Convex Optimization for Bundle Size Pricing Problem

• 成果类型: Article
• 署名作者: Li, Xiaobo; Sun, Hailong; Teo, Chung Piaw
• 署名单位: National University of Singapore; National University of Singapore; National University of Singapore
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2021.4148
• 发表日期: 2022
• 页码: 1095-1106
• 关键词: Discrete choice; bundle size pricing; Convex Optimization; Semidefinite programming

摘要

We study the bundle size pricing (BSP) problem in which a monopolist sells bundles of products to customers and the price of each bundle depends only on the size (number of items) of the bundle. Although this pricing mechanism is attractive in practice, finding optimal bundle prices is difficult because it involves characterizing distributions of the maximum partial sums of order statistics. In this paper, we propose to solve the BSP problem under a discrete choice model using only the first and second moments of customer valuations. Correlations between valuations of bundles are captured by the covariance matrix. We show that the BSP problem under this model is convex and can be efficiently solved using off-the-shelf solvers. Our approach is flexible in optimizing prices for any given bundle size. Numerical results show that it performs very well compared with state-of-the-art heuristics. This provides a unified and efficient approach to solve the BSP problem under various distributions and dimensions.