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 to be a critical success driver both by an increasing number of industries, as well as in the context of the design of optimal policy-level interventions. 

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 policy planner offer, or what interventions it should pursue 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 and policy makers, still struggle to make effective and data-driven ‘assortment’ decisions. A key challenge is how to accurately and effectively model and capture 'consumer choices', namely their preferences across alternatives. The increasing availability of `big' data allows us to build more granular models of how consumers choose. Unfortunately, these same granular choice models give rise to assortment optimization models that are extremely challenging to solve.

Intellectual Merit. The work under this project contributed to the development of a unified practical approach to study the relationship between empirically documented behavioral features regarding how consumers make purchasing (or other) choices, and the theoretical and practical computational tractability of the corresponding assortment optimization problems. More specifically, the work under the grant has yielded several important theoretical and practical contributions:

First, it is shown that, computationally, general assortment optimization problems are theoretically  intractable not only to solve optimally but even approximately. 

Second, the work develops new consumer choice models that explicitly capture empirically documented behavioral mechanisms from the psychology and marketing literature regarding how consumers make purchasing decisions, and give rise to theoretically and practically tractable assortment optimization models and optimal algorithms. In particular, the newly developed models and algorithms are shown, on industry as well as synthetic data, to be superior compared to existing state-of-the-art models currently used in the academic literature and in practice. 

Third,  the general new framework establishes a direct connection between choice model complexity and computational tractability. 

Fourth, for several core variants of dynamic assortment models, where assortment and inventory decisions are optimized simultaneously, the work develops a range of computationally tractable greedy-like (i.e., extremely practical) approximation algorithms that not only admit analytical worst-case guarantees and reveal fundamental structural properties of the underlying models, but have superior empirical performance in computational experiments. 

Finally, the work develops the first known analytical data-driven consumer choice models to capture consumption of fresh vegetables and fruits or more generally healthy food as a function of access and value. The models explains known empirical finding from field data. In particular, the newly developed models capture the potential impact of several existing policy interventions related to the challenge of ‘food deserts’ (i.e., poor neighborhoods with no access to healthy food), and inform tractable optimization models that provide important policy level insights.

Broader Impact. The research outcomes of the grant were disseminated into fourteen academic articles that are published or in advanced stages of review in top peer-reviewed academic journals in management science and operations research. Moreover, variants of several of the algorithms and the frameworks developed under the grant were used in industry settings with some preliminary promising results. In addition, this grant enabled the training of several PhD students, including three female students. One of the students that was supported by the grant currently holds a faculty position in a premiere university in Europe. Some of the grant research outcomes have already been disseminated into graduate courses and are used to train the next generation of researchers. 

Last Modified: 02/09/2020
Modified by: Retsef Levi