Nonparametric advertising budget allocation with inventory constraint

In this paper, we study the optimization problem of the advertising budget allocation for revenue management faced by a marketer. Besides the advertising budget, the marketer is subject to an inventory constraint during the promotion season. The marketer can affect sales by spending on advertising but does not initially know the relationship between the advertising expense and consequent sales. We propose a nonparametric learning-while-doing budget allocation policy for the problem. Specifically, we first conduct a sequence of advertising experiments to learn (predict) the market sales response through observing realized sales (exploration), then based on the learned sales function determine the following budget allocation planning (exploitation). In particular, during the exploration and exploitation phases, we need to balance the advertising and inventory budgets simultaneously. We show that our policy is asymptotically optimal as the size of the market increases. By constructing a worst-case example, we show that our policy achieves near-best asymptotic performance. We also provide numerical illustrations to show how our policy works, and discuss how its performance changes as the system parameters vary. We also glen some managerial implications of our model and policy from the numerical results.