We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.
Finding the optimal product prices and product assortment are two fundamental problems in revenue management. Usually, a seller needs to jointly determine the prices and assortment while managing a network of resources with limited capacity. However, there is not yet a tractable method to efficiently solve such a problem. Existing papers studying static joint optimization of price and assortment cannot incorporate resource constraints. Then we study the revenue management problem with resource constraints and price bounds, where the prices and the product assortments need to be jointly determi…
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）
Duke University（杜克大学）；Purdue University（普渡大学）；George Washington University（乔治华盛顿大学）；University of Michigan（密歇根大学）
We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this…
We consider an online assortment problem with $[n]:=\{1,2,\ldots,n\}$ sellers, each holding exactly one item $i\in[n]$ with initial inventory $c_i\in \mathbb{Z}_+$, and a sequence of homogeneous buyers arriving over a finite time horizon $t=1,2,\ldots,m$. There is an online platform whose goal is to offer a subset $S_t\subseteq [n]$ of sellers to the arriving buyer at time $t$ to maximize the expected revenue derived over the entire horizon while respecting the inventory constraints. Given an assortment $S_t$ at time $t$, it is assumed that the buyer will select an item from $S_t$ based on the…
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）
A fundamental problem in revenue management is to optimally choose the attributes of products, such that the total profit or revenue or market share is maximized. Usually, these attributes can affect both a product's market share (probability to be chosen) and its profit margin. For example, if a smart phone has a better battery, then it is more costly to be produced, but is more likely to be purchased by a customer. The decision maker then needs to choose an optimal vector of attributes for each product that balances this trade-off. In spite of the importance of such problems, there is not ye…
