Dynamic allocation of display advertising impressions in dual sales channels

We study a multi-period ad allocation problem faced by an online publisher who sells ad impressions on websites through two sales channels. In the guaranteed sales channel, advertisers submit heterogeneous offers for contracts under which the publisher guarantees delivery of a certain number of ad impressions over a certain period; in the real-time bidding (RTB) sales channel, the publisher runs an RTB auction to sell ad impressions. In each period, the publisher decides whether to accept or reject contract proposals; how to allocate ad impressions across existing contracts; and how many impressions to sell via RTB. The publisher faces uncertain demand from advertisers and an uncertain supply of impressions, which are generated by viewers visiting the publisher’s websites. We formulate the problem as a finite-horizon stochastic dynamic program, which poses significant methodological challenges. We first present structural properties of optimal policies under certain cases. To avoid the curse of dimensionality in dynamic programming, we develop an approach involving Lagrangian relaxations. We decompose the problem into a series of solvable subproblems and derive optimal policies. We further develop Lagrangian policies with performance guarantees. We show that when Lagrange multipliers depend on more signal history, the linear term’s weight of the number of contract types in the performance upper bound decreases. Furthermore, if the Lagrange multipliers depend on the full signal history, the corresponding Lagrangian policies will be asymptotically optimal to the number of contract types. We also explore a more suitable case for large-scale real-time ad allocation and create Lagrangian policies that yield comparable performance guarantees. Finally, we extend our main results to four new scenarios.