Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment

Irvin Lustig (), Patricia Randall () and Robert Randall ()
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Irvin Lustig: Princeton Consultants, Princeton, New Jersey 08540
Patricia Randall: Princeton Consultants, Princeton, New Jersey 08540
Robert Randall: Princeton Consultants, Princeton, New Jersey 08540

Interfaces, 2021, vol. 51, issue 5, 347-360

Abstract: Birchbox created a mixed-integer programming formulation to determine the products that it will send to its subscribers in individual boxes on a monthly basis. The goal of this formulation is to produce a set of different box configurations that are then assigned to customers to meet the diverse needs of its varied customer base. As Birchbox’s business grew, the mixed-integer program was taking days to solve, and experimenting with different business requirements to determine the best set of configurations became impossible. Therefore, Princeton Consultants created the Reciprocating Integer Programming technique to reduce these solution times, thus decreasing them to typically under 20 minutes. This has dramatically changed the way that Birchbox can run its subscription business.

Keywords: mixed-integer programming; column generation; e-commerce (search for similar items in EconPapers)
Date: 2021
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