Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

We introduce a new optimization model, dubbed the display optimization problem, that captures a common aspect of choice behavior, known as the framing bias. In this setting, the objective is to optimize how distinct items (corresponding to products, web links, ads, etc.) are being displayed to a heterogeneous audience, whose choice preferences are influenced by the relative locations of items. Once items are assigned to vertically differentiated locations, customers consider a subset of the items displayed in the most favorable locations, before picking an alternative through Multinomial Logit choice probabilities.The main contribution of this paper is to derive a constant-factor approximation for the display optimization problem. Our algorithm relies on a decomposition into polynomially-many instances of the maximum generalized assignment problem with additional side constraints, constructed through approximate dynamic programming and randomization methods. The theoretical guarantees we attain are rather surprising, in light of strong inapproximability bounds for closely related models, when optimizing in the face of a parametric mixture of Multinomial Logit preferences. In computational experiments, our algorithm dominates various natural heuristics -- greedy methods, local-search algorithms, and priority rules -- with significant improvements of the expected revenue, ranging from 5% to 11% on synthetic instances, as well as better robustness.