A Joint Dynamic Pricing and Multi-Channel Advertising Model with Stochastic Demand

To attract potential customers and to effectively sell their inventories over time, retailers often invest in different advertising channels and apply dynamic pricing strategies. However, to compose a beneficial marketing mix in dynamic settings is challenging. The high problem complexity is further increased if one seeks to account for stochastic and inventory-dependent demand, which is essential for various practical applications. In this paper, we examine such stochastic dynamic pricing and advertising models under a finite as well as an infinite time horizon. For a fairly general demand formulation with asymmetric advertising channels, we generalize the classical condition of Dorfman-Steiner to dynamic multi-channel advertising. Further, we show how to transform the multi-dimensional control problem into a two-dimensional one, simplifying the analytical complexity. Finally, for well-established cases with isoelastic and exponential demand, we present optimal closed-form solutions, which allow for detailed sensitivity analyses. Using numerical examples, we illustrate and analyze optimally controlled sales processes and infer managerial insights. Our explicit results provide general qualitative and quantitative insights in the complex interplay of marketing mix controls over time