When to Broadcast? An Analysis of Inventory Disclosure Policies for Online Flash Sales

Abstract

The extant literature on sales of limited inventory has provided evidence for the impact of disclosing inventory on the expected sales. However, an important question still remains: when is the best timing for the disclosure? In this paper, we analyze common disclosure policies: always-to-disclose, never-to-disclose, and fixed threshold policies. We also propose and analyze a time-dependent threshold policy, which is optimal under certain assumptions. We first derive the expected total sales under a given threshold and then develop a dynamic-programming-based algorithm to optimize the parameters of the proposed policy. We also develop a customer choice model under a Bayesian updating framework, which captures the observational learning and scarcity effects. Through a numerical study, we find that both threshold policies outperform the two simple policies when the learning effect dominates the scarcity effect, and the fixed threshold policy is near optimal in such cases. However, when the scarcity effect dominates, employment of a threshold policy may backfire, as the customers may interpret not disclosing as a signal of slow sales. Moreover, when both effects are weak, there is clearly room for improvement in the fixed threshold policy, and it is desirable for the platform to employ the proposed policy. Therefore, our study provides not only efficient procedures for policy optimization but valuable guidelines for policy selection under different customer behaviors.