Dynamic Learning for Joint Pricing, Advertising, and Inventory Management

Problem Definition: Startup firms, often small in size, face the challenge of making cross-functional decisions due to the absence of distinct departments like marketing and operations. These interdependent decisions are further complicated by the lack of historical customer data. As a result, these firms must learn about customer preferences while making marketing decisions (such as pricing and advertising) and operational decisions (such as inventory levels). This paper examines a scenario where a firm jointly determines pricing, advertising, and inventory decisions over T periods while learning about demand and advertising response models. Methodology/Results: We first characterize a set of sufficient conditions to achieve exponentially fast learning rates with cross-functional decisions. Based on these sufficient conditions, we propose an easy-to-implement policy that is asymptotically optimal, showing that the gap between the profit of this policy and that of a clairvoyant with perfect information on the demand and advertising models is of order log T. Numerical experiments reveal that joint learning about the advertising and demand models is crucial for good profit performance. Managerial Implications: Our findings emphasize the need to jointly consider marketing and operational decisions for better business outcomes, providing valuable insights for entrepreneurs and managers. Our learning conditions highlight that the connections between cross-functional decisions play a key role in learning the impact of these decisions on consumers. Moreover, our numerical studies indicate that deviating from our learning conditions to avoid experimentation results in poor profit performance. Overall, our integrated approach can lead to better resource allocation, improved customer understanding, and increased profitability for firms.