Pricing Promotional Products Under Upselling

Upselling is offering an additional product to a customer who just made a purchase. Most catalogers and online sellers, in addition to some traditional retailers, use upselling often to clear inventories of slow–moving items. We investigate the pricing and discounting questions for such an item, which we call the promotional product. In our model, an arriving customer may purchase this promotional product or one of the other products that the firm sells. If the customer purchases one of the other products, the promotional product is offered to the customer, possibly with a discount. While deciding whether to offer a discount and, if so, how big a discount to offer, the firm uses the information that the customer has just bought a certain product with a certain price. We investigate how discounting decisions depend on the inventory levels, time, type of pricing policy in use, and the relationship between the customers' reservation prices for the promotional product and the other products (negatively or positively correlated). In particular, we find that if the firm sets prices and discounts dynamically and the customers' reservation prices for the promotional product are negatively correlated with their reservation prices for the product they purchased, then customers are always offered a discount regardless of the inventory levels and time. On the other hand, if the customers' reservation prices for the promotional product are positively correlated with their reservation prices for the product they purchased, then the customer may or may not be offered a discount, depending on the inventory levels and time. Our numerical study shows that the benefit to the firm from using customer purchase information is high when the firm uses a static price, but chooses discounts dynamically. We also find that although dynamic discounting decisions bring modest improvements, setting the price dynamically seems to have a more significant effect on the firm's profits.