Personalized Retail Promotions through a DAG-based Representation of Customer Preferences

We propose a back-to-back procedure for running personalized promotions in retail operations contexts, from the construction of a nonparametric choice model where customer preferences are represented by directed acyclic graphs (DAGs) to the design of such promotions. The source data includes a history of purchases tagged by customer id, and product availability and promotion data for a category of products. In each customer DAG nodes represent products and directed edges represent the relative preference order between two products. Upon arrival to the store, a customer samples a full ranking of products within the category consistent with her DAG, and purchases the most preferred option among the available ones. We describe the DAG construction process and explain how to mount a parametric, multinomial logit model (MNL) over it. We provide new bounds for the likelihood of a DAG and show how to conduct the MNL estimation. We test our model to predict purchases at the individual level on real retail data and verify that it outperforms state-of-the-art benchmarks. Finally, we illustrate how to use it to run personalized promotions. Our framework leads to significant revenue gains over the sample data that make it an attractive candidate to be tested in practice.