On upper bounds for assortment optimization under the mixture of multinomial logit models

The assortment optimization problem under the mixture of multinomial logit models is NP-complete and there are different approximation methods to obtain upper bounds on the optimal expected revenue. In this paper, we analytically compare the upper bounds obtained by the different approximation methods. We propose a new, tractable approach to construct an upper bound on the optimal expected revenue and show that it obtains the tightest bound among the existing tractable approaches in the literature to obtain upper bounds.