Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

53 Pages Posted: 2 Jan 2016 Last revised: 19 Sep 2019

See all articles by Ali Aouad

Ali Aouad

London Business School

Danny Segev

Tel Aviv University - School of Mathematical Sciences

Date Written: December 31, 2015

Abstract

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.
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 develop the notion of approximate assortments, that may be of independent interest and applicable in additional revenue management settings.

Lastly, we conduct extensive numerical studies to validate the proposed modeling approach and algorithm. Experiments on a public hotel booking data set demonstrate the superior predictive accuracy of our choice model vis-a-vis the Multinomial Logit choice model with location bias, proposed in earlier literature. In synthetic computational experiments, our approximation scheme dominates various benchmarks, including natural heuristics -- greedy methods, local-search, priority rules -- as well as state-of-the-art algorithms developed for closely-related models.

Keywords: Choice Models, Display Optimization, Approximation Schemes, Revenue Management

Suggested Citation

Aouad, Ali and Segev, Danny, Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences (December 31, 2015). Available at SSRN: https://ssrn.com/abstract=2709652 or http://dx.doi.org/10.2139/ssrn.2709652

Ali Aouad

London Business School ( email )

Sussex Place
Regent's Park
London, London NW1 4SA
United Kingdom

Danny Segev (Contact Author)

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

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