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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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