Price Optimization Under the Finite-Mixture Logit Model

We consider price optimization under the finite-mixture logit model. This model assumes that customers belong to one of a number of customer segments, where each customer segment chooses according to a multinomial logit model with segment-specific parameters. We reformulate the corresponding price optimization problem and develop a novel characterization. Leveraging this new characterization, we construct an algorithm that obtains prices at which the revenue is guaranteed to be at least (1-epsilon) times the maximum attainable revenue for any prespecified epsilon>0. Existing global optimization methods require exponential time in the number of products to obtain such a result, which practically means that the prices of only a handful of products can be optimized. The running time of our algorithm, however, is exponential in the number of customer segments and only polynomial in the number of products. This is of great practical value, since in applications the number of products can be very large, while it is has been found in various contexts that a low number of segments is sufficient to capture customer heterogeneity appropriately. The results of our numerical study show that our algorithm runs fast on a broad range of problem instances.