Probability-free solutions to the non-stationary newsvendor problem

This paper concerns the multi-period newsvendor problem. In this problem, the decision maker has to decide the order quantity of an item in the subsequent period in which the demand is usually unknown. No statistical assumptions are made about the unknown demand. We adopt an online learning method from the field of prediction with expert advice to study the non-stationary newsvendor problem. We propose newsvendor strategies for both real-valued and integer order quantities. Taking the non-stationary strategies that can switch between different order quantities as benchmark, we prove that our proposed strategies can guarantee that the newsvendor’s cumulative gains are almost as large as those of the best switching strategies with not too many switches. Simple computational experiments are further performed to illustrate the effectiveness of our strategies.