Research on design and optimization of gift card promotion strategy with multi-products

In recent years, with the intensification of market competition, more and more firms tend to use gift cards promotion. In this paper, we develop a promotion strategy model in which the retailer offers gift cards to consumers who purchase a certain amount of money. We analyze cases in which the category of the products is multiple in terms of prices and qualities. We show that the optimal face value of the gift card and the maximal profit of the retailer vary widely according to different purchase amount threshold.