Projection neural networks for sample-regular product optimization model

Reducing product fit uncertainty is a critical strategy for retailers to enhance sales and profitability in e-commerce. This paper proposes an optimization-based product sampling strategy to improve sales promotion and profits using recurrent neural networks (RNN) method. Unlike conventional selling modes, the strategy allows consumers to purchase discounted product samples while receiving coupons for subsequent full-priced purchases. A profit optimization model is formulated incorporating constraints such as production costs. The methodological breakthrough lies in introducing RNN to solve this constrained optimization problem, offering a novel approach to dynamic pricing and marketing strategy optimization. In addition, a projection method has been introduced to avoid the additional operation of normalizing product prices in existing methods. The proposed RNN-based framework ensures real-time adaptability, robustness, and efficient convergence, which addresses the complexities of sample distribution and coupon redemption and provides a new perspective on pricing strategies for retailers. The feasibility and effectiveness of the model are demonstrated through numerical simulations, providing valuable insights for retailers seeking promotion-driven pricing strategies. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.