Quantitative Methods for Omnichannel Decision-Making

Omnichannel retail has emerged as the new standard in today's commerce landscape, with retailers integrating their physical and online channels to enhance the customer shopping experience. However, such integration presents significant challenges for retailers, particularly in relation to optimizing their product assortments. This thesis comprises three chapters, each addressing different aspects of omnichannel assortment optimization under various assumptions. In the first chapter, we introduce the multichannel attraction model (MAM), a discrete choice model designed specifically for omnichannel environments. Focusing on a dual-channel setting, we formulate the assortment optimization problem under the MAM as a mixed-integer linear program, and provide a computationally efficient heuristic method for solving large-scale instances of this problem. We also describe general effects of the implementation of widely-used omnichannel initiatives on the MAM parameters and explore the properties of optimal assortments through numerical experiments.

In the second chapter, we generalize our modeling framework to the case of a retailer managing both an online store and a network of physical stores. Additionally, we incorporate demand stochasticity and inventory management considerations into the assortment optimization problem under the MAM. We show that overlooking the demand variability can result in suboptimal assortment decisions due to the demand pooling effect. We derive complexity results for the assortment optimization problem, which we then formulate as a mixed-integer second-order cone program. We also develop two heuristic algorithms based on different relaxations of the formulated optimization problem. Our findings indicate that an increasing coefficient of variation of demand has a dual effect on optimal assortment sizes, initially causing a decrease in online assortment size due to rising costs, followed by an increase in online assortment size because of the demand pooling effect.

Finally, in the third chapter, we address a key limitation of the MAM by developing a modeling framework for omnichannel assortment optimization that accounts for basket shopping behavior of customers. We model customer choices using a Markov random field -- in particular, the Ising model -- which captures pairwise demand dependencies as well as the individual attractiveness of each product. We provide theoretical insights into the structure of optimal assortments based on the graphical representation of the Ising model, and develop a customized metaheuristic algorithm for obtaining high-quality solutions to the assortment optimization problem. Lastly, we perform an extensive numerical analysis to gather insights into the properties of optimal assortments and evaluate the benefits of omnichannel assortment optimization as opposed to optimizing assortments in siloed channels.