The growing trend in online shopping has sparked the development of increasingly more sophisticated product recommendation systems. We construct a model that recommends a personalized discounted product bundle to an online shopper that considers the trade-off between profit maximization and inventory management, while selecting products that are relevant to the consumer's preferences. Academic/ practical relevance: We provide analytical performance guarantees that illustrate the complexity of the underlying problem, which combines assortment optimization with pricing. We implement our algorithms in two separate case studies on actual data from a large U.S. e-tailer and a premier global airline. Methodology: We focus on simultaneously balanc...