Pricing and rebate policies for the newsvendor problem in the presence of stochastic redemption rate

This paper develops the pricing/rebate/ordering policies of a profit-maximizing vendor, faced with a stochastic rebate-redemption rate and a price/rebate-dependent random demand, all within the single-period framework of the newsvendor problem. The profitability of these policies directly relates to the redemption rate, which in turn depends upon the rebate value by itself and relative to the sales price. A random element accounts for the uncertainty in the estimation of such rate. The decision variables are the sales price, the rebate value and the order size. A numerical example and various sensitivity analyses illustrate the main managerial insights of the model. One of the key results is that the introduction of uncertainty in the redemption rate, contrary to what happens when moving from a deterministic to a stochastic demand, leads the rebate policy to dominate its price–discount counterpart.