Partition and Prosper: Design and Pricing of Single Bundle
研究了在多元正态估值下，从一系列产品中选择并定价单一捆绑的优化问题，发现当协方差矩阵可分解为固定秩的正定矩阵时问题可多项式求解，并提出了结合贝叶斯优化与锥整数规划的算法。
Design and Pricing of a Single Bundle Product bundling is a widely used selling strategy among multiproduct firms, yet designing and pricing bundles optimally remain a complex challenge. In “Partition and Prosper: Design and Pricing of a Single Bundle,” Sun, Li, and Teo show that the selection and pricing of a single bundle from a range of products under multivariate normal valuations is polynomial-time solvable, provided that the associated covariance matrix can be decomposed into a positive diagonal matrix minus a positive semidefinite matrix of (small) fixed rank. Interestingly, they also show that if the individual product prices are predetermined, the optimization problem becomes NP hard even if customer valuations are independent. The authors use a Bayesian optimization algorithm combined with a novel conic integer programming reformulation to solve the problem under general valuation distributions and demonstrate the superior numerical performance of the algorithm via extensive simulations.