Optimal ordering and pricing decisions for a company issuing product-specific gift cards

In this paper, we investigate gift card's influence on retailers' ordering decisions and analyse the benefits of issuing product-specific gift cards. We propose an optimal ordering model for retailers' decision problems with gift cards being issued. We also solve the problem with the analytical forms of optimal order quantities and expected profits. By comparing the results with the classical newsvendor problem, we classify the benefits of issuing gift cards into three categories: (1) the demand stimulating; (2) the pre-payment, and (3) the non-redemption. We step further to explore a retailer's problem on how to determine the optimal discount for gift cards, which is characterized by a joint optimal policy on the ordering quantity and the discount. We derive the optimal condition on this joint policy. Numerical examples are conducted to illustrate the model results and analyse the influences of parameters. A sample average approximation method is also been introduced to solve the optimization model.