«b, J. Matthew Singletonb a School of Industrial and Systems Engineering, Georgia Institute of Technology 765 Ferst Drive, Atlanta, Georgia 30332 b ...»
Strategic Planning in Fractional Aircraft
Yufeng Yaoa*, Özlem Erguna, Ellis Johnsona, William Schultzb, J. Matthew Singletonb
School of Industrial and Systems Engineering, Georgia Institute of Technology
765 Ferst Drive, Atlanta, Georgia 30332
CitationShares, Greenwich American Centre
5 American Lane,Greenwich, CT 06831
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,
Abstract In the fractional ownership model, the partial owner of an aircraft is entitled to certain flight hours per year, and the management company is responsible for all the operational considerations of the aircraft and for making an aircraft available to the owner at the requested time and place. In the recent years although the industry as a whole has experienced significant growth, most of the major fractional jet management companies have been unprofitable. To increase profitability a management company must minimize its operating costs and increase its crew and aircraft utilization. In this paper, we present a methodology for efficiently scheduling the available resources of a fractional jet management company that takes into consideration the details in real world situations. We then discuss several strategic planning issues, including aircraft maintenance, crew swapping, demand increase and differentiation, and analyze their effects on the resource utilization and profitability.
Key words: Aircraft routing, crew scheduling, column generation, set partitioning, decision making
1. Introduction As partial (time-share or fractional) owners, customers share a given resource, using it for a fraction of the time and at various service levels, depending on the amount they pay. In the fractional jet ownership models, the owners do not compete for time on a particular plane but are entitled to their time whenever they ask for it. Furthermore, the fact that the operational and maintenance issues are taken care of by a management company makes it a convenient option for the owners.
Although fractional ownership of private aircraft has been around since the 1960’s as a business model, it has become increasingly popular over the last ten years. More and more individuals and businesses prefer to become partial owners of an aircraft because this model offers low cost (relative to whole aircraft ownership), flexibility, privacy, and guaranteed availability (with eight hours of advance notice), without the worry of hiring crews or maintaining the aircraft, since the management company provides those services. The fractional owner can fly directly anywhere among 5,500 airports (compared to 500 airports for commercial airlines) at anytime with few check-in or security delays, or lost baggage concerns, a significant benefit relative to commercial airline travel.
The fractional ownership programs provide share sizes from one-sixteenth with 50 flying hours per year to one-second with 400 flying hours per year (Levere 1996; Zagorin 1999). Usually, a partial owner requests a flight, by specifying a departure station, a departure time, an arrival station, and an arrival time, only days or hours ahead of time. The management company must assign a crew and an available aircraft to serve this flight. While scheduling all the requested flights, the management company tries to minimize total operational costs. There are five major operational expenditures: (i) repositioning cost, incurred when an empty aircraft is flown to a requested departure station; (ii) upgrade cost, incurred when a flight is upgraded to a larger aircraft; (iii) transportation cost, incurred when a crew travels to the aircraft or back to the crew base via a commercial airline; (iv) overtime cost, incurred when a crew works an extra day;
and (v) charter cost, incurred when additional aircraft must be chartered at a high cost to cover a requested flight. The customer pays for the fuel and crew costs of an actual customer trip, so they are not considered as an operational cost.
Unfortunately, the growth in the demand for fractional aircraft ownership has not translated into profitability for most management companies. In fact, recently only one of the four largest management companies reported profits. We believe that decreasing operational costs and increasing asset (crew and aircraft) utilization will have a positive effect on the profitability of such businesses. In this paper, we first develop a methodology that will help the fractional management companies in assigning and scheduling aircraft and crews so that all flight requests are covered at the lowest possible cost. Then, to aid with strategic decision-making, we analyze the impact of several tactical and operational strategies on profitability using real operational data.
1. The effect of scheduled and unscheduled maintenance on operational costs.
2. The effect on operational cost and crew and aircraft utilization of (i) allowing the crew to be separated from its initially assigned aircraft during a duty period when the crew’s aircraft goes under long maintenance or when the management company has more crews available than aircraft, (ii) allowing flexibility on the leg departure times, and (iii) increasing demand by introducing a new product, “jet-card”, whereby customers buy flight hours without becoming fractional owners.
In our models, we first assign crews to aircraft in the beginning of a duty, and then assign crews to a sequence of flight legs. This process is called crew pairing or crew scheduling. The crew-pairing problem in the commercial airline industry has been addressed in numerous studies and various solution methods have been developed. The problem is generally formulated as a set partitioning problem (Marsten and Shepardson, 1981). One method that is commonly used to solve set partitioning problems is column generation. Column generation was initially introduced in Dantzig and Wolfe (1960) and there exist a number of papers where it was applied to solve airline crew scheduling problems (see for example Crainic and Rousseau (1987), Lavoie et al.
(1988), and Barnhart et al. (1994)). Furthermore, there exist studies that integrate aircraft routing and crew scheduling problems in one model. Cordeau et al. (2001) and Mercier et al. (2003) apply Benders decomposition to simultaneously solve a single type of aircraft routing and crew scheduling problem. Klabjan et al. (2002) propose a solution approach for integrating aircraft and crew pairing by considering time window and plane count constraints in the crew pairing problem and Cohn and Barnhart (2003) incorporate aircraft key maintenance routing decisions within the crew-scheduling model.
For a fractional aircraft ownership program, the crew pairing problem poses a unique situation. Unlike the commercial airlines, the flight legs in a fractional program differ from day to day and week to week, and most are not known in advance. Repositioning requires flying an aircraft without any passengers on board, and repositioning may comprise 35% or more of the total flying. A crew (or an aircraft) starts or finishes its duty at a different location based on the demand each day. Moreover, fractional programs provide point-to-point service, compared to the commercial airlines. Therefore, the approaches for crew scheduling in commercial airlines can not be directly applied to this particular application.
Keskinocak and Tayur (1998), the first paper in this field, study the fractional aircraftscheduling problem for a single type of aircraft. They develop and test a zero-one IP for smalland medium-size problems (up to 20 planes and 50 trips) and provide a heuristic for solving larger instances. In their work, the multiple fleet types and crew duty restrictions are not considered. Ronen (2000) presents a decision-support system for scheduling charter aircraft. He develops a set-partitioning model that combines the fleet assignment and routing problems and incorporates maintenance activities and crew availability constraints. Larger scale problems (up to 48 aircraft and 92 trips) in one-day and two-day planning horizons are solved to minimize total cost of scheduling flights, subcontracting flights, and idling aircraft. He includes subcontractor aircraft as a part of the company-owned aircraft but with different cost. Recently, Martin et al.
(2002, 2003) extend the methods developed in Keskinocak and Tayur (1998) by including multiple types of aircraft and crew constraints. Their model considers multiple-day planning periods with 10-hour overnight rest between each day. Karaesmen et al. (2005) develop several mathematical models and heuristics that take into account the presence of multiple types of aircraft, scheduled maintenance, and crew constraints. They analyze the efficiency of these models through a computational study by solving daily scheduling problems. Yang et al. (2006) extend this work to multi-day horizons. Most recently, Hicks et al. (2005) develop an integrated optimization system for Bombardier Flexjet (www.flexjet.com), a large fractional aircraft management company. A column generation approach is applied to solve a large-scale mixed-integer nonlinear programming model, which is based on an integer multi-commodity network flow problem.
A branch-and-bound approach is used to obtain integer solutions from selected columns, which represent the aircraft itineraries and crew schedules.
In this paper, we develop a scheduling method for a fractional aircraft ownership program, which takes into account the real operational issues, such as crew transportation and overtime.
To the best of our knowledge, none of the previous studies consider the overtime costs. The consideration of crew transportation cost only appears in the recent paper by Hicks et al. (2005). According to our study, these two issues make-up up to 15% of the total cost. Although, the scheduling method we present here is very effective with respect to computational time and solution accuracy compared to the algorithms presented in the previous studies, the real contribution of this paper lies with the insights we were able to provide on the effects of aircraft maintenance, crew swapping, demand increase and differentiation on resource utilization and profitability. Using the scheduling tool we developed we were able to run various scenario analysis on real operational data and assist the fractional management company in making strategic and tactical planning decisions.
2. Problem Description and Basic Terminology A fractional management company requires that the owners request their flights at least eight hours before their desired departure time. In general, the management company does not change a customer’s request. The fractional management company may operate a non-homogenous fleet with aircraft of different sizes. When an owner requests a flight, the management company is obliged to serve this request with an aircraft that is at least as big as the owner’s aircraft type.
That is, the company may provide a larger aircraft without any additional expenses for the owner if it believes that the total operational costs can be decreased by this “complimentary upgrade.” On the other hand, an owner can request an “upgrade” or a “downgrade,” that is a flight request on a larger or a smaller aircraft, respectively. If a requested upgrade or downgrade is approved then the number of flight hours to be deducted from the customer’s account is adjusted with respect to the aircraft type. As a result, the remaining flight hours will be fewer when an upgrade is made and more if a downgrade is made. Moreover, the customer is required to pay the operating expenses associated with the aircraft flown.
We refer to a customer requested flight as a “leg.” A “crew” of two pilots and an aircraft are assigned for flying each leg. If the assigned aircraft is not already at the departure station of the leg, the assigned crew flies the empty aircraft to this station. This empty flight is called a “reposition” move. A “trip” is either a reposition move or a leg. A minimum “turn time,” that is time spent at the gate, is required between two trips.
We define a “duty” as a sequence of flights and related activities, such as briefing and debriefing, within a crew work day. The legality of crew composition and operations is defined by the Federal Aviation Administration (FAA) regulations. According to these regulations, only certain pairs of pilots are allowed to fly a certain aircraft type given their current expertise and training status. The “duty time”, the time span of a duty, cannot exceed fourteen hours and the maximum flying time is limited to ten hours. Furthermore, a ten-hour overnight rest is required to take place between two duties. A crew is notified of any trip assignments (including any changes to an assigned trip due to owner requests or unscheduled maintenance) at least two hours prior to departure. Also when a pilot travels by a commercial airline, a three-hour minimum connection time, due to the time needed to go through security, check in etc. at commercial airports, before the departure time of the commercial flight is assumed to be incurred. This connection time is also counted as a portion of the duty time.
In general, the pilots work on a schedule in which they will be on-duty for a specified number of days (e.g. one week) followed by an off-duty period (e.g. one week). We denote crew pairs consisting of pilots who are starting their on-duty period as “coming-duty” crews. Comingduty crews travel from their crew bases to their assigned aircraft locations after their rest period.
“Off-duty” crews are the crew pairs that go back to their crew bases at the end of their on-duty period. Sometimes the management company may ask a coming-duty crew to fly to the station where an aircraft is located the day before the crew’s duty-period starts to cover an early morning flight the next day. Also an off-duty crew may arrive to its home base a day after the end of its duty period due to flying a late flight the day before. In both of these cases, the pilots are paid “overtime.” The exchange of a crew with another crew to fly an aircraft is called a “crew-swap” and the days of the week that the coming-duty crew starts its shift and the off-duty crew ends its shift are called “designated duty shift days”.