In this paper, we study the optimal policies of retailers who operate their inventory with a single period model (i.e., newsvendor model) under a free shipping offer where a fixed shipping fee is exempted if an order quantity is greater than or equal to a given minimum quantity. Zhou et al. (2009) have explored this model, and we further investigate their analysis for the optimal ordering policies which they did not sufficiently develop. Based on the investigation, we extend the base model in order to deal with the practically important aspect of inventory management when the exact distribution function of demand is not available. We incorporate the aspect into the base model and present the optimal policies for the extended model with a numerical example. Finally, we conduct extensive numerical experiments to evaluate the performance of the extended model and analyze the impacts of minimum free shipping quantity and the fixed shipping fee on the performance. 
A minimax distribution-free procedure for a newsvendor problem with free shipping