Price discounts and personalized product assortments under multinomial logit choice model: A robust approach

With increasing availability of consumer data and rapid advancement and application of technologies, online retailers are gaining better knowledge of customers’ shopping behavior and preferences. Thus more and more retailers are providing personalized product assortment to better match the needs of customers and generate more sales. In this article, we study a two-stage revenue management model. In the first stage, the retailer decides non-personalized price discounts for each product. In the second stage (upon the arrival of customers), the retailer offers a personalized assortment to each type of customer. Based on this assortment, the customer then makes a purchase decision according to the Multinomial logit choice model. We employ a robust approach for the joint discounts and personalized assortment optimization problem in order to handle data uncertainty from estimating customer preferences and distribution of different customer segments. We analyze the structural properties of the problems and propose efficient computational methods to solve the problems with/without a cardinality constraint on the assortment. In certain cases, our algorithm converges at a superlinear rate. When there is a cardinality constraint on the assortment, we find that the retailer should offer greater discounts as the constraint becomes more restrictive. We also discuss the value of our robust solution and the extension of when the customer discount sensitivity function is also uncertain. Finally, our extensive numerical study shows that the solutions under the robust approach perform very well when compared to the one assuming accurate information, and are robust when there is uncertainty.