Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment

2020 Daniel H. Wagner Finalist Birchbox is an innovator in the Internet box subscription business. A core operational issue is to determine the right number of configurations of boxes that would meet the needs of their diverse subscriber base. Gurobi was taking close to 2 days to find good solutions. We describe a reformulation of the problem and the development of the Reciprocating Integer Programming (RIP) Technique. RIP leverages the power of the Gurobi mixed integer programming solver in multiple ways in a column generation scheme, which led to a 99% reduction in solve times and has transformed Birchbox’s operations.