Polyhedral Analysis and Algorithms for a Demand-Driven Refleeting Model for Aircraft Assignment

Abstract

xzhu@vt.edu} T he current airline practice in conducting fleet assignments is to begin assigning aircraft capacity to scheduled flights well in advance of departures. However, the accuracy of the passenger demand forecast improves markedly over time, and revisions to the initial fleet assignment become naturally pertinent when the observed demand differs considerably from the assigned aircraft capacities. The demand-driven refleeting (DDR) approach proposed in this paper offers a dynamic reassignment of aircraft capacities to the flight network, when improved demand forecasts become available, so as to maximize the total revenue. Because of the need to preserve the initial crew schedule, this reassignment approach is limited within a single family of aircraft types and to the flights assigned to this particular family. This restriction makes it computationally tractable to include more relevant path-level demand information into the DDR model. Accordingly, we construct a mixedinteger programming model for this enhanced problem context and study its polyhedral structure to explore ways for tightening its representation and for deriving certain classes of valid inequalities. Various schemes for implementing such reformulation techniques are investigated and tested using a set of simulated and real instances obtained from United Airlines.

Integrated Airline Schedule Design and Fleet Assignment: Polyhedral Analysis and Benders' Decomposition Approach

“…Prior to describing our model, we present the following notation that is based on a standard timespace network representation for all the fleet types (for example, see Berge and Hopperstad 1993, Hane et al 1995, Sherali et al 2005). …”

“…As fleet assignment decisions need to be made well in advance of departures for the purpose of scheduling crews (although demand is highly uncertain at this point), Sherali et al (2005) proposed a mixed-integer programming demand-driven refleeting model to be solved subsequently under more accurate demand forecasts while considering pathlevel or itinerary-level demands as in Barnhart et al (2002), where the reassignments of aircraft to flight legs are limited within the same family of aircraft so as to preserve serviceability by the same 501 crew. The advantage of this approach lies in the potential utilization of a more accurate and detailed demand forecast as departure times approach.…”

Revenue management with aircraft reassignment flexibility

“…For example, a simulation study performed by United Airlines, considering only simple "swappable round-trip loops, 3 " exhibited high benefits of such demand-driven swapping strategies (in the order of $35-45 million per year); results from several Continental Airlines studies, again considering such loop swaps, are similar [4]. Consequently, it is not surprising that several airlines are studying such approaches, including American Airlines, Continental Airlines, United Airlines (with whom we have collaborated in our research), Austrian Airlines, Finnair, Lufthansa Airlines, and KLM [e.g., [4,8,16,19], and the references therein]. At this late swapping phase, only "simple" swaps are viable, such as the loop swaps studied by United Airlines and Continental Airlines, for the following reasons: (1) These swaps will have a small and localized impact on the original fleet assignment, reducing problems with operations and maintenance.…”

Robust airline schedule design in a dynamic scheduling environment

“…Flight leg re-fleeting changes the fleet type assigned to a flight leg with higher than planned demand to a larger aircraft type, and the fleet type assigned to a flight leg with lower than planned demand to a smaller aircraft type while still maintaining aircraft flow balance. Representative literature describing flight leg re-fleeting can be found in [6], [7], and [8]. In flight leg re-timing, flight departure and arrival times of a flight leg are altered to create new connecting itineraries through the hub to serve markets with higher than expected demands.…”

“…Focusing on models and solution approaches for the dynamic re-fleeting problem, [8] proposes to study the interaction between an original schedule and subsequent dynamic re-fleeting decisions. To our knowledge, the results of this study have not been reported to date.…”