Qian Liu, Yongbo Xiao, and Dan Zhang. 2022. Opaque Selling of Multiple Substitutable Products with Finite Inventories. Naval Research Logistics, 69(4):529-549.
Opaque selling, in which a seller offers opaque goods (OGs), in addition to physical goods, has been shown to be an effective strategy to segment a market and improve the seller’s profit. This paper studies opaque selling with stochastic demand and fixed initial inventories of multiple products, where the seller dynamically controls the product offers and determines the product assignment to fulfill the demand for OGs over time. The problem is formulated as a stochastic dynamic program. Due to the curse of dimensionality, we study the fluid control problem that gives a time-based fluid policy and a stationary probabilistic fulfillment strategy. We show that the fluid policy is asymptotically optimal when the arrival rates and initial inventory level are scaled up linearly. Furthermore, we propose a decomposition heuristic based on the corresponding fluid solution. The decomposition heuristic is shown to provide a tighter upper bound than the fluid control problem. Numerical study on a set of test instances illustrates the performance and efficacy of opaque selling.