O.R. ApplicationsStrategic planning in fractional aircraft ownership programs
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 10 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 5500 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. We examine
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The effect of scheduled and unscheduled maintenance on operational costs.
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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., 1998, Barnhart et al., 1994). Furthermore, there exist studies that integrate aircraft routing and crew scheduling problems in one model. Cordeau et al., 2001, 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 cannot be directly applied to this particular application.
Keskinocak and Tayur (1998), the first paper in this field, study the fractional aircraft scheduling problem for a single type of aircraft. They develop and test a zero-one IP for small- and 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 costs. Recently, Martin et al., 2002, Martin et al., 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 analyses on real operational data and assist the fractional management company in making strategic and tactical planning decisions.
Section snippets
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
Basic assumptions
We first assume that during its duty period a crew stays with one aircraft unless a long maintenance event occurs. Although this assumption provides schedules with low plane utilization, due to the high transportation costs and times incurred when the crews travel by commercial airlines and the increased operational complexity, most fractional management companies prefer to operate with such initial schedules and modify them in an ad hoc manner if necessary. In our analysis, we will relax this
Analysis of different tactical and operational strategies
The main goal of this study is to identify initiatives that will decrease operational costs by increasing plane utilization. Two major factors affect plane utilization: (i) unavailability of planes to fly a customer leg due to maintenance problems and (ii) idling of the planes on the ground due to the lack of crew who can feasibly operate the plane or to the lack of customer demand. Using data based on the real operational data provided to us by CitationShares (www.citationshares.com), first,
Conclusions
In this paper, we propose a methodology for solving the combined crew scheduling and aircraft routing problem for a fractional aircraft ownership management company. Our scheduling approach considers: crew transportation and overtime costs, scheduled and unscheduled maintenance effects, crew rules, and the presence of non-crew-compatible fleets. We analyze several tactical and operational issues that are faced by fractional management companies and demonstrate how these issues affect
References (18)
- et al.
A column-generation technique for the long-haul crew-assignment problem
Optimization in Industry
(1994) - et al.
Improving crew scheduling by incorporating key maintenance routing decisions
Operations Research
(2003) - et al.
Benders decomposition for simultaneous aircraft routing and crew scheduling
Transportation Science
(2001) - et al.
The column generation principle and the airline crew scheduling program
INFOR
(1987) - et al.
Decomposition principle for linear programs
Operations Research
(1960) - et al.
Bombardier flexjet significantly improves its fractional aircraft ownership operations
Interfaces
(2005) - Karaesmen, I., Keskinocak, P., Tayur, S., Yang, W., 2005. Scheduling multiple types of time shared aircraft: Models and...
- et al.
Scheduling of time-share aircraft
Transportation Sciences
(1998) - et al.
Airline crew scheduling with time windows and plane count constraints
Transportation Science
(2002)
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