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Monotone Approximation of Decision Problems

Author

Listed:
  • Naveed Chehrazi

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

  • Thomas A. Weber

    (Department of Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

Many decision problems exhibit structural properties in the sense that the objective function is a composition of different component functions that can be identified using empirical data. We consider the approximation of such objective functions, subject to general monotonicity constraints on the component functions. Using a constrained B-spline approximation, we provide a data-driven robust optimization method for environments that can be sample-sparse. The method, which simultaneously identifies and solves the decision problem, is illustrated for the problem of optimal debt settlement in the credit-card industry.

Suggested Citation

  • Naveed Chehrazi & Thomas A. Weber, 2010. "Monotone Approximation of Decision Problems," Operations Research, INFORMS, vol. 58(4-part-2), pages 1158-1177, August.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-2:p:1158-1177
    DOI: 10.1287/opre.1100.0814
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    3. Omar Besbes & Robert Phillips & Assaf Zeevi, 2010. "Testing the Validity of a Demand Model: An Operations Perspective," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 162-183, June.
    4. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    Citations

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    Cited by:

    1. Naveed Chehrazi & Thomas A. Weber, 2015. "Dynamic Valuation of Delinquent Credit-Card Accounts," Management Science, INFORMS, vol. 61(12), pages 3077-3096, December.
    2. Kenneth Judd & Garrett van Ryzin, 2010. "Preface to the Special Issue on Computational Economics," Operations Research, INFORMS, vol. 58(4-part-2), pages 1035-1036, August.
    3. Jian Hu & Junxuan Li & Sanjay Mehrotra, 2019. "A Data-Driven Functionally Robust Approach for Simultaneous Pricing and Order Quantity Decisions with Unknown Demand Function," Operations Research, INFORMS, vol. 67(6), pages 1564-1585, November.
    4. Naveed Chehrazi & Peter W. Glynn & Thomas A. Weber, 2019. "Dynamic Credit-Collections Optimization," Management Science, INFORMS, vol. 67(6), pages 2737-2769, June.
    5. Omar Besbes & Assaf Zeevi, 2015. "On the (Surprising) Sufficiency of Linear Models for Dynamic Pricing with Demand Learning," Management Science, INFORMS, vol. 61(4), pages 723-739, April.
    6. Jerry Anunrojwong & Santiago R. Balseiro & Omar Besbes, 2024. "The Best of Many Robustness Criteria in Decision Making: Formulation and Application to Robust Pricing," Papers 2403.12260, arXiv.org.
    7. Emre Barut & Warren Powell, 2014. "Optimal learning for sequential sampling with non-parametric beliefs," Journal of Global Optimization, Springer, vol. 58(3), pages 517-543, March.
    8. 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.

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