Assortment optimization over time

In this note we introduce the problem of assortment optimization over time. We have a sequence of time steps and can introduce one new product per time step. Once introduced a product cannot be removed. The goal is to determine which products to introduce so as to maximize revenue over all time steps under some choice model. Given a 1/α1/α-approximation algorithm for the capacitated assortment optimization problem we give a 1/2α1/2α-approximation algorithm for this problem.