Self-Improving Neural-Guided Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing
About
Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed bundling models capture this structure but become computationally intractable because the number of candidate bundles grows exponentially with the number of products. We develop a graph neural network (GNN)-guided pruning-then-optimization framework for bundle pricing with (non-)additive valuations. The method represents each instance as a compact segment-product graph, predicts segment-product inclusion probabilities, and accordingly prunes the exponential bundle space into a small candidate family; the final prices and bundle offerings are obtained by solving the mixed bundling formulation over the retained bundles, possibly refined by a GNN-guided local search. Because exact labels are available only at small scales, we further propose an iterative self-improvement procedure: the current GNN policies generate high-quality solutions on large-scale instances, which serve as near-optimal labels for training a stronger model at larger scales. Theoretically, we show that under mild conditions the proposed edge-output GNN class is expressive enough to represent the optimal product-assignment mapping, justifying the edge-level learning target. Numerical experiments show that the fastest proposed policy delivers 13-21% higher profit than bundle-size pricing on instances with up to 100 products at about 2% of its runtime.