A Trailblazing E-Commerce Business


Subscription e-commerce is a fast-growing online buying market in which products are tailored to a subscriber’s needs and preferences and delivered periodically. Since launching as one of the first such services in 2010, Birchbox has stood out with a strong value proposition that engages underserved, overlooked, “casual” beauty and grooming consumers.

Birchbox had developed a mixed-integer programming (MIP) model to group products and assign subscribers according to proprietary objectives and constraints tied to subscriber profiles, history, and activity, product and vendor attributes. As the customer base grew and offerings expanded, the model’s solution time slowed to 30-50 hours, jeopardizing production deadlines. When Birchbox leaders sought to improve the box experience and increase flexibility in assigning products to a box, they needed a far more robust, scalable model.


A Princeton Consultants team interviewed Birchbox business and technical personnel about the existing model’s functionality, and reviewed documentation of the existing formulation. Analysis of the existing model uncovered causes of the poor performance.

In reformulating the model, the team leveraged its deep understanding of Gurobi, the optimization solver licensed by Birchbox, and advanced linear programming and MIP techniques. The team created the innovative Reciprocating Integer Programming (RIP) technique to address this challenge.


Big Data: Choosing appropriate box configurations for millions of customers creates a problem of enormous complexity, requiring advanced modeling and algorithmic techniques to achieve reasonable solution times.


The reformulated model generates better results that reduce the required number of box configurations to meet the subscriber needs. Birchbox executives can create a larger number of clusters in its machine learning approach, resulting in greater customization per subscriber. The new model’s average run time is 99% faster. The transformed performance allows the Birchbox team to tweak inputs and re-run the model—and therefore evaluate different parameters, levels of subscriber aggregation, definitions of a “good” box, and even optimize on box value. With the innovations created by the Princeton team, Birchbox executives are transforming their technology, operations and service, as they further solidify their position as a leading subscription box service.