Online ordering policies for a two-product, multi-period stationary newsvendor problem

This paper formulates a two-product, multi-period newsvendor problem in which the two products' total demands are fixed and the newsvendor must decide his order quantity for each product in the subsequent period. This paper adopts the online learning method advanced in prediction with expert advice to study the formulated newsvendor problem. Following stationary expert advice that the order quantities for each product be kept at the same values throughout all periods, this study begins by providing a newsvendor online ordering policy that determines real-valued order quantities. Then, it obtains theoretical results that guarantee that the online ordering policy can achieve competitive cumulative gain compared with the best expert advice. An online ordering policy for deciding integer-valued order quantities and its theoretical guarantee are then proposed. Finally, computational experiments are presented to illustrate the effectiveness of the online ordering policies proposed herein.