Multichannel Advertising: Budget Allocation in the Presence of Spillover and Carryover Effects

Problem definition: This paper explores budget allocation strategies for a multichannel ad campaign, where a marketing agency strives to maximize the total conversions by dynamically adjusting budget allocation over marketing channels. A salient feature of the problem is the interplay of spillover and carryover effects; namely, customers are exposed to ads through multiple channels, and thus ads from one channel affect the effectiveness of the subsequent ads from other channels. Methodology/results: We construct a simple model that captures the essential features of this problem. Our theoretical analysis yields two main insights. First, motivated by common practice based on the last-click attribution method, we examine a class of budget allocation policies that are oblivious to the spillover and carryover effects. If the agency decreases the budget on a channel based on past low conversions while neglecting to account for the fact that the ads from that channel induced conversions through other channels, then the conversions from that channel will decrease. Consequently, the agency will further decrease the budget on the channel. This pattern repeats, eventually leading to suboptimal performance in the long run. Second, we derive a fluid approximation to consumer dynamics across multiple channels, which lends itself to characterizing structural properties of optimal dynamic budget allocation policies that internalize the cross-channel interactions. To enable practical implementation, we propose a static budget allocation policy that is both tractable in practice and near optimal for long campaigns. Managerial implications: Our theoretical results provide normative guidance for budget allocation in multichannel ad campaigns. We illustrate the efficacy of our proposed method through a numerical study based on data from an online multichannel ad campaign. Funding: This work was supported by the Hong Kong Research Grants Council [ECS Grant 26504219, GRF Grant 16212821, C6020-21GF]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0293 .