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A Data-Driven Functionally Robust Approach for Simultaneous Pricing and Order Quantity Decisions with Unknown Demand Function

Author

Listed:
  • Jian Hu

    (Department of Industrial and Manufacturing Systems Engineering, University of Michigan–Dearborn, Dearborn, Michigan 48128)

  • Junxuan Li

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Sanjay Mehrotra

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

We consider a retailer’s problem of optimally pricing a product and making order quantity decisions without knowing the function specifying price–demand relationship. We assume that the price is set only once after collecting data, possibly from history or a market study, and that the price–demand relationship is a decreasing convex or concave function. Different from the classic approach that fits a function to the price–demand data, we propose and study a maximin framework introducing a novel concept of function robustness. This function robustness concept also provides an alternative mechanism for performing sensitivity analysis for decisions in the presence of data fitting errors. The overall profit maximization model is a nonconvex optimization problem in a function space. A two-sided cutting surface algorithm is developed to solve the maximin model. An analytical approach to compute the rate of decrease of optimal profit is also given for the purposes of sensitivity analysis. Experiments show that the proposed function robust model provides a framework for risk–reward tradeoff in decision making. A Porterhouse beef price and demand data set is used to study the performance of the proposed algorithm and to illustrate the properties of the solution of the joint pricing and order quantity decision problem.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:6:p:1564-1585
    DOI: 10.1287/opre.2019.1849
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    as
    1. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    2. Naveed Chehrazi & Thomas A. Weber, 2010. "Monotone Approximation of Decision Problems," Operations Research, INFORMS, vol. 58(4-part-2), pages 1158-1177, August.
    3. Edwin S. Mills, 1959. "Uncertainty and Price Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 73(1), pages 116-130.
    4. Sanjay Mehrotra & David Papp, 2013. "A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization," Papers 1306.3437, arXiv.org, revised Aug 2014.
    5. Jian Hu & Sanjay Mehrotra, 2015. "Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization," IISE Transactions, Taylor & Francis Journals, vol. 47(4), pages 358-372, April.
    6. Yingjie Lan & Huina Gao & Michael O. Ball & Itir Karaesmen, 2008. "Revenue Management with Limited Demand Information," Management Science, INFORMS, vol. 54(9), pages 1594-1609, September.
    7. Hu, Jian & Bansal, Manish & Mehrotra, Sanjay, 2018. "Robust decision making using a general utility set," European Journal of Operational Research, Elsevier, vol. 269(2), pages 699-714.
    8. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    9. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    10. Greenhut,Melvin L. & Norman,George & Hung,Chao-Shun, 1987. "The Economics of Imperfect Competition," Cambridge Books, Cambridge University Press, number 9780521315647.
    11. T. M. Whitin, 1955. "Inventory Control and Price Theory," Management Science, INFORMS, vol. 2(1), pages 61-68, October.
    12. Zizhuo Wang & Shiming Deng & Yinyu Ye, 2014. "Close the Gaps: A Learning-While-Doing Algorithm for Single-Product Revenue Management Problems," Operations Research, INFORMS, vol. 62(2), pages 318-331, April.
    13. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    14. Wang Chi Cheung & David Simchi-Levi & He Wang, 2017. "Technical Note—Dynamic Pricing and Demand Learning with Limited Price Experimentation," Operations Research, INFORMS, vol. 65(6), pages 1722-1731, December.
    15. Ayşe Kocabıyıkoğlu & Ioana Popescu, 2011. "An Elasticity Approach to the Newsvendor with Price-Sensitive Demand," Operations Research, INFORMS, vol. 59(2), pages 301-312, April.
    16. Maxime C. Cohen & Georgia Perakis & Robert S. Pindyck, 2015. "Pricing with Limited Knowledge of Demand," NBER Working Papers 21679, National Bureau of Economic Research, Inc.
    17. Paul Klemperer & Margaret Meyer, 1986. "Price Competition vs. Quantity Competition: The Role of Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 17(4), pages 618-638, Winter.
    18. Omar Besbes & Assaf Zeevi, 2009. "Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms," Operations Research, INFORMS, vol. 57(6), pages 1407-1420, December.
    19. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    20. Greenhut,Melvin L. & Norman,George & Hung,Chao-Shun, 1987. "The Economics of Imperfect Competition," Cambridge Books, Cambridge University Press, number 9780521305525.
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