Product line pricing for services with capacity constraints and dynamic substitution

In this paper, we address a service provider's product line pricing problem for substitutable products in services, such as concerts, sporting events, or online advertisements. For each product, a static price is selected from a pre-defined set such that the total revenue is maximised. The products are differentiated by some of their attributes, and their availability is restricted due to individual capacity constraints. Furthermore, they are simultaneously sold during a common selling period at the end of which the service is delivered. Consumers differ from one another with respect to their willingness to pay, and, hence, their reservation prices vary depending on the product. In the event of a purchase, they choose the product that maximises their consumer surplus. Even if the number of consumers, the sequence of their arrival, and their product-specific reservation prices are known, the selection of optimal prices is computationally expensive. Due to capacity constraints, products can be sold out early during the selling period, which causes spill and recapture effects by dynamic substitution. In other words, consumers can switch from their preferred products to other products. To model the resulting choice process and optimise total revenue, we propose a linear mixed-integer program. For the solution of this program, we present a branch and bound procedure as well as several heuristic algorithms and evaluate their performances in computational experiments. (C) 2011 Elsevier B.V. All rights reserved.