In traditional assortment optimization, profits may be improved by making some products unavailable as part of the lost demand flows to higher margin products. The refined assortment optimization problem takes a subtler approach to improving profits without necessarily making some unavailable. This is done by judiciously making some products less appealing thereby steering demand to more profitable products. We develop a theoretical framework and provide tight revenue bounds.

We study efficient real-time data collection approaches for an online retailer that dynamically personalizes the assortment offerings based on customers’ attributes to learn their preferences and maximize revenue. We study the structure of efficient exploration in this setting, prove a performance lower bound, and propose efficient learning policies. We illustrate the superior performance of our policies over existing benchmark using a dataset from a large Chilean retailer.

We investigate assortment problem under distributionally robust and robust satisficing formulations. We generalize the optimality of revenue-ordered set for both distributionally robust assortment and robust assortment satisficing problems. We further discuss the choice model based on worst-case distribution and derive managerial insights by theoretical analysis. Moreover, we discuss the two robust formulations of assortment problem with cardinality constraint and develop efficient algorithms.