  In this paper, we study the assortment optimization problem faced by many
online retailers such as Amazon. We develop a \emph{cascade multinomial logit
model}, based on the classic multinomial logit model, to capture the consumers'
purchasing behavior across multiple stages. Different from existing studies,
our model allows for repeated exposures of a product, i.e., the same product
can be displayed multiple times across different stages. In addition, each
consumer has a \emph{patience budget} that is sampled from a known distribution
and each product is associated with a \emph{patience cost}, which captures the
cognitive efforts spent on browsing that product. Given an assortment of
products, a consumer sequentially browses them stage by stage. After browsing
all products in one stage, if the utility of a product exceeds the utility of
the outside option, the consumer proceeds to purchase the product and leave the
platform. Otherwise, if the patience cost of all products browsed up to that
point is no larger than her patience budget, she continues to view the next
stage. We propose an approximation solution to this problem.
