Convex Optimization for Bundle Size Pricing Problem

Author:

Li Xiaobo12ORCID,Sun Hailong2ORCID,Teo Chung Piaw3ORCID

Affiliation:

1. Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore 117576;

2. Institute of Operations Research and Analytics, National University of Singapore, Singapore 117576;

3. Department of Analytics and Operations, National University of Singapore, Singapore 117576

Abstract

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. This paper was accepted by David Simchi-Levi, revenue management and market analytics.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Management Science and Operations Research,Strategy and Management

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Bounds and Heuristics for Multiproduct Pricing;Management Science;2023-12-15

2. Picking winners: Diversification through portfolio optimization;Production and Operations Management;2023-04-30

3. Customer-driven Bundle Promotion Optimization at Scale;SSRN Electronic Journal;2022

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