The d-Level Nested Logit Model: Assortment and Price Optimization Problems

We consider assortment and price optimization problems under the d-level nested logit model. In the assortment optimization problem, the goal is to find the revenue-maximizing assortment of products to offer, when the prices of the products are fixed. Using a novel formulation of the d-level nested logit model as a tree of depth d, we provide an efficient algorithm to find the optimal assortment. For a d-level nested logit model with n products, the algorithm runs in O4dn logn5 time. In the price optimization problem, the goal is to find the revenue-maximizing prices for the products, when the assortment of offered products is fixed. Although the expected revenue is not concave in the product prices, we develop an iterative algorithm that generates a sequence of prices converging to a stationary point. Numerical experiments show that our method converges faster than gradient-based methods, by many orders of magnitude. In addition to providing solutions for the assortment and price optimization problems, we give support for the d-level nested logit model by demonstrating that it is consistent with the random utility maximization principle and equivalent to the elimination by aspects model.