We study the problem of finding the optimal assortment that maximizes expected revenue under the decision forest model, a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in particular, can be used to represent non-rational customer behavior. This problem is of practical importance because it allows a firm to tailor its product offerings to profitably exploit deviations from rational customer behavior, but at the same time is challenging due to the extremely general nature of the decision forest model. We approach this problem from a mixed-integer optimization perspective and present two different formulations. We theoretically compare the two formulations in strength, and analyze when they are integral in the special case of a single tree. We further propose a methodology for solving the two formulations at a large-scale based on Benders decomposition, and show that the Benders subproblem can be solved efficiently by primal-dual greedy algorithms when the master solution is fractional for one of the formulations, and in closed form when the master solution is binary for both formulations. Using synthetically generated instances, we demonstrate the practical tractability of our formulations and our Benders decomposition approach, and their edge over heuristic approaches. In a case study based on a real-world transaction data, we demonstrate that our proposed approach can factor the behavioral anomalies observed in consumer choice into assortment decision and create higher revenue.
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）
Assortment optimization given basket shopping behavior using the Ising model
Imperial College Business School, Imperial College London（伦敦帝国理工学院商学院）；Department of Statistical Science, University College London (UCL)（伦敦大学学院统计科学系）；International Institute for Management Development (IMD)（国际管理发展学院）
Admission and Assortment Optimization for Multi-size Automated Parcel Lockers
Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral（自然科学与数学学院，厄瓜多尔高等理工学院）；Department of Computing and Software, Faculty of Engineering, McMaster University（麦克马斯特大学工程学院计算与软件系）；School of Industrial & Intelligent Systems Engineering, Faculty of Engineering, Tel Aviv University（特拉维夫大学工程学院工业与智能系统工程学院）
