When to Push Ads: Optimal Mobile Ad Campaign Strategy Under Markov Customer Dynamics

Problem definition: We investigate a seller’s optimal advertising strategy targeting customers who interact with the seller over time. We model each customer’s engagement by a continuous-time (hidden) Markov chain with two states: active and inactive. While in the active state, customers make purchases according to a Poisson process; in contrast, customers in the inactive state make no purchases. The seller can use advertisements to activate customers and the activation probability may be affected by customers’ fatigue to promotion. The objective of the seller is to maximize the long-term average expected profit by designing an optimal ad campaign strategy based on customers’ purchase histories. Methodology/results: For a single customer without promotion budget constraints, we demonstrate the optimality of a triple-threshold policy based on both the elapsed time since the last purchase or ad campaign and the number of repeated ad campaigns. When confronted with a budget constraint on the overall ad cost, we suggest first solving a relaxed problem and then implementing a separate triple-threshold policy for each customer with a specified budget. We establish the asymptotic optimality of this policy and show that the order of loss is $O(\sqrt{\log \hspace{0.17em}T/T})$ for the general problem and $O(\sqrt{1/T})$ for a special case. Managerial implications: We find that the seller tends to push ads earlier to customers with low ad costs, high purchase rewards, high activation probabilities, high purchase rates, and low recapture rates (i.e., low transition rates from an inactive state to an active state). Surprisingly, we also find that the seller should push ads earlier to customers with intermediate churn rates (i.e., intermediate transition rates from an active state to an inactive state) compared with those with small or large churn rates. Overall, our work reveals important insights of the optimal ad campaign problem and provides a useful strategy in practice.

Funding: G. Li’s research was supported by the Social Sciences and Humanities Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada [Grant DG RGPIN-2021-02973]. P. Gao’s research was supported by the National Natural Science Foundation of China [Grants 72522026, 72201234, and 72192805], Collaborative Research Funding [Grant C6032-21G] of the Hong Kong Research Grants Council, and the Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001]. Z. Wang’s research was supported by the National Natural Science Foundation of China [Grants 72425013 and 72394361], the Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [Grant 2023B1212010001], and the 1+1+1 CUHK-CUHK(SZ)-GDSTC Joint Collaboration Fund [Grant 2025A0505000079].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0320.