Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

We introduce a new optimization model, dubbed the display problem, that captures common aspect of choice behavior, known as framing bias. In this setting, objective is to optimize how distinct items (corresponding products, web links, ads, etc.) are being displayed heterogeneous audience, whose preferences influenced by relative locations items. Once assigned vertically differentiated locations, customers consider subset in most favorable before picking an alternative through multinomial logit probabilities. The main contribution paper derive polynomial-time approximation scheme for problem. Our algorithm based on approximate dynamic programming formulation exploits various structural properties compact state space representation provably near-optimal item-to-position assignment decisions. As byproduct, our results improve existing constant-factor approximations closely related models and apply general distributions over consideration sets. develop notion assortments may be independent interest applicable additional revenue management settings. Lastly, we conduct extensive numerical studies validate proposed modeling approach algorithm. Experiments public hotel booking data set demonstrate superior predictive accuracy model vis-à-vis with location bias, earlier literature. synthetic computational experiments, dominates benchmarks, including natural heuristics—greedy methods, local search, priority rules—and state-of-the-art algorithms developed models. This was accepted Yinyu Ye, optimization.