Technical Note—The Multinomial Logit Model with Sequential Offerings: Algorithmic Frameworks for Product Recommendation Displays

In this paper, we consider the assortment problem under the multinomial logit (MNL) model with sequential offerings recently proposed by Liu et al. [INFORMS J. Comput., 2020] to capture a multitude of applications, ranging from appointment scheduling in hospitals, restaurants, and fitness centers to product recommendations in e-commerce settings. In this problem, the purchasing dynamics of customers sequentially unfold over T stages. Within each stage, the retailer selects an assortment of products to make available for purchase with the intent of maximizing expected revenue. However, motivated by practical applications, the caveat is that each product can be offered in at most one stage. Moving from one stage to the next, the customer either purchases one of the currently offered products according to MNL preferences and leaves the system or decides not to make any purchase at that time. In the former scenario, the retailer gains a product-associated revenue; in the latter scenario, the customer progresses to the next stage or eventually leaves the system once all T stages have been traversed. We focus our attention on the most general formulation of this problem, in which purchasing decisions are governed by a stage-dependent MNL choice model, reflecting the notion that customers’ preferences may change from stage to stage because of updated perceptions, patience waning over time, etc. Concurrently, we consider a more structured formulation in which purchasing decisions are stage-invariant, utilizing a single MNL model across all stages. Our main contribution comes in the form of a strongly polynomial-time approximation scheme for both formulations of the sequential assortment problem in their utmost generality. We provide evidence for the practical relevance of these theoretical findings through extensive numerical experiments. Finally, we fit our sequential model to historical search data from Expedia’s hotel booking platform. We observe substantial gains in fitting accuracy when our model is benchmarked against other well-known choice models designed for the setting at hand.