Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Choice Preferences
46 Pages Posted: 2 Jan 2016 Last revised: 2 Feb 2018
Date Written: December 31, 2015
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 polynomial-time approximation scheme for the display optimization problem. Our algorithm is based on an approximate dynamic programming formulation that exploits various structural properties to derive a compact state space representation of provably near-optimal item-to-position assignment decisions.
These properties include unimodality of the expected revenue function, precedence order across subsets of items, and parametric rounding techniques, just to name a few. As a by-product, our results improve on existing constant-factor approximations for closely related models, and apply to general distributions over consideration sets. We also develop the notion of "approximate assortments'', that may be of independent interest and applicable in additional revenue management settings. In computational experiments, our algorithm dominates various benchmarks, including natural heuristics -- greedy methods, local-search algorithms, and priority rules -- as well as state-of-the-art algorithms proposed for closely-related problems.
Keywords: Choice Models, Display Optimization, Approximation Schemes, Revenue Management
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