Personalized Promotions in Practice: Dynamic Allocation and Reference Effects

Partnering with a large online retailer, we consider the problem of sending daily personalized promotions to a userbase of over 20 million customers. We propose an efficient policy for determining, every day, the promotion that each customer should receive (10%, 12%, 15%, 17%, or 20% off), while respecting global allocation constraints. This policy was successfully deployed to see a 4.5% revenue increase during an A/B test, by better targeting promotion-sensitive customers and also learning intertemporal patterns across customers. We also consider theoretically modeling the intertemporal state of the customer. The data suggests a simple new combinatorial model of pricing with reference effects, where the customer remembers the best promotion they saw over the past $\ell$ days as the "reference value", and is more likely to purchase if this value is poor. We tightly characterize the structure of optimal policies for maximizing long-run average revenue under this model -- they cycle between offering poor promotion values $\ell$ times and offering good values once.