EXPRESS: Optimizing Size-Based Bundle Promotions: Balancing Customer Appeal and Product Costs

Size-based bundle promotions (“ p -for- s ”) are widely used in retail to increase basket size, but designing them is challenging when product costs and customer preferences are heterogeneous. Customers favor high-value products; however, including such items increases the bundle’s cost and may require a higher price to sustain profitability. Existing models typically assume identical costs or uniform preferences and therefore largely overlook the interaction between cost heterogeneity and customer preferences. To examine this interaction, we begin with the “ p -for-1” case under classical MNL and mixed MNL models and provide clear structural insights: (i) cost heterogeneity makes assortment selection nontrivial, motivating joint optimization of assortment and pricing; (ii) preference heterogeneity makes optimization under mixed MNL models computationally difficult; and (iii) extending MNL to “ p -for- s ” settings requires approximations and becomes intractable as s grows. Building on these insights, we develop an optimization framework for general “ p -for- s ” promotions with multiple concurrent offers. Our approach uses sample average approximation (SAA) to approximate the valuation distribution with a finite sample of customer valuations and reformulates the resulting problem as a discrete bilevel program that captures surplus-maximizing customer behavior. To improve computational tractability, we combine the SAA-based mixed-integer reformulation with low-rank completion, customer clustering, and consideration-set construction. Finally, a large-scale case study using data from a major e-commerce retailer shows that our framework yields substantially higher model-implied profit than the cost-threshold heuristic and outperforms other bundle-promotion benchmarks.