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

Flash sales have gained popularity among online retail platforms, including Amazon lightning deals and eBay daily deals. The extant literature has provided evidence that disclosure of inventory levels of a flash sale can affect customers' purchase behavior and thus, the total sales of the product. However, an important question still remains: when is the best timing for the disclosure of inventory? We consider and analyze the commonly employed “always-to-broadcast,” “never-to-broadcast,” and fixed threshold disclosure policies; we also propose and analyze a time-dependent threshold policy. The first two policies are indeed special cases of the fixed threshold policy, which requires the platform to broadcast once its inventory drops below a certain level, no matter when it occurs. The proposed time-dependent threshold policy, in contrast, requires that the platform to reveal information only if the inventory level drops faster than expected. We derive the probabilistic distribution of the future sales after the disclosure as well as the expected total sales under a given threshold. This enables us to find the optimal inventory-level threshold under the fixed threshold policy. We also develop a dynamic-programming-based algorithm to optimize the proposed time-dependent threshold policy, which indeed is the optimal policy under certain reasonable assumptions. Finally, we study the relative performances of these policies via a numerical experiment, where demand patterns are characterized by the following measures: the normal demand-inventory ratio and the speed of change in the demand rate before inventory is broadcasted, as well as the max-min ratio of demand adjustment factors and the inventory-time elasticity after inventory is broadcasted. Therefore, our study provides not only efficient algorithms to optimize the policies considered, but also valuable guidelines for the selection of a policy for various products with different demand characteristics