Technical Note: A Simple Greedy Algorithm for Assortment Optimization in the Two-Level Nested Logit Model

We consider the assortment optimization problem under the classical two-level nested logit model. We establish a necessary and sufficient condition for the optimal assortment, and use this optimality condition to develop a simple greedy algorithm that iteratively removes at most one product from each nest, until the optimality condition is satisfied. Our algorithm also exploits the beautiful “lumpy” structure of the optimal solution, where in each nest, a certain set of “consecutive” products will always appear together in the optimal assortment. The algorithm is simple, intuitive, and extremely fast. For a problem with m nests, with each nest having n products, the running time is O(nm logm). This is the fastest known running time for this problem.