Opaque Selling of Multiple Substitutable Products with Finite Inventories

Opaque selling, in which a seller offers a menu of opaque products from a collection of physical products, has been shown to be an effective strategy to segment a market and improve the seller's profit. We study opaque selling with stochastic demand and fixed initial inventory, where we consider two scenarios. In the exogenous fulfillment scenario, the assignment of physical products to fulfill customer demand is based on pre-announced probabilities. In the endogenous fulfillment scenario, the assignment is dynamically determined by the seller. In both settings, the seller dynamically controls the offering of opaque products over time to maximize the total expected revenue. The existing literature has well studied the mechanism of opaque selling and its benefits over other selling strategies. However, much of the literature considers only a single opaque product. This paper contributes to the literature by considering multiple opaque products and focusing on the practice implementation of opaque selling. We formulate the seller's problem as a stochastic dynamic program. Due to the well-known curse of dimensionality, we study the fluid control problem and develop decomposition heuristic for both scenarios based on the corresponding fluid solution. We show that the fluid control problem can provide a time-based fluid policy that is asymptotically optimal. In particular, we show that adopting a stationary probabilistic fulfillment strategy for the endogenous fulfillment scenario is asymptotically optimal. The numerical study shows that offering multiple opaque products can substantially improve the seller's revenue under certain conditions. Our results provide guidance for sellers on how to implement the opaque selling practically when they have finite inventories of multiple substitutable products