this model, such as the Independence of Irrelevant Alternatives property, make it inadequate for many applications. Consequently, more complex choice models have been developed to capture a richer class of substitution behaviors. Such models include the nested logit model (Williams 1977) and the mixture of Multinomial logit model (McFadden et al. 2000). Nonetheless, the increase in model complexity makes their estimation and assortment optimization problems significantly more difficult. Hence, one of the key challenges in assortment planing is choosing a model that strikes a good balance between its predictability and tractability, as there is a fundamental tradeoff between these desirable properties.