Revenue Management Under a Mixture of Independent Demand and Multinomial Logit Models

We consider assortment optimization problems when customers choose under a mixture of independent demand and multinomial logit models. In the assortment optimization setting, each product has a fixed revenue associated with it. The customers choose among the products according to our mixture choice model. The goal is to find an assortment that maximizes the expected revenue from a customer. We show that we can find the optimal assortment by solving a linear program. We establish that the optimal assortment becomes larger as the relative size of the customer segment with the independent demand model increases. Moreover, we show that the Pareto-efficient assortments that maximize a weighted average of the expected revenue and the total purchase probability are nested, in the sense that the Pareto-efficient assortments become larger as the weight on the total purchase probability increases. Considering the assortment optimization problem with a capacity constraint on the offered assortment, we show that the problem is NP-hard, even when each product consumes unit capacity, so that we have a constraint on the number of offered products. We give a fully polynomial-time approximation scheme. In the assortment-based network revenue-management problem, we have resources with limited capacities, and each product consumes a combination of resources. The goal is to find a policy for deciding which assortment of products to offer to each arriving customer to maximize the total expected revenue over a finite selling horizon. A standard linear-programming approximation for this problem includes one decision variable for each subset of products. We show that this linear program can be reduced to an equivalent one of substantially smaller size. We give an expectation-maximization algorithm to estimate the parameters of our mixture model. Our computational experiments indicate that our mixture model can provide improvements in predicting customer purchases and identifying profitable assortments.