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

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.