Newsvendor model with voucher sales: a distributionally robust approach

Vouchers as a popular short-term marketing tool are widely used by many firms, through which retailers can lock in customers and obtain working capital in advance. Consumers can use the voucher to reduce the product purchase price to an equal face value or purchase the product at a discount. We apply the classical newsvendor model to study the merits of vouchers for the retailer's ordering decision in the face of uncertainties in both the market demand and voucher redemption rate. We propose a distributionally robust approach to solve this newsvendor problem. The approach only requires the first and second moments of the demand and redemption rate distributions and yields a lower bound on the expected profit. Specifically, we derive the optimal ordering decision in closed form and obtain the optimal expected profit based on the limited distribution information. We find that a higher redemption rate does not necessarily increase the retailer's profit and the voucher quantity, but always increases the retailer's order quantity. Interestingly, we show that when the buyback price of the voucher is relatively high, increasing the voucher redemption rate is more profitable for the retailer. In addition, the retailer's profit, and the quantities of the product and the voucher decrease with the buyback price of the voucher.