IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v31y2019i1p2-20.html
   My bibliography  Save this article

Data-Driven Decisions for Problems with an Unspecified Objective Function

Author

Listed:
  • Zhen Sun

    (School of Business, GeorgeWashington University, Washington, DC 20052)

  • Milind Dawande

    (Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080)

  • Ganesh Janakiraman

    (Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080)

  • Vijay Mookerjee

    (Naveen Jindal School of Management, The University of Texas at Dallas, Richardson, Texas 75080)

Abstract

This study develops a data-driven approach to solve constrained optimization problems in which the decision maker does not have an analytic form for the objective function but knows what decision variables affect the function. The approach makes direct use of the available data, rather than first using the data to estimate the objective function and then solving the problem as a traditional optimization problem. The difficulty in first estimating the unknown objective function is that the decision maker needs to have sufficient knowledge of its properties that are necessary to guide the estimation process. Thus, our approach is appropriate for situations where such structural knowledge is absent, either because the domain is very complex or because the knowledge is deliberately hidden by a partner firm that has a vested interest in the outcome of the decision. Our approach comes with a worst-case performance guarantee that improves with the characteristics (size, pervasiveness) of the available data. We illustrate our technique on a traffic-stream mixing problem encountered by a supply side Internet advertising network that wishes to optimize the click revenue earned from ads. A head-to-head comparison (with the existing method used) on real data shows a significant increase (≥10%, on average) in the revenue. We also demonstrate the value of our approach under more general conditions.

Suggested Citation

  • Zhen Sun & Milind Dawande & Ganesh Janakiraman & Vijay Mookerjee, 2019. "Data-Driven Decisions for Problems with an Unspecified Objective Function," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 2-20, February.
    • Handle: RePEc:inm:orijoc:v:31:y:2019:i:1:p:2-20
    DOI: 10.1287/ijoc.2018.0818
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/ijoc.2018.0818
    Download Restriction: no
    File URL: https://libkey.io/10.1287/ijoc.2018.0818?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Naveed Chehrazi & Thomas A. Weber, 2010. "Monotone Approximation of Decision Problems," Operations Research, INFORMS, vol. 58(4-part-2), pages 1158-1177, August.
    2. Ho-Yin Mak & Zuo-Jun Max Shen, 2014. "Pooling and Dependence of Demand and Yield in Multiple-Location Inventory Systems," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 263-269, May.
    3. Sunder Kekre & Nicola Secomandi & Erkut Sönmez & Kenneth West, 2009. "OM Practice--Balancing Risk and Efficiency at a Major Commercial Bank," Manufacturing & Service Operations Management, INFORMS, vol. 11(1), pages 160-173, December.
    4. Adam J. Mersereau, 2015. "Demand Estimation from Censored Observations with Inventory Record Inaccuracy," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 335-349, July.
    5. Joel Goh & Melvyn Sim, 2010. "Distributionally Robust Optimization and Its Tractable Approximations," Operations Research, INFORMS, vol. 58(4-part-1), pages 902-917, August.
    6. Philipp Afèche & Barış Ata, 2013. "Bayesian Dynamic Pricing in Queueing Systems with Unknown Delay Cost Characteristics," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 292-304, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Long He & Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2017. "Service Region Design for Urban Electric Vehicle Sharing Systems," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 309-327, May.
    2. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    3. Zhi Chen & Melvyn Sim & Huan Xu, 2019. "Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," Operations Research, INFORMS, vol. 67(5), pages 1328-1344, September.
    4. Ho-Yin Mak & Zuo-Jun Max Shen, 2014. "Pooling and Dependence of Demand and Yield in Multiple-Location Inventory Systems," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 263-269, May.
    5. Gauvin, Charles & Delage, Erick & Gendreau, Michel, 2017. "Decision rule approximations for the risk averse reservoir management problem," European Journal of Operational Research, Elsevier, vol. 261(1), pages 317-336.
    6. Chassein, André & Goerigk, Marc, 2018. "Compromise solutions for robust combinatorial optimization with variable-sized uncertainty," European Journal of Operational Research, Elsevier, vol. 269(2), pages 544-555.
    7. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    8. Viet Anh Nguyen & Daniel Kuhn & Peyman Mohajerin Esfahani, 2018. "Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator," Papers 1805.07194, arXiv.org.
    9. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    10. Jinil Han & Chungmok Lee & Sungsoo Park, 2014. "A Robust Scenario Approach for the Vehicle Routing Problem with Uncertain Travel Times," Transportation Science, INFORMS, vol. 48(3), pages 373-390, August.
    11. Walid Ben-Ameur & Adam Ouorou & Guanglei Wang & Mateusz Żotkiewicz, 2018. "Multipolar robust optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 395-434, December.
    12. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    13. R. Tyrrell Rockafellar, 2024. "Distributional robustness, stochastic divergences, and the quadrangle of risk," Computational Management Science, Springer, vol. 21(1), pages 1-30, June.
    14. Paula Rocha & Daniel Kuhn, 2013. "A Polynomial-Time Solution Scheme for Quadratic Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 576-589, August.
    15. Guanglei Wang & Hassan Hijazi, 2018. "Mathematical programming methods for microgrid design and operations: a survey on deterministic and stochastic approaches," Computational Optimization and Applications, Springer, vol. 71(2), pages 553-608, November.
    16. Xuan Wang & Jiawei Zhang, 2015. "Process Flexibility: A Distribution-Free Bound on the Performance of k -Chain," Operations Research, INFORMS, vol. 63(3), pages 555-571, June.
    17. Ruidi Chen & Ioannis Ch. Paschalidis, 2022. "Robust Grouped Variable Selection Using Distributionally Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1042-1071, September.
    18. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    19. Fanwen Meng & Jin Qi & Meilin Zhang & James Ang & Singfat Chu & Melvyn Sim, 2015. "A Robust Optimization Model for Managing Elective Admission in a Public Hospital," Operations Research, INFORMS, vol. 63(6), pages 1452-1467, December.
    20. Antonio J. Conejo & Nicholas G. Hall & Daniel Zhuoyu Long & Runhao Zhang, 2021. "Robust Capacity Planning for Project Management," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1533-1550, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:31:y:2019:i:1:p:2-20. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.