Operations Management and Econometrics

Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice

Professor Susan Xu, Penn State University, Smeal College of Business

21st Oct 2010  11:00 am - Room 498, Merewether Building

In response to competitive pressures, firms are increasingly adopting revenue management opportunities afforded by advances in information and communication technologies. Motivated by applications in industry, we consider a dynamic pricing problem facing a firm that sells given initial inventories of multiple substitutable and perishable products over a finite selling horizon. In these applications, since individual product demands are linked through consumer choices, the seller must formulate a joint dynamic pricing strategy while explicitly incorporating consumer behaviour. For a general model of consumer choice, we model this multi-product dynamic pricing problem as a stochastic dynamic program and characterize its optimal prices. In addition, since consumer behaviour depends on the nature of product differentiation, we specialise the general choice model to capture vertical and horizontal differentiation. When products are vertically differentiated, our results show monotonic properties of the optimal prices and reveal that the optimal prices can be determined by considering aggregate inventories of products rather than their individual inventory levels. Accordingly, we develop a polynomial-time exact algorithm for determining the optimal prices. When products are horizontally differentiated, we find that analogous structural properties do not hold and the behaviour of optimal prices is substantially different. To solve this problem, we develop a variant of the backward induction algorithm that uses cubic spline interpolation to construct the value functions at each stage. We demonstrate that this interpolation-based algorithm has low memory requirements and is very effective in generating near-optimal solutions that result in an average error of less than 0.15%.

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