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

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.