Dynamic Learning for Joint Pricing, Advertising, and Inventory Management

Startup firms typically are small and by their nature their founders are required to make cross-functional decisions because disciplinary departments—for example, marketing and operations—simply do not exist as separate entities in their firms. Simultaneously considering marketing and operational decisions which are interdependent is challenging, but considerably more so in the absence of actionable data regarding customers. Such firms may be required to learn about their customers' preferences while actually deciding marketing decisions such as pricing and advertising and operational decisions such as inventory levels. This paper studies a setting where a firm jointly determines pricing, inventory, and advertising decisions for T periods while learning demand and advertising response models. Solving for the optimal policy in this setting is computationally complex. Therefore, we first characterize a family of policies that can achieve exponentially fast learning rates. Furthermore, we provide an easy-to-implement policy that is asymptotically optimal—we establish that the gap between this policy's profit and that of a clairvoyant with perfect information of the demand and advertising models is O(logT). We numerically show that learning about the advertising model is necessary to learn about the pricing model