Dynamic Pricing with Money‐Back Guarantees

Money‐back guarantees (MBGs), which allow customers to return products that do not meet their expectations, are widely used in the retail industry. In this study, we study a retailer's MBG policy with dynamic pricing of limited inventory. A key decision for the retailer is to decide whether to offer MBGs. When the product can be returned instantly, we find that the optimal MBG policy is a simple threshold policy: given the inventory level, it is optimal to offer an MBG if and only if the remaining selling time is longer than a threshold. Moreover, the threshold is decreasing with the inventory level. We also address the problem of dynamic pricing with positive return times. Due to the complexity, we analyze the associated fluid model, which has an infinite number of constraints. We consider a series of relaxations that have a nested structure and use the Lagrangian approach to explicitly solve these relaxed problems. This allows us to develop an iterative approach that is guaranteed to solve the fluid model in finite iterations. Our numerical analysis shows that the deterministic solution is asymptotically optimal for the stochastic system.