An Innovative Optimization and Computational Framework for Assortment Problems Under Consider-Then-Rank Choice Models

找到各种选定的替代方案的挑战（例如，越来越多的行业已经认识到，在面对对各种替代品有不同偏好的不同客户群体时，最大限度地提高总收入、利润或福利的技术（产品或服务）是成功的主要战略和运营驱动力。这类问题抓住了基本的规划挑战，如：“什么选择的产品应该显示的电子零售商为每个搜索查询？一个实体零售商如何决定每个商店的产品种类？中央计划者应该提供什么服务来最大化异质人口的社会福利？" 尽管人们越来越意识到分类决策的重要性，并且越来越多的可用商业软件工具支持它们，但许多公司（如果不是大多数公司）仍然难以做出有效的数据驱动的分类决策。一个关键的挑战是如何准确有效地捕捉客户选择模型，即客户对替代品的偏好。越来越多的“大”数据使我们能够建立更细粒度的客户选择模型。不幸的是，这些相同的粒度选择模型会产生非常具有挑战性的分类优化模型。这个项目的目标是开发一个统一的方法来研究记录的行为特征之间的关系，客户如何作出购买选择，和相应的分类优化问题的计算易处理性。该项目旨在从理论上进一步理解各种分类模型的学习和计算局限性，并开发有效的计算方案来解决大规模的实际分类问题。该项目旨在开发一个创新的优化和基于计算动态规划的框架，以研究和解决基于排序选择模型的分类优化问题，这在市场营销和心理学中得到了广泛的研究。在排序后选择模型中，假设顾客在两个阶段中做出选择。首先，他们应用各种启发式方法来建立他们愿意考虑的产品考虑集，然后在考虑集中进行排名。给定一个分类，假设客户选择最喜欢的产品，可从他们的考虑设置。如果成功的话，该框架将允许开发的研究如何不同的假设，对物流客户适用于形成各自的考虑集和排名影响计算的易处理性的分类问题。这将是通过一个创新的图形描述的基础动态程序，产生“最小”枚举的动态编程子问题。理论分析将集中在发展严格的界限上的一些子问题。此外，“最小”枚举技术将被用来开发有效的实用算法来解决大规模的实际分类问题。与行业合作伙伴的合作将被用来提高这个研究项目的实际影响，并丰富学生的课堂经验。

The challenge of finding an assortment of selected alternatives (e.g., products or services) that maximize the total revenue, profit or welfare in the face of heterogeneous customer segments, who have different preferences across alternatives, has been recognized by an increasing number of industries to be a major strategic and operational driver of success. This generic class of problems captures fundamental planning challenges, such as: "What selection of products should an e-retailer display for each search query?", "How does a brick and mortar retailer determine the product assortment in each store?" and "What services should a central planner offer to maximize the social welfare of heterogeneous population?" In spite of increased awareness to the importance of assortment decisions, and an increasing number of available commercial software tools to support them, many if not most firms, still struggle to make effective and data-driven assortment decisions. A key challenge is how to accurately and effectively capture a customer choice model, namely the preferences of customers across alternatives. The increasing availability of `big' data allows us to build more granular models of how customers choose. Unfortunately, these same granular choice models give rise to assortment optimization models that are extremely challenging to solve. The goal of this project is to develop a unified approach to study the relationship between documented behavioral features regarding how customers make purchasing choices, and the computational tractability of the corresponding assortment optimization problems. The grant aims to significantly advance the theoretical understanding of the learning and computational limitations of various assortment models, and the development of effective computational schemes to solve practical assortment problems at large scale.This project aims to develop an innovative optimization and computational dynamic-programming based framework to study and solve assortment optimization problems under consider-then-rank choice models, which have been studied extensively in marketing and psychology. Under consider-than-rank choice models, customers are assumed to make choices in two phases. First they apply various heuristics to establish a consideration set of products they are willing to consider, and then they rank within the consideration set. Given an assortment, customers are assumed to choose the most preferred product available from within their consideration set. If successful, the framework to be developed would allow the study of how different assumptions regarding the heuristics customers apply to form their respective consideration sets and rankings affect the computational tractability of the resulting assortment problems. This will be done via an innovative graphical description of the underlying dynamic program that gives rise to "minimal" enumeration of dynamic programming sub-problems. The theoretical analysis will focus on developing tight bounds on the number sub-problems. Moreover, the "minimal" enumeration techniques will be leveraged to develop efficient practical algorithms to solve large scale practical assortment problems. Collaboration with industry partners will be used to enhance the practical impact of this research project, and to enrich the classroom experience for students.