Optimizing Revenue over Data-driven Assortments

We revisit the problem of assortment optimization under the multinomial logit choice model with general constraints and propose new efficient optimization algorithms. Our algorithms do not make any assumptions on the structure of the feasible sets and in turn do not require a compact representation of constraints describing them. For the case of cardinality constraints, we specialize our algorithms and achieve time complexity sub-quadratic in the number of products in the assortment (existing methods are quadratic or worse). Empirical validations using the billion prices dataset and several retail transaction datasets show that our algorithms are competitive even when the number of items is ∼ 105 and beyond (100x larger instances than previously studied), supporting their practicality in data driven revenue management applications.