Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters

We consider assortment optimization problems under the multinomial logit model, where the parameters of the choice model are random. The randomness in the choice model parameters is motivated by the fact that there are multiple customer segments, each with different preferences for the products, and the segment of each customer is unknown to the firm when the customer makes a purchase. This choice model is also called the mixture-of-logits model. The goal of the firm is to choose an assortment of products to offer that maximizes the expected revenue per customer, across all customer segments. We establish that the problem is NP-complete even when there are just two customer segments. Motivated by this complexity result, we focus on assortments consisting of products with the highest revenues, which we refer to as revenue-ordered assortments. We identify specially structured cases of the problem where revenue-ordered assortments are optimal. When the randomness in the choice model parameters does not follow a special structure, we derive tight approximation guarantees for revenue-ordered assortments. We extend our model to the multi-period capacity allocation problem, and prove that, when restricted to the revenue-ordered assortments, the mixture-of-logits model possesses the nesting-by-fare-order property. This result implies that revenue-ordered assortments can be incorporated into existing revenue management systems through nested protection levels. Numerical experiments show that revenue-ordered assortments perform remarkably well, generally yielding profits that are within a fraction of a percent of the optimal.