Managing operations in the
time-shared jet business
Pinar Keskinocak and Sridhar Tayur
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Outline
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Overview of the time-shared jet business
Strategic and operational decisions
Scheduling of time-shared jets
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Objectives and constraints
Modeling using linear integer programming
Heuristic solution approaches
What do students learn from this case?
Experiences with the case
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Problems with commercial flights
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Delays or cancelled flights
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Being “bumped” from a flight or downgrades due to
overbooking
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52,000 passengers on 9 major airlines were involuntarily denied
boarding in 1994
No direct flights between certain cities
Long check-in and connection times
Misplaced or lost baggage
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In 1996, 38.3 percent of all domestic flights by 10 major airlines
were not on time
2.4 million complaints over misplaced baggage in 1996
Limited first/business class seats
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Private aviation
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Private planes can save huge amounts of time, and
provide comfort, convenience and privacy
Private planes have high costs, operation and
maintenance expenses
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Gulfstream V
$37.5 million
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Gulfstream IV-SP $27.5 million
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Challenger 604
$21 million
A plausible SOLUTION
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Time sharing of jet aircraft.
Become a “partial owner” of a jet.
Becoming a fractional owner of a
corporate jet
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Purchase a portion of a specific aircraft based on the
number of actual flight hours needed annually
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one-eight-share: 100 hours of flying time per year
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one-quarter-share: 200 hours
Access to the aircraft any day of the year, 24 hours a
day, with as little as four hours notice
5
Booking a flight in a time-shared
corporate jet
Pittsburgh
May 5, 10:00
San Francisco
May 6, 12:00
Austin
May 6, 21:00
DC
Positioning leg
(empty flight)
• Departure time
• Departure location
• Destination
Leading fractional jet ownership programs
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NetJets (operated by Executive Jet Aviation)
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offers up to 12 different aircraft types, including Cessna Citation,
Raytheon, Gulfstream and Boeing jets
$900 million in revenues for 1998 and climbing at an average rate
of 35 percent annually.
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Leading fractional jet ownership programs
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NetJets
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Flexjet (operated by Bombardier Business JetSolutions)
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offers Learjet 31A, Learjet 60 and Challenger aircraft
has more than 350 clients, growing at an estimated 100 new
fractional owners per year
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Leading fractional jet ownership programs
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NetJets
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Flexjet
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Raytheon Travel Air (a subsidiary of Raytheon Aircraft)
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offers Beech King Air B200, Beechjet 400A and Hawker 800XP
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serving more than 300 fractional owners
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Fees of fractional jet ownership
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A one-time purchase price for the fractional interest in
the plane
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Fractional ownership provides tax benefits to the buyer
and can usually be sold back after a few years.
A monthly management fee
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Ownership rights usually expire after five years.
Covers maintenance, insurance, administrative and pilot
costs; and
An hourly fee for the time the jet is used
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Fees of fractional jet ownership
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Example: Gulfstream IV-SP jet
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$4.03 million for a one-eight-share
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Management fees are $20,500 a month
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Hourly rate is $2,890
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Private aviation options
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Full ownership
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cost-justifiable when the annual flight hours exceed 400
Chartering
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cost efficient for flying less than 50 hours a year
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chartering an aircraft whenever needed is not guaranteed
Fractional ownership
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best fits the needs of individuals and companies who fly
between 50 and 400 hours a year
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Who are the participants of time-shared
jet programs?
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Small to midsize companies
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“We are still a relatively small company, so the idea of
having an airplane was something we really didn't consider
until we learned about NetJets fractional ownership.
I never believed that business aviation would be practical
or affordable until we became aware of NetJets.”
JIM McCANN
CEO of 1-800-Flowers.com
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Who are the participants of time-shared
jet programs?
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Small to midsize companies
Corporations looking to supplement their corporate
flight departments' requirements
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“Our first involvement in fractional ownership stemmed from
the number of flight hours that we were doing that involved
deadheads.
Twenty-five percent of our flying involved deadheads.
We took the position that we would use fractional aircraft
ownership to do those things that we can't do efficiently.”
NORRIS DAVIDSON
Aviation Manager
The Dow Chemical Co.
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“Fractional ownership offers more than just supporting
deadhead missions.
You can guarantee a seamless transportation to management.
If an in-house aircraft breaks down, you don't have to cancel the
trip.
Also, from a maintenance point of view, it allows us to run
our in-house airplanes right up to the hour for scheduled
maintenance and still continue to accept schedules.”
FORTUNE 100 COMPANY
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Who are the participants of time-shared
jet programs?
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Small to midsize companies
Corporations looking to supplement their corporate
flight departments' requirements
Private individuals, celebrities, top executives
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"I expect the convenience of NetJets ownership to extend
my playing career by a year or two. Buying a NetJets interest
was one of the best decisions I ever made.”
PETE SAMPRAS
Tennis Professional
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"As a Jet NetJets fractional aircraft owner,
I had 3 1/2 years to examine the service of NetJets before
Berkshire Hathaway purchased Executive Jet.
We knew we were purchasing the premier provider of aviation
solutions in the world.”
WARREN BUFFET
Chairman and Chief Executive Officer
Berkshire Hathaway Inc.
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Challenges in managing a fleet of timeshared jets
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Strategic decisions
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Tactical decision
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Size and mix of the fleet and crew
Assigning off-days to crew members
Planned maintenance
Operational decisions
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Scheduling and routing of the aircraft
Crew scheduling
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Issues in scheduling the aircraft
Major Costs
• Operating costs (fuel, maintenance etc.)
• Cost of subcontracting
Objectives
• Minimize the cost of positioning legs
• Minimize the cost of subcontracting
Constraints
• Customer requests
• Maintenance restrictions of the aircraft:
flight hours, landings, time of availability
• Pre-scheduled trips (or maintenance)
initial location
2
330
4
15
15
13
13
0
100
200
300
400
500
600
700
Time
(minutes)
initial location
2
2
330
4
4
trip 8
Aircraft 1
trip 3
8
1
8
trip 13 4
Aircraft 2
6
15
7
departure location
11 trip 11
12
15 trip 7
3
15
trip 1
5
10
13
4 trip 12
4 trip 5 8
Aircraft 5
4
trip 10
trip 2
1
100
14 trip 9 15
9
8
13
0
4
7
trip 4
trip 6
destination
200
300
400
500
5
600
700
Time
(minutes)
Optimum schedule
trip 8
trip 3
trip 13
trip 11
trip 4
trip 6
trip 7
trip 5
trip 1
trip 10
trip 9
trip 12
trip 2
How to construct a feasible schedule?
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Which trips can be served by each aircraft?
Which pairs of trips can be served consecutively by
the same aircraft?
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How to construct a feasible schedule?
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Which trips can be served by each aircraft?
AT(i,j) = 1, if trip j can be served by aircraft i
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Which pairs of trips can be served consecutively by
the same aircraft?
TT(j,k) = 1, if trip k can be served immediately after
trip j by the same aircraft
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initial location
2
2
330
4
4
trip 8
Aircraft 1
trip 3
8
1
8
trip 13 4
Aircraft 2
6
15
7
departure location
11 trip 11
12
15 trip 7
3
15
trip 1
5
10
13
4 trip 12
4 trip 5 8
Aircraft 5
4
trip 10
trip 2
1
100
14 trip 9 15
9
8
13
0
4
7
trip 4
trip 6
destination
200
300
400
500
5
600
700
Time (minutes)
AT(2,11)=0 AT(1,8)=1 AT(6,3)=0 AT(2,3)=1 TT(4,7)=0 TT(3,4)=0 TT(10,9)=1
Student exercises
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Determining entries of the AT and TT matrices
Determining whether a given schedule is feasible
Proposing alternative feasible schedules for the
example given in the case
Checking whether a given feasible schedule is a
“good” one
Determining the type of data needed to create a
feasible schedule
Proposing heuristics
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Heuristic solution approaches
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Develop a heuristic that constructs a (feasible) solution
from scratch
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For what type of problems would this heuristic work
best?
Improvement heuristics: Develop a heuristic that takes
a feasible schedule and modifies it to improve the
objective function value
Develop a heuristic that takes a feasible schedule and
modifies it to satisfy a new trip request
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Modeling the aircraft scheduling problem
as a linear integer program
Variables
Sj = 1, if trip j is subcontracted; 0, otherwise
Zijk = 1, if aircraft i serves trip k immediately after trip j
AT(i,j)=1, AT(i,k)=1, TT(j,k)=1
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Modeling the aircraft scheduling problem
as a linear integer program
Minimize
 c1(empty flight hours) + c2(subcontracted hours)
Subject to
 Each trip must be served by one of the aircraft of must
be subcontracted
 Maintenance restrictions should be satisfied
 Aircraft flow-balance constraints should be satisfied
Note that preprocessing takes care of pre-scheduled trip
constraints.
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Special cases and complexity
Maintenance
restrictions
Scheduled
trips
Problem P1
NO
NO
Model as a minimum cost
flow problem
Problem P2
NO
YES
NP-complete
Problem P3
YES
NO
NP-complete
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Additional considerations
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Time windows for departure times
Substituting one type of aircraft for another
Coordinating aircraft schedules with crew schedules
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Off-day assignments
Crew qualifications
Crew workday rules
Scheduling with uncertain demand
Creating “robust” schedules
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What do students learn from this case?
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An introduction to a relatively new business
Understanding and modeling a real world problem
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Alternative solution approaches in solving a model
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What kind of data do we need?
What kind of assumptions do we make?
The importance of preprocessing data
Linear/integer programming
Construction and improvement heuristics
Advantages and limitations of different solution
approaches
Learning how to use a modeling language and a solver
Additional considerations and related problems
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Aircraft case in classroom
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Tools and Environments for Optimization
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Anuj Mehrotra, Graduate School of Industrial Administration
(GSIA), Carnegie Mellon University
Sequencing and Scheduling
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Steve Wright, Computer Sciences Dept., University of Wisconsin
Modeling for Management Science Applications
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Michael C. Ferris, Computer Sciences Dept., University of
Wisconsin
Fatma Sibel Salman, GSIA, Carnegie Mellon University
Supply Chain Management
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Sridhar Tayur, M.S. in E-Commerce Program (Joint between
Computer Science and GSIA), Carnegie Mellon University
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Aircraft case in classroom (cont.)
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Deterministic Optimization
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Production Scheduling
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Pinar Keskinocak, School of Industrial and Systems Engineering,
Georgia Institute of Technology
Cliff Stein, Department of IEOR Columbia University
Analytical Techniques for Management Consulting
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Ignacio Castillo and Abdullah Dasci, School of Business, University
of Alberta
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Questions
Comments
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