  The assortment planning problem is a central piece in the revenue management
strategy of any company in the retail industry. In this paper, we study a
robust assortment optimization problem for substitutable products under a
sequential ranking-based choice model. Our modeling approach incorporates the
cumulative effect of finding multiple unavailable products on the customers'
purchase decisions. To model the highly uncertain order in which a customer
explores the products to buy, we present a bi-level optimization approach to
maximize the expected revenue under the worst-case order of products in the
preference lists of customers. We provide a polynomial-time algorithm that
optimally solves a special case of the unconstrained assortment planning
problem under our choice model. For the general constrained version of the
problem, we devise a solution procedure that includes a single-level
reformulation and a cutting-plane approach to iteratively tighten the solution
space. We also provide a greedy algorithm that can quickly solve large
instances with small optimality gaps.
