Results: We solve for the optimal dynamic, state dependent bidding and allocation policies as a function of the number of ad impressions in queue, for both the finite horizon and steady state cases. We develop solution methods for bid optimization and viewer allocation and perform a sensitivity analysis with respect to the key problem parameters.
Methodology: New ad campaigns and viewers are treated as Poisson arrivals and the resulting model is a Markov decision process where the state of the system is the number of undelivered impressions in queue for each campaign type in each period. Our methodology jointly determines optimal bidding and viewer allocation strategies and obtains insights about the characteristics of the optimal policies. In practice, ad hoc strategies are often deployed. Academic/Practical Relevance: Determining a rigorous solution methodology is complicated by uncertainties in the arrival rates of viewers and campaigns, as well as uncertainty in the outcomes of bids on the ad exchange. They need to develop bidding policies to obtain viewers on an ad exchange and allocate them to the campaigns to maximize the agency's profits, subject to the goals of the ad campaigns. Problem Definition: Managers in ad agencies are responsible for delivering digital ads to viewers on behalf of advertisers, subject to the terms specified in the ad campaigns. Furthermore, we show that in competitive setting, a substantial web traffic increase for one publisher may lead all publishers to lose profits as a consequence of a price war. We show that the optimal CPM price may increase in the number of ads rotating among slots. We show that the optimal price increases in the number of impressions made of each ad, which is in contrast to the quantity-discount commonly offered in practice. We derive a closed-form solution for the steady-state probabilities of the number of advertisers and show how the optimal CPM price is affected by the number of slots, the web traffic, the number of requested impressions, and other operational parameters. We formulate the problem as a novel queuing system, where the advertising slots correspond to service channels with the service rate of each server synchronized with other active servers. In this paper, we determine the optimal cost-per-impression (CPM) prices of display ads for a web publisher facing uncertain demand from advertisers requesting space on its website and uncertain supply of impressions from viewers. The Internet has been a fast growing advertising medium.
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