December 1999 In today's global economy, a growing number of executives or "elite" travelers believe that private aviation is the only smart way to travel. With the number of passengers increasing every year, travelers face several problems (see box) when using commercial flights, including: delays, cancelled flights, being "bumped" from a flight or downgraded due to overbooking, no direct flights between certain cities (especially small cities), long connection times, long check in times, misplaced baggage and lack of enough first class or business class seats [Wade 1995, 1997]. Private planes can save huge amounts of time, as well as provide comfort, convenience and privacy. However, due to its high cost (as much as $30 million for a Gulfstream jet), operation and maintenance expenses, a private jet isn't for everyone. Luckily, elite travelers or companies seeking more efficient use of executives' travel times have an option that can be cost effective: buying a share of a business jet. Fractional jet ownership programs offer companies and individuals all the benefits of private flying, without the high cost of complete ownership and without the headache of maintaining a corporate flight department with its own maintenance staff and pilots. A fractional owner purchases a portion of a specific aircraft based on the number of actual flight hours needed annually. For example, one-eight-share owners get 100 hours flying time per year, while one-quarter-share owners are entitled to 200 hours. Fractional owners have access to the aircraft any day of the year, 24 hours a day, with as little as four hours notice. Fractional jet ownership programs are relatively new, but are growing at a fast pace. NetJets (operated by Executive Jet Aviation, www.netjets.com), Flexjet (operated by Bombardier Business JetSolutions, www.aero.bombardier.com/htmen/A7.htm) and Raytheon Travel Air (a subsidiary of Raytheon Aircraft, www.raytheon.com/rac/travelair/) are among the leading fractional jet ownership programs. NetJets, which has the largest market share, offers up to 12 different aircraft types, including Cessna Citation, Raytheon, Gulfstream and Boeing jets (Zagorin 1999). Executive Jet Aviation revenues were projected at $900 million for 1998 and climbing at an average rate of 35 percent annually. Introduced in May 1995, the Flexjet program offers Learjet 31A, Learjet 60 and Challenger aircraft. FlexJet has more than 350 clients, and its current growth rate is estimated at 100 new fractional owners per year. Raytheon Travel Air program, which was started in 1997 and is currently serving more than 300 fractional owners, features three of the aircraft in the Raytheon Aircraft product line: Beech King Air B200, Beechjet 400A and Hawker 800XP. To "book a flight," a fractional owner calls the company managing the jets and specifies the departure time, departure location and destination. In contrast to chartering, the owners are charged only for actual flight time, not for deadhead and repositioning (i.e. for the time it takes a plane to reach the customer for pickup and to return to its base after drop-off) [Del Valle 1995]. A partial owner pays three separate fees for this program: a one-time purchase price for the fractional interest in the plane; a monthly management fee, which covers maintenance, insurance, administrative and pilot costs; and an hourly fee for the time the jet is used. For example, the purchase price of one-eight-share of a Gulfstream IV-SP jet is $4.03 million, management fees are $20,500 a month and the hourly rate is $2,890 [Zagorin, 1999]. Ownership rights usually expire after five years. Like full ownership, fractional ownership provides tax benefits to the buyer and can usually be sold back after a few years. The program has its widest appeal among small to midsize private companies who have business travel requirements, but cannot justify the cost of an entire business aircraft. Other owners include private individuals, celebrities, top executives or corporations looking to supplement their corporate flight departments' requirements. Fractional ownership best fits the needs of individuals and companies who fly between 50 and 400 hours a year [Levere 1996]. Full ownership is typically cost-justifiable when the annual flight hours exceed 400. Chartering tends to be cost efficient for flying less than 50 hours a year on day trips. One has to keep in mind that chartering an aircraft whenever needed is not guaranteed, whereas most ownership programs guarantee the availability of the aircraft to the partial owners any time of the day. Challenges in Managing a Fleet of Time-Shared Jets To achieve their ambitious goals on growth, profitability and customer satisfaction, fractional ownership programs need to manage their operations in an efficient way, and this can be a challenging task. At the strategic level, capital investments for growing the fleet or for increasing the size of the crew have to be made carefully, since aircraft are very expensive to purchase and to maintain. At the operational level, aircraft and crew need to be scheduled and maintained to satisfy the customers' requests on time, at minimum possible cost to the company. The aircraft-scheduling problem that has to be solved on a day-to-day basis can be described as follows: At any time, aircraft might be serving a customer or parked at one of many different locations. New customer requests arrive, each consisting of a departure location, departure time and destination. Usually it is necessary to relocate the aircraft to the departure locations. These flights are called "positioning legs" or "empty flights." Every customer request must be satisfied on time, possibly by subcontracting extra aircraft. Two major types of costs need to be considered in scheduling the aircraft: operating costs (fuel, maintenance, etc.) for flying the aircraft and the penalty costs for not being able to meet some customer requests without subcontracting extra aircraft. One has to create a flight schedule for the fleet to satisfy the customer requests (by subcontracting extra aircraft if necessary) at minimum cost under additional constraints of maintenance requirements and pre-scheduled trips. Each aircraft has to go to maintenance periodically. When an aircraft comes out of maintenance, it can fly only a limited number of hours before its next maintenance, so the schedulers have to make sure that the available flight hours of the aircraft are not exceeded in any schedule. Similarly, an aircraft can do only a limited number of landings before its next maintenance. Some aircraft may have previously (or manually) assigned trips to them, and these assignments should not be changed while creating a new schedule. For example, a pre-scheduled trip may actually be a scheduled maintenance. Maintenance is done only at certain locations, and if an aircraft is scheduled for maintenance at a certain location at a certain time, the schedulers have to make sure that it will be there on time. Since customers only pay for actual hours flown, minimizing the cost of empty flight hours and subcontracted hours is the main objective. Each client owns a share of a particular type of aircraft; however, in certain cases it is possible to substitute one type of aircraft for another. In general, bigger and faster aircraft — for example, a Learjet 60 — can be substituted for smaller and slower aircraft, such as a Learjet 31. Companies managing these jets use the substitution flexibility, especially if there is excess demand for a particular type of fleet. However, allowing substitution between different types of aircraft also makes the scheduling problem larger and more complicated. Note that the time-shared jet aircraft scheduling problem is different from the commercial airline scheduling problems in several respects. First, since many customers use these aircraft to travel between remote locations where not many commercial flights are available, it is very difficult to forecast the demand. Second, schedules have to be changed dynamically as new customer requests arrive. Since partial owners can request to use an aircraft any time of the day, the schedules have to be flexible to accommodate new trip requests. Third, a tradeoff has to be made between minimizing the costs due to positioning legs and the costs due to subcontracting. With these in mind, the time-shared jet aircraft-scheduling problem, in isolation from the crew issues, resembles the multiple depot vehicle-scheduling problem with additional constraints [Bodin et al. 1983]. Aircraft schedules also have to be coordinated with crew schedules. For example, in the NetJets program, workday schedules (also called a duty roster) are published 60 days in advance so that pilots can easily plan for birthdays, anniversaries, etc., and maintain a home life outside of their regular work schedule. Different work rules, such as minimum off-day requirements (e.g. at least two out of every seven days should be assigned off-duty for each pilot) and maximum work stretches (i.e., maximum number of consecutive days a pilot is on-duty), need to be considered while creating duty rosters, long before the actual trip requests are known. In addition to the work rules, which are based on contracts or FAA regulations, one also has to consider pilot qualifications to make sure that enough pilots with the desired qualifications are available to fly the aircraft on any given day. To fly most jet aircraft, at least two crew members are needed, where one is qualified as a "pilot" and the other is qualified as a "co-pilot." For example, a crew member who qualifies as a "pilot" for a Lear 31 jet and as a "co-pilot" for a Lear 60 jet may not be qualified as a "pilot" for a Lear 60 jet. Note that having the same number of crew members (with arbitrary qualifications) on-duty every day does not guarantee enough crew coverage for each aircraft type. Related to the problem of creating flexible crew workday schedules is the strategic question of how many crew members with each possible set of qualifications is needed, and how much the company has to invest for training the existing crew members to attain additional qualifications. In terms of operational flexibility, it is advantageous to have crew members who are qualified to perform more than one task. However, training is costly and with each additional qualification, the salary of a crew member, as well as his likelihood of leaving the company for a job elsewhere, also increases. The strategic and operational problems faced by the time-shared jet ownership business are challenging problems for OR/MS researchers as well as practitioners. An initial attempt at studying some of the problems faced by this growing industry has been conducted by Keskinocak and Tayur [1997, 1998], but the area is still wide open for innovative research. Commercial Air's Growing Pains The first commercial flight in the United States occurred on Jan 1, 1914 in Florida when Tony Jannus flew A. C. Pheil the 21 miles across the bay from St. Petersburg to Tampa in a two-seat Benoist at an altitude of 15 feet. Eighty-four years later, in 1998, U.S. carriers flew more than 615 million passengers. Unfortunately, as the number of commercial passengers soared, so did the number of complaints. In an effort to maximize revenue, airlines routinely "overbook" seats, especially during business hours. According to figures reported to the Department of Transportation, the nine major domestic airlines "bought out" 757,000 volunteers in 1994; another 52,000 passengers on these airlines were listed as "bumped" or involuntarily denied boarding. In January 1996, only 62.7 percent of all domestic flights by 10 major airlines were reported on time, that is, on the ground within 15 minutes of their schedule. Late arrivals meant late departures and delays for later flights at other airports. For travel between relatively small or remote cities, it may be difficult to find a flight, let alone a direct flight. Flying from Rochester, N.Y., to Wilmington, Del., on a commercial airline takes 10 hours with connections, but less than two hours on a private jet. In some cases, the trip between small cities may even be "intermodal," which means that although the airline ticket covers the whole distance, part of the trip is traveled by bus. Among other problems commercial air travelers face are long check-in times and misplaced baggage (luggage that has been lost, stolen, delayed or damaged). In 1996, the 10 biggest U.S. airlines reported almost 2.4 million complaints over misplaced baggage, an average of 5.3 for every 1,000 passengers. Sources: Department of Transportation, New York Times. References L. Bodin, B. Golden, A. Assad, M. Ball, 1983, "Routing and Scheduling of Vehicles and Crews: The State of the Art," Computers and Operations Research, Vol. 10, pgs. 63-211. C. Del Valle, 1995, "Can't Afford a Lear? Buy a Piece of One," Business Week, Sept. 11. P. Keskinocak and S. Tayur, 1997, "Assigning off-days to multiple types of workers in seven-days-a-week operations," GSIA working paper, Carnegie Mellon University, Pittsburgh, Pa. P. Keskinocak and S. Tayur, 1998, "Scheduling of Time-shared Jet Aircraft," Transportation Science, Vol. 32, pgs. 277-294. J.L. Levere, 1996, "Buying a Share of a Private Jet," The New York Times, July 21. B. Wade, 1995, "Passengers Play the Airlines' Bumping Game," The New York Times, May 21. B. Wade, 1995, "When the Plane is Really a Bus," The New York Times, Dec. 14. A. Zagorin, 1999, "Rent-a-Jet Cachet," Time Magazine, Sept. 13. Pinar Keskinocak is an assistant professor in the School of Industrial and Systems Engineering at Georgia Institute of Technology. She has worked on the development of a decision-support system for aircraft scheduling and crew off-day assignment for one of the leading fractional ownership programs. Table of Contents OR/MS Today Home Page OR/MS Today copyright © 1999 by the Institute for Operations Research and the Management Sciences. All rights reserved. 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