Outer Approximation and Super-modular Cuts for Constrained Assortment Optimization under Mixed-Logit Model (2407.18532v1)

Abstract: 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.