When to Broadcast? Inventory Disclosure Policies for Online Sales of Limited Inventory

Online sales of limited inventory such as flash sales and lightning deals have become popular among e-commerce retailers including Amazon and eBay. Motivated by empirical studies on how inventory information affects demand in flash sales, we study the retailer’s best timing of disclosing inventory information to maximize the expected sales in a finite horizon. We build a model of customers’ utility within a Bayesian updating framework to capture the observational learning and scarcity effects of customers. We analyze the following common policies in practice: “always disclose,” “never disclose,” and the fixed threshold policy, which broadcasts the inventory level once it drops below a predetermined level. We also propose a novel time-dependent threshold policy that compares the current time and a time-threshold related with the current inventory level. We show that this new policy is the optimal policy under certain assumptions that are consistent with the empirical findings of the extant literature. For both threshold policies, we devise efficient algorithms to optimize the policy parameters, and we compare all policies through a numerical study. We find that both threshold policies significantly outperform the two simple policies. In particular, when the observational learning (herding) effect and the scarcity effect are equally influential, the fixed threshold policy can achieve significant improvement. However, when the scarcity effect dominates, the proposed time-dependent threshold policy provides substantial further improvement over the fixed threshold policy. Therefore, our study provides not only effective and efficient algorithms for policy optimization but also guidelines for policy selection.

History: Hsing Kenneth Cheng, Senior Editor; Zhengrui Jiang, Associate Editor.

Supplemental Material: The online appendices are available at https://doi.org/10.1287/isre.2023.0746.