Robust Dynamic Pricing with Two Substitutable Products

We consider a practical dynamic pricing problem with two substitutable products involving a number of business rules commonly seen in practice. Demand substitution exists between the two products (interproduct substitution) and may also exist across different time periods (intertemporal substitution). However, there is limited demand information such that the underlying probability distributions of the demand cannot be characterized precisely. We use an interval to represent, respectively, the demand for each individual product in each period, the aggregate demand for the two products in each period, and the total aggregate demand for the two products across multiple time periods. We propose a robust optimization model for this problem to maximize the worst-case total revenue. For the problem with interproduct demand substitution only, we develop a dynamic programming algorithm and show that the search spaces in the DP can be reduced greatly, which enables the algorithm to generate optimal solutions in a ...