  In this paper, we study the assortment optimization problem under the
mixed-logit customer choice model. While assortment optimization has been a
major topic in revenue management for decades, the mixed-logit model is
considered one of the most general and flexible approaches for modeling and
predicting customer purchasing behavior. Existing exact methods have primarily
relied on mixed-integer linear programming (MILP) or second-order cone (CONIC)
reformulations, which allow for exact problem solving using off-the-shelf
solvers. However, these approaches often suffer from weak continuous
relaxations and are slow when solving large instances. Our work addresses the
problem by focusing on components of the objective function that can be proven
to be monotonically super-modular and convex. This allows us to derive valid
cuts to outer-approximate the nonlinear objective functions. We then
demonstrate that these valid cuts can be incorporated into Cutting Plane or
Branch-and-Cut methods to solve the problem exactly. Extensive experiments show
that our approaches consistently outperform previous methods in terms of both
solution quality and computation time.
