In this paper, we propose an dynamic optimization model to maximize a web publisher's online display advertising revenues. Specifically, our model dynamically selects which advertising requests to accept and dynamically delivers the promised advertising impressions to viewers so as to maximize revenue, accounting for uncertainty in advertising requests and website traffic. After characterizing the structural properties of our model, we propose a Certainty Equivalent Control heuristic and then show with a real case study that our optimization-based method typically outperforms common practices. Our analysis thus highlights the importance of integrating the sales function with the advertisement delivery function in web publishing companies for globally maximizing revenues.

D isplay advertising is a $25 billion business with a promising upward revenue trend. In this paper, we consider an online display advertising setting in which a web publisher posts display ads on its website and charges based on the cost-per-click pricing scheme while promising to deliver a certain number of clicks to the ads posted. The publisher is faced with uncertain demand for advertising slots and uncertain traffic to its website as well as uncertain click behavior of visitors. We formulate the problem as a novel queueing system, where the slots correspond to service channels with the service rate of each server inversely related to the number of active servers. We obtain the closed-form solution for the steady-state probabilities of the number of ads in the publisher's system. We determine the publisher's optimal price to charge per click and show that it can increase in the number of advertising slots and the number of promised clicks. We show that the common heuristic used by many web publishers to convert between the cost-per-click and cost-per-impression pricing schemes using the so-called click-through-rate can be misleading because it may incur substantial revenue loss to web publishers. We provide an alternative explanation for the phenomenon observed by several publishers that the click-through-rate tends to drop when they switch from the cost-per-click to cost-per-impression pricing scheme.

Display advertising has a 39% share of the online advertising market and is its fastest-growing category. In this paper, we consider an online display advertising setting in which a web publisher posts display ads on its website and charges based on the cost-per-impression (CPM) pricing scheme while promising to deliver a certain number of impressions on the ads posted. The publisher faces uncertain demand for advertising slots and uncertain supply of visits from viewers. We formulate the problem as a queueing system, where the advertising slots correspond to service channels with the service rate of each server synchronized with other active servers. We determine the publisher’s optimal price to charge per impression and show that it can increase in the number of impressions made of each ad, which is in contrast to the quantity discount commonly offered in practice. We show that the optimal CPM price may increase in the number of ads rotating among slots. This result is typically not expected because an increase in the number of rotating ads in the system can be interpreted as an increase in the service capacity. However, the capacity increase leads to an increase in the fill rate of the demand (the portion of demand satisfied by the publisher). Hence, the publisher can afford to optimally decrease the arrival rate by increasing the price. The electronic companion is available at https://doi.org/10.1287/opre.2017.1697 .

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