Pricing Problems Under the Nested Logit Model with a Quality Consistency Constraint

Abstract

We consider pricing problems when customers choose among the products according to the nested logit model and there is a quality consistency constraint on the prices charged for the products. We consider two types of quality consistency constraint. In the first, there is an inherent ordering between the qualities of the products in a particular nest and the price for a product of a higher quality should be larger. In the second type of constraint, different nests correspond to different quality levels; the price for any product in a nest corresponding to a higher quality level should be larger than the price for any product in a nest corresponding to a lower quality level. Prices for the products are chosen from a finite set of possible prices. We develop algorithms to find the prices to charge for the products to maximize the expected revenue obtained from a customer, while adhering to a quality consistency constraint. Our algorithms are based on solving linear programs whose sizes scale polynomially with the number of nests, number of products, and number of possible prices for the products. We also give extensions to the cases beyond the two types of quality consistency constraints. Numerical experiments indicate that our algorithms can effectively compute the optimal prices even when there is a large number of products in consideration.