Constrained Assortment Optimization Problem under the Multilevel Nested Logit Model

Abstract

We study the choice‐based constrained assortment optimization problem under the multilevel nested logit model with a no‐purchase option in every choice stage. For this problem, each candidate product is associated with a fixed profit. The goal is to identify the optimal assortment satisfying a cardinality constraint to maximize the expected profit per customer. There is a cardinality limitation imposed on nodes in the second lowest level. A polynomial‐time algorithm with computational complexity O(nmax{m, k}) is provided to locate the optimal assortment for the m‐level nested logit model with n products, where k is the maximum number of products within any node in level m − 1.