  In this work, we study a scenario where a publisher seeks to maximize its
total revenue across two sales channels: guaranteed contracts that promise to
deliver a certain number of impressions to the advertisers, and spot demands
through an Ad Exchange. On the one hand, if a guaranteed contract is not fully
delivered, it incurs a penalty for the publisher. On the other hand, the
publisher might be able to sell an impression at a high price in the Ad
Exchange. How does a publisher maximize its total revenue as a sum of the
revenue from the Ad Exchange and the loss from the under-delivery penalty? We
study this problem parameterized by \emph{supply factor $f$}: a notion we
introduce that, intuitively, captures the number of times a publisher can
satisfy all its guaranteed contracts given its inventory supply. In this work
we present a fast simple deterministic algorithm with the optimal competitive
ratio. The algorithm and the optimal competitive ratio are a function of the
supply factor, penalty, and the distribution of the bids in the Ad Exchange.
  Beyond the yield optimization problem, classic online allocation problems
such as online bipartite matching of [Karp-Vazirani-Vazirani '90] and its
vertex-weighted variant of [Aggarwal et al. '11] can be studied in the presence
of the additional supply guaranteed by the supply factor. We show that a supply
factor of $f$ improves the approximation factors from $1-1/e$ to $f-fe^{-1/f}$.
Our approximation factor is tight and approaches $1$ as $f \to \infty$.
