Pricing contracts and planning stochastic resources in brand display advertising

Publishers, advertisers, and users are the three players in online display advertising, where the traded object is an impression (i.e., a user's visit). The publisher usually sells impressions months in advance of their physical appearance by signing contracts on prices and quantities with advertisers. With the introduction of ad exchanges, the publisher can also sell impressions that are unsold in the contracting market in a spot market. We build a bi-objective optimization problem to maximize the publisher's expected revenue and the advertisers' fairness of impression allocation in the presence of a spot market and impression supply uncertainty. Here, the publisher decides on the contract prices and creates a plan for impression allocations. The problem is a non-convex program, solved by integrating local and global heuristic methods. We also set a lower bound and an upper bound to facilitate and justify the solutions. Numerical examples indicate that ignoring supply uncertainty may over-estimate the expected revenue, and that fairness may be achieved by sacrificing a small portion of revenue. However, too much fairness may reduce the revenue. It is also shown that the heuristic algorithms are computationally effective.