Optimal pricing and order quantity for the newsvendor problem with free shipping

To attract and keep customers, companies, especially those in e-business, are increasingly offering free shipping to buyers whose order sizes exceed the free shipping quantity. In this paper, given the supplier offers free shipping and the retailer faces stochastic demand, we determine the retailer's (i.e., the newsvendor's) optimal order quantity and the optimal selling price simultaneously. We consider two different ways in which price affects the demand distribution, namely price only affects the location or scale of the demand distribution. We explicitly incorporate the supplier's quantity discount and transportation cost into the models. The transportation cost function is very general, which includes those most commonly used in the literature. We numerically examine the impacts of free shipping, quantity discount, transportation cost, and demand variance on the retailer's optimal order quantity and pricing decisions. We find that even though the retailer faces uncertain demand, free shipping can effectively encourage the retailer to order more of the good and can benefit the supplier, the retailer, and the end customers. An increase in transportation cost or a decrease in purchase price will induce the retailer to order more of the good and decrease the retail price. With increasing demand variance, the retailer should order more of the good. We also find that the newsvendor can cope with demand variance by taking advantage of free shipping.