Airline Fleet Assignment with Time Windows

Abstract

Current fleet assignment models allow no variability in the scheduled departure time of flights even though exploiting this variability can result in more flight connection opportunities and a more cost effective fleet assignment. We present a generalized model that exploits this variability, simultaneously assigning aircraft types to flights and scheduling flight departures.We model this problem as a simple variant to current fleet assignment models, assigning a time window to each flight and then discretizing each window, allowing the model to select the departure time. As problem size can become formidable, much larger than current fleet assignment models, we develop two algorithmic approaches for solving the model. Our direct solution approach is good for speed and simplicity, while 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.

Airline Schedule Planning: Accomplishments and Opportunities

“…Removal of the superfluous ground arc decision variables, referred to as node consolidation, is just one example of variable elimination techniques used in modeling and solving airline problems. Related techniques, including arc consolidation and islands, have been identified in Hane et al (1995) and Rexing et al (2000). Applying such reduction techniques to an extended fleet assignment model, Rexing et al (2000) reduced their model size by more than 40%, allowing formerly intractable problem instances to be solved.…”

“…Because the core schedule design problem has not been successfully modeled in all its complexity, researchers have focused on determining incremental changes to flight schedules to allow a better matching of flight schedules and fleetings. In one such approach, proposed by Rexing et al (2000), the fleet assignment model is modified to allow small retimings of flight-leg departures (on the order of 5 to 20 minutes). This retiming can allow additional aircraft assignments.…”

“…While a planner can readily recognize the value of a single retiming such as this, an optimization approach is required to track its networkwide effects and to determine the optimal set of retimings. Rexing et al (2000) show that allowing scheduled departures to be retimed within 20-minute intervals results in significantly improved fleetings, saving $20 to $50 million annually for one major airline. Interestingly, the economic gains come both from increased revenues achieved through a reduction in spill costs, and increased aircraft productivity.…”

Integration of the Load-Matching and Routing Problem with Equipment Balancing for Small Package Carriers

“…First, instead of a network in which nodes represent physical locations (in this case, carrier facilities), we use a time-space network (for other examples, see [8], [24], [27]), in which nodes represent both locations and points in time. An arc from node {f 1 , t 1 } to node {f 2 , t 2 } indicates the movement of trailers leaving facility f 1 at time t 1 and arriving at facility f 2 at time t 2 .…”

Integrated Gate and Bus Assignment at Amsterdam Airport Schiphol

“…They propose a solution approach based on Benders decomposition and show that solving these two problems as one integrated problem yields significant cost savings. Other integrations that have been considered are schedule assignment and the fleet assignment problems (see Rexing et al [9] and Lohatepanont and Barnhart [8]) and the integration of the fleet assignment and the crew scheduling problems (see Gao [7], Clarke et al [1], and Sandhu and Klabjan [10]). …”