Optimizing Product Pool Selection and Pricing for Size-Based Bundling Promotions

Abstract

We study size-based bundling promotions in the form of "p for s pieces". Existing bundle promotion studies often assume that all products are included in the promotion pool and fail to consider the impact of diverse product costs and customer preferences. To address these challenges, we develop a bundle choice model that extends the multinomial logit (MNL) model for size-based bundle settings and jointly optimizes the pricing and the promotion product pool selection from products with heterogeneous costs. We demonstrate that the promotion product pool selection problem is NP-hard and propose an approximation algorithm for optimal bundle promotion design with a strong performance guarantee. Furthermore, we present two tractable parameter estimation methods: one using utility-based data and the other using choice-based data, both involving either closed-form solutions or convex optimization. Numerical experiments reveal that the choice-based approach offers superior predictive power. Structural insights into the optimal promotion product pool are derived for special cases, including cost-interval and cost-nested structures under different conditions. Our study equips decision-makers with tools to design profitable size-based bundling promotions by optimizing product pools and pricing while accounting for customer preferences and cost variations. The proposed IEBCM framework and efficient estimation methods enable data-driven decision-making, enhancing the effectiveness of bundling strategies in multi-purchase settings.

Keywords: promotion design, choice model, bundling, bundle size pricing, assortment planning