Airline fleet assignment with time windows

Recognizing that allowing variability in scheduled flight departure times can result in improved flight connection opportunities and a more cost effective fleet assignment, we present a generalized fleet assignment model for simultaneously assigning aircraft types to flights and scheduling flight departures. Our model, a simple variant of basic fleet assignment models, assigns a time window to each flight and then discretizes each window, allowing flight departure times to be optimized. Because problem size can become formidable, much larger than basic fleet assignment models, we develop two algorithmic approaches for solving the model. Our direct solution approach is good for speed and simplicity, whereas our iterative technique minimizes memory usage. Using data from a major U.S. airline, we show that our model can solve real, large-scale problems, and we evaluate the effects of schedule flexibility. In every test scenario, the model produces a fleet assignment with significantly lower costs than the basic model, and, in a separate analysis, the model is used to tighten the schedule, potentially saving aircraft.