Problem definition: 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 balancing personalization through individualized functions of consumer propensity-to-buy, inventory management for long-run profitability, and tractability for practical business implementation. We develop two classes of approximation algorithms, multiplicative and additive, to produce a real-time output for use in an online setting. Results: Our computational results demonstrate significant lifts in expected revenues over current industry pricing strategies on the order of 2%-7% depending on the setting. We find that on average our best algorithm obtains 92% of the expected revenue of a full-knowledge clairvoyant strategy across all inventory settings, and in the best cases this improves to 98%. Managerial implications: We compare the algorithms and find that the multiplicative approach is relatively easier to implement and on average empirically obtains expected revenues within 1%-6% of the additive methods when both are compared with a full-knowledge strategy. Furthermore, we find that the greatest expected gains in revenue come from high-end consumers with lower price sensitivities, and that predicted improvements in sales volume depend on product category and are a result of providing relevant recommendations.