Motivated by applications in e-retail and online advertising, we study the problem of assortment optimization under visibility constraints, that we refer to as APV. Here, we are given a universe of substitutable products and a stream of customers. The objective is to determine the optimal assortment of products to offer to each customer in order to maximize the total expected revenue, subject to exogenously-given visibility constraints, stating that each product should be shown to a minimum number of customers. We assume that customer choices follow a Multinomial Logit model (MNL). We provide a structural characterization of optimal assortments and present a linear time algorithm for solving APV. To this end, we introduce a novel function called the ``expanded revenue" of an assortment and establish its supermodularity; our algorithm takes advantage of this structural property. Additionally, we prove that APV can be formulated as a compact linear program. Next, we consider APV with cardinality constraints, which limit the maximum number of products that can be included in an assortment. We prove this problem to be strongly NP-hard and not admitting a Fully Polynomial Time Approximation Scheme (FPTAS), even when all products have identical prices. Subsequently, we devise a Polynomial Time Approximation Scheme (PTAS) for APV under cardinality constraints with identical prices. We also examine the revenue loss resulting from the enforcement of visibility constraints, comparing it to the unconstrained problem. To offset this loss, we propose a novel strategy to distribute the loss incurred among the products subject to visibility constraints, charging each vendor an amount proportional to their product's contribution to the revenue loss.
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）
Huge-Scale Assortment Optimization with Customer Choice: A Parallel Primal-Dual Approach
The Institute of Statistical Mathematics（统计数学研究所）；The University of Tokyo（东京大学）；Institute of Operations Research and Analytics, National University of Singapore（新加坡国立大学运筹与分析研究院）；Department of Industrial Systems Engineering and Management, National University of Singapore（新加坡国立大学工业系统工程与管理系）；ZOZO Next, Inc.（ZOZO Next公司）
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）
A Re-solving Heuristic for Dynamic Assortment Optimization with Knapsack Constraints
Stern School of Business, New York University（纽约大学斯特恩商学院）；Department of Statistics and Operations Research, University of North Carolina（北卡罗来纳大学统计与运筹学系）；Naveen Jindal School of Management, University of Texas at Dallas（德克萨斯大学达拉斯分校纳文·金达尔管理学院）；Yau Mathematical Sciences Center & Department of Mathematical Sciences, Tsinghua University（清华大学丘成桐数学科学中心及数学科学系）
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）
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）
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）
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）
