In an Advance Booking Discount Program (ABDP), a firm offers a product at a price discount prior to the selling season. In the selling season the product is sold at a regular price. The aim of the paper is to study the strategic value of an ABDP under uncertainty with respect to a specific consumer characteristic. The setup is a duopolistic market, modelled by Hotelling's "linear city" where two firms, A and B, are located at the boundaries of the city. A and B are uncertain about consumers' transportation costs. Firm~A only has the option to implement an ABDP.

Three scenarios emerge, each generating a particular outcome. In the first scenario it is not optimal for A to set up an ABDP. The reason typically is that the selling price of B is considerably larger than that of A and there is no incentive to implement the program. In the two other scenarios, A implements an ABDP in which the reduced price enables A to attract customers from B. If consumers' transportation costs are sufficiently low, B actually exits the market. We show that when A does not implement an ABDP, its expected profit increases as uncertainty about consumers' transportation cost increases. We also show that the gain of implementing an ABDP may depend on uncertainty in various ways.