Assortment Optimization with Mixtures of Logits

In this paper, we consider an assortment optimization problem with multiple customer classes. The demand from each customer class follows a multinomial logit choice model with class-dependent parameters and the total demand is given by a mixture of logits. The objective is to choose an assortment of products that maximizes the expected prot across all customer classes. We show that the problem is NP-complete even with two customer classes and give a polynomial time approximation scheme. Furthermore, we establish an approximation guarantee for the class of assortments consisting of products with the highest prots. Finally, we show that this class of assortments is optimal for an additive utility model, where the mean utility that a customer assigns to each product can be written as the sum of class-specic and product-specic terms. Our numerical experiments show that the class of assortments consisting of products with the highest prots performs very well even when the mean utilities are not additive, yielding prots that are on average within 1% of the optimal.