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.
Optimal Online and Offline Algorithms for Contextual MNL with Applications to Assortment and Pricing
Stern School of Business, New York University（纽约大学斯特恩商学院）；China Europe International Business School (CEIBS)（中欧国际工商学院）；Department of Management Science & Engineering, Stanford University（斯坦福大学管理科学与工程系）
Learning an Optimal Assortment Policy under Observational Data
Stern School of Business, New York University（纽约大学斯特恩商学院）；Center for Data Science, Peking University（北京大学数据科学中心）；Department of Management Science & Engineering, Stanford University（斯坦福大学管理科学与工程系）
Two-sided Assortment Optimization: Adaptivity Gaps and Approximation Algorithms
Cornell Tech, Cornell University（康奈尔理工学院，康奈尔大学）；Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California（南加州大学丹尼尔·J·艾普斯坦工业与系统工程系）
Do You Have My Size In Stock? Assortment and Inventory Optimization Under the Consider-Fit-Then-Choose Choice Model
School of Management, University College London（伦敦大学学院管理学院）；Anderson School of Management, University of California, Los Angeles（加州大学洛杉矶分校安德森管理学院）；Olin Business School, Washington University in St. Louis（华盛顿大学圣路易斯分校奥林商学院）
