Mining Utility-Maximizing Prices for Mixed Bundles

We study a data-driven bundle pricing problem with the following objective: given a predefined set of bundles, determine prices that maximize revenue under utility-maximizing consumer behavior. Classical mixed bundling models either assume a complete bundle menu with single-bundle choice or impose simplified pricing structures to ensure scalability. In contrast, we consider a setting in which the seller offers a restricted and potentially overlapping bundle catalog, allowing consumers to optimally select multiple non-overlapping bundles. This setting necessitates addressing two tightly coupled challenges: determining the price of each bundle and computing the revenue it generates under dependent consumer choice. Together, these challenges introduce additional combinatorial complexity in consumer decision-making and preserve strong price interdependencies across bundles. To address these challenges, we propose the Integrated Price Mining Method (IPMM), a scalable approach that approximates fully conditional pricing while explicitly accounting for dependent demand. We formalize consumer response as a utility maximization problem and show that it corresponds to a weighted set packing formulation. For price determination, IPMM combines balanced partitioning, sequential price search guided by competitive independence, dominance-based pruning, and cross-partition refinement to manage price dependence efficiently. Extensive experiments on synthetic instances and curated real-world bundle catalogs demonstrate that IPMM consistently achieves higher revenue coverage than classical and modern pricing baselines while remaining computationally tractable.