We consider the problem of optimally locating a single facility anywhere in a network to serve both on‐network and off‐network demands. Off‐network demands occur in a Euclidean plane, while on‐network demands are restricted to a network embedded in the plane. On‐network demand points are serviced using shortest‐path distances through links of the network (e.g., on‐road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst‐case distance. We solve our formulations using the “Big Segment Small Segment” global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi‐facility problems by solving a sequence of single‐facility problems. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(4), 271–282 2016

We propose a novel idea in the allocation and serving of online advertising. We show that by using predetermined fixed-length streams of ads (which we call patterns) to serve advertising, we can incorporate a variety of interesting features into the ad allocation optimization problem. In particular, our formulation optimizes for representativeness as well as user-level diversity and pacing of ads, under reach and frequency requirements. We show how the problem can be solved efficiently using a column generation scheme in which only a small set of best patterns are kept in the optimization problem. Our numerical tests suggest that with parallelization of the pattern generation process, the algorithm has a promising run time and memory usage.