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Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment

Author

Listed:
  • Irvin Lustig

    (Princeton Consultants, Princeton, New Jersey 08540)

  • Patricia Randall

    (Princeton Consultants, Princeton, New Jersey 08540)

  • Robert Randall

    (Princeton Consultants, Princeton, New Jersey 08540)

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.

Suggested Citation

  • Irvin Lustig & Patricia Randall & Robert Randall, 2021. "Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment," Interfaces, INFORMS, vol. 51(5), pages 347-360, September.
    • Handle: RePEc:inm:orinte:v:51:y:2021:i:5:p:347-360
    DOI: 10.1287/inte.2021.1081
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    References listed on IDEAS

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    1. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. François Vanderbeck, 2005. "Implementing Mixed Integer Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 331-358, Springer.
    3. Robert E. Bixby & John W. Gregory & Irvin J. Lustig & Roy E. Marsten & David F. Shanno, 1992. "Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods," Operations Research, INFORMS, vol. 40(5), pages 885-897, October.
    4. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    5. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    6. Ruslan Sadykov & François Vanderbeck & Artur Pessoa & Issam Tahiri & Eduardo Uchoa, 2019. "Primal Heuristics for Branch and Price: The Assets of Diving Methods," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 251-267, April.
    7. MARCHAND, Hugues & MARTIN, Alexander & WEISMANTEL, Robert & WOLSEY, Laurence, 2002. "Cutting planes in integer and mixed integer programming," LIDAM Reprints CORE 1567, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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