A Demand Driven Re-fleeting Approach for Aircraft Assignment Under Uncertainty
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The current airline practice is to assign aircraft capacity to scheduled flights well in advance of departure. At such an early stage in this process, the high uncertainty of demand poses a major impediment for airlines to best match the airplane capacities with the final demand. However, the accuracy of the demand forecast improves markedly over time, and revisions to the initial fleet assignment become naturally pertinent when the observed demand considerably differs from the assigned aircraft capacity. The Demand Driven Re-fleeting (DDR) approach proposed in this thesis offers a dynamic re-assignment of aircraft capacity to the flight network, as and when improved demand forecasts become available, so as to maximize the total revenue. Because of the need to preserve the initial crew schedule, this re-assignment approach is limited within a single family of aircraft and to the flights assigned to this particular family. This restriction significantly reduces the problem size. As a result, it becomes computationally tractable to include path level demand information into the DDR model, although the problem size can then get very large because of the numerous combinations of composing paths from legs. As an extension, models considering path-class level differences, day-of-week demand variations, and re-capture effects are also presented. The DDR model for a single family with path level demand considerations is formulated as a mixed-integer programming problem. The model's polyhedral structure is studied to explore ways for tightening its representation and for deriving certain classes of valid inequalities. Various approaches for implementing such reformulation techniques are investigated and tested. The best of these procedures for solving large-scale challenging instances of the problem turns out to be an integrated approach that uses certain selected model augmentations and valid inequalities generated via a suitable separation routine and a partial convex hull construction process. Using this strategy in concert with properly selected CPLEX options reduces the CPU time by an average factor of 7.48 over an initial model for a test-bed of problems each having 200 flights in total. Prompted by this integrated heuristic approach, a procedure for finding solutions within a prescribed limit of optimality is suggested. To demonstrate the effectiveness of these developed methodologies, we also solved two large-scale practical-sized networks that respectively involve 800 and 1060 flights, and 18196 and 33105 paths in total, with 300 and 396 flights belonging to the designated family. These problems were typically solved within 6 hours on a SUN Ultra 1 Workstation having 260 MB RAM and a clock-speed of 167 MHz, with one exception that required 14 hours of CPU time. This level of computational effort is acceptable considering that such models are solved at a planning stage in the decision process.
- Masters Theses