A combinatorial algorithm for constrained assortment optimization under nested logit model

TL;DR

This paper introduces a fast combinatorial algorithm for solving the constrained assortment optimization problem under the nested logit model, efficiently identifying optimal assortments within a large candidate set.

Contribution

The paper develops a novel algorithm that efficiently finds optimal assortments under disjoint-cardinality constraints in nested logit models, improving computational speed.

Findings

Algorithm runs in $O(m n^2 \,\log mn)$ time.

Candidate set of size $O(m n^2)$ contains at least one optimal assortment.

Efficient solution for constrained assortment optimization under nested logit models.

Abstract

We consider the assortment optimization problem with disjoint-cardinality constraints under two-level nested logit model. To solve this problem, we first identify a candidate set with $O(mn^2)$ assortments and show that at least one optimal assortment is included in this set. Based on this observation, a fast algorithm, which runs in $O(m n^2 \log mn)$ time, is proposed to find an optimal assortment.