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

We consider a retailer’s problem of optimal pricing and inventory stocking decisions for a product. We assume that the price-demand curve is unknown, but data is available that loosely specifies the price-demand relationship. We propose a conceptually new framework that simultaneously considers pricing and inventory decisions without a priori fitting a function to the price-demand data. The framework introduces a novel concept of functional robustness. We consider two situations: (i) where the price-demand function is decreasing convex, and (ii) where the price-demand function is decreasing concave. Under these assumptions the decision problem is to simultaneously specify the demand function, the optimal selling price and the order quantity. The solution of the proposed maxmin optimization model returns the demand function and the desired pricing and order quantity decisions. A cutting surface algorithm is developed for the convex case; and a monolithic reformulation is given for the concave case. The features of the model and the algorithm are illustrated using public data on porterhouse beef price and demand.