Opaque Selling of Multiple Substitutable Products with Finite Inventories

35 Pages Posted: 15 Dec 2019

See all articles by Qian Liu

Qian Liu

Dept. of IEDA, HKUST, Hong Kong

Yongbo Xiao

School of Economics and Management, Tsinghua University

Dan Zhang

University of Colorado at Boulder

Date Written: November 28, 2019

Abstract

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.

Keywords: Revenue Management; Probabilistic/Opaque Selling; Customer Choice Behavior; Asymptotic Optimality; Approximate Dynamic Programming

Suggested Citation

Liu, Qian and Xiao, Yongbo and Zhang, Dan, Opaque Selling of Multiple Substitutable Products with Finite Inventories (November 28, 2019). Available at SSRN: https://ssrn.com/abstract=3494686 or http://dx.doi.org/10.2139/ssrn.3494686

Qian Liu (Contact Author)

Dept. of IEDA, HKUST, Hong Kong ( email )

Yongbo Xiao

School of Economics and Management, Tsinghua University ( email )

Beijing, 100084
China

Dan Zhang

University of Colorado at Boulder ( email )

1070 Edinboro Drive
Boulder, CO 80309
United States

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