| Summary: | Product assortment selection is among the most critical decisions facing retailers: product variety and relevance is a fundamental driver of consumers' purchase decisions and ultimately of a retailer's profitability. In the last couple of decades an increasing number of firms have gained the ability to frequently revisit their assortment decisions during a selling season. In addition, the development and consolidation of online retailing have introduced new levels of operational flexibility, and cheap access to detailed transactional information. These new operational features present the retailer with both benefits and challenges. The ability to revisit the assortment decision frequently over time allows the retailer to introduce and test new products during the selling season, and adjust on the fly to unexpected changes in consumer preferences, and use customer profile information to customize (in real time) online shopping experience. Our main objective in this thesis is to formulate and solve assortment optimization models addressing the challenges present in modern retail environments. We begin by analyzing the role of the assortment decision in balancing information collection and revenue maximization, when consumer preferences are initially unknown. By considering utility maximizing consumers, we establish fundamental limits on the performance of any assortment policy whose aim is to maximize long run revenues. In addition, we propose adaptive assortment policies that attain such performance limits. Our results highlight salient features of this dynamic assortment problem that distinguish it from similar problems of sequential decision making under model uncertainty. Next, we extend the analysis to the case when additional consumer profile information is available; our primary motivation here is the emerging area of online advertisement. As in the previous setup, we identify fundamental performance limits and propose adaptive policies attaining these limits. Finally, we focus on the effects of competition and consumers' access to information on assortment strategies. In particular, we study competition among retailers when they have access to common products, i.e., products that are available to the competition, and where consumers have full information about the retailers' offerings. Our results shed light on equilibrium properties in such settings and the effect common products have on this behavior.
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