Per-seat, on-demand air transportation Part I: Problem description and an integer multicommodity flow model

The availability of relatively cheap small jet planes has led to the creation of on-demand air transportation services in which travelers call a few days in advance to schedule a flight. A successful on-demand air transportation service requires an effective scheduling system to construct minimum-cost pilot and jet itineraries for a set of accepted transportation requests. We present an integer multicommodity network flow model with side constraints for such dial-a-flight problems. We develop a variety of techniques to control the size of the network and to strengthen the quality of the linear programming relaxation, which allows the solution of small instances. In Part II, we describe how this core optimization technology is embedded in a parallel, large-neighborhood, local search scheme to produce high-quality solutions efficiently for large-scale real-life instances.