Robust optimization for spread quality and shortfall in guaranteed targeted display advertising planning

The problem addressed in this paper is the impression allocation planning of Guaranteed Targeted Display Advertising (GTDA) problem in online display advertising market. In this problem, a publisher desires (1) an even spread of impressions, i.e., ad exposures, across various audience segments, and (2) a maximum delivery of ads, i.e., fulfillment of the advertisers' required impressions. For the publisher, the allocation of impressions needs to be appropriately planned to guarantee spread quality and delivery fulfillment simultaneously. The impression supplies are commonly assumed to be deterministic. In reality, however, they are stochastic due to the nature of unpredictability beforehand and variability with individual differences and social hotspots. We study a stochastic GTDA problem, and propose a stochastic programming model under uncertain impression supplies, where chance constraints are employed. Facing the challenge of data scarcity, we propose a novel distributional robust optimization formulation, which optimizes the spread quality, measured by Gini-based metrics, together with delivery shortfall minimization, under the worst case probability distribution of impression supplies. To efficiently solve the problem, the distributionally robust chance constrained formulation is conservatively approximated by a parametric second-order cone program, for which an efficient interactive iteration heuristic approach is proposed. Computational experiments are conducted to show the advantages of our model, and effectiveness and robustness of our algorithm in comparison with several adapted state-of-the-art methods. Further managerial insights are also drawn.