Convex Optimization for Bundle Size Pricing Problem

Xiaobo Li (), Hailong Sun () and Chung Piaw Teo ()
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Xiaobo Li: Department of Industrial Systems Engineering and Management, National University of Singapore, Singapore 117576; Institute of Operations Research and Analytics, National University of Singapore, Singapore 117576
Hailong Sun: Institute of Operations Research and Analytics, National University of Singapore, Singapore 117576
Chung Piaw Teo: Department of Analytics and Operations, National University of Singapore, Singapore 117576

Management Science, 2022, vol. 68, issue 2, 1095-1106

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.

Keywords: discrete choice; bundle size pricing; convex optimization; semidefinite programming (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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