Abstract: In this work, we study the conic quadratic mixed-integer formulation for assortment optimization problem under the mixture of multinomial logit (MMNL) model. The MMNL model generalizes the widely studied multinomial logit choice model and can approximate any random utility model with an arbitrary additive error. An important operational decision problem in revenue management is assortment optimization problem, which aims to find a subset of products to make available to customers that maximizes the expected revenue of the retailer. It is known that assortment optimization problem under the MMNL model is NP-hard and inapproximable within any constant performance guarantee. Commonly used methods for solving such problem are heuristical approaches or customized combinatorial optimization approaches. In the meanwhile, studies related to global optimization approaches are relatively scarce. We propose an enhanced conic quadratic mixed-integer formulation for solving assortment optimization problem under the MMNL model with a higher computational efficiency. Furthermore, we conduct extensive numerical experiments to demonstrate that the proposed reformulation significantly outperforms the existing conic reformulations for assortment optimization under the MMNL model.

Key words: Assortment optimization, MMNL model, Conic reformulation, Capacitated constrained