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United Airlines Network
(simplified)Capt Mike Brisker
LT Andy Olson
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UA is world’s largest airline by amount of passenger traffic
Over 5000 flights/day on six continents Serves 234 airports in the US (63 of which
are considered in this model) Operates 14 different types of aircraft (five
of which are considered in this model)
Background
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◦ Only allowing network to run for two hops◦ Network only includes the 63 busiest US airports◦ Network starts with all aircraft at a hub◦ All edges between airports are fair game to an
aircraft at that airport; network does not force match a particular type of aircraft for a given edge
◦ UA is incentivized to use certain planes for certain edges based on profit available
Problem Formulation
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◦ Any edge can be run multiple times, but multiple runs of the same edge are successively less profitable
◦ Network is time-agnostic◦ Not requiring aircraft to return to point of origin◦ The network does not include the largest or
smallest planes UA uses◦ Aircraft are allocated to each hub proportionally to
the number of edges coming out of the hub
Formulation continued…
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Plane Type
Seats Range (nm)
Speed (mph)
Number in UA Fleet (Active/Stored)
Variable Cost/Hour
A319 132 3740 535 55/0 $7526B737 144 3050 530 239/138 $8860B757 164 3900 540 153/5 $12213B767 209 3850 550 56/8 $14500B777 300 5235 550 74/0 $10000
Airplane Data
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The cost of flying a given edge for a plane of type j is
The profit available for a plane of type j flying a given edge is
Profits
( )( ) ( )
( ) ( ) ( )
VariableCost jPlaneMiles j VariableCost jhour
PlaneMiles j Seats j Seat jhour
( ) ( )1.5( ) ( )
VariableCost j VariableCost jProfitSeat j Seat j
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Types of nodes◦ Hubs◦ Types of aircraft at a hub◦ Routes available from that hub◦ Legs of those routes◦ Cost nodes (created for the purpose of allowing
multiple flights on edges at reduced profit)
Network Description
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Total number of nodes: 5,917 Total number of edges: 40,371 Output file length (w/o attacks): 1,107 lines Number of legs flown (w/o attacks): 602
Network Vital Stats
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Abbreviated Network ModelModeled as Min-Cost Flow
S THubs
Aircraftat Hubs
ItineraryFrom Hub
Legs ofthe Flight
Cost Nodes
(0,0,∞) (0,0,1)
(0,0,maxnumber of aircraft)
(0,0,1)
(-profit,0,1)
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A Closer Look…
SFO B737 SFO-LAX-SFO(0,0,1)
Full Profit
Less Profit
Still Less ProfitLAX B737 LAX-SFO-LAX
SFO-LAX
LAX-SFO
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Still Closer…
Type of aircraftat hub (0,0,1
)
ItineraryFrom Hub (0,0,1)
Full Profit
Less Profit
Still Less Profit
(-profit,0,1)
(-.9*profit,0,1)(-.8*profit,0, ∞)
(¿ 𝑙𝑒𝑔𝑠 ) ·∑ 𝑦 𝑖𝑎−∑ 𝑦𝑎𝑖=0
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How badly does the removal of a hub affect the overall flow of the network?
Research Questions
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Network Reaction to Attack to One Hub
LAX SFO CLE IAD EWR DEN IAH ORD78
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82
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88
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92
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96
Percentage of Flights Still Operating with Hub Attacked
Hub Attacked
Perc
enta
ge o
f Fl
ight
s
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Network Reaction to Attacks to Two Hubs
CLE-LA
X
LAX-SFO
CLE-SF
O
EWR-LA
X
IAD-LA
X
DEN-LA
X
IAD-SF
O
LAX-ORD
EWR-SF
O
IAH-LA
X
CLE-EW
R
CLE-IA
D
CLE-DEN
DEN-SF
O
CLE-ORD
ORD-SF
O
CLE-IA
H
IAH-SF
O
EWR-IA
D
DEN-IA
D
DEN-EW
R
EWR-ORD
IAD-IA
H
EWR-IA
H
IAD-ORD
DEN-IA
H
DEN-ORD
IAH-ORD
0
10
20
30
40
50
60
70
80
90
Percentage of Flights Still Operating with Two Hubs Attacked
Pair of Hubs Attacked
Perc
enta
ge o
f Fl
ight
s
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Network Reaction to Attack on a Specific Type of Aircraft
Percentage of Flights Still Operating When Plane Attacked
A319 B767 B777 B757 B7370
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30
40
50
60
70
80
90
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Percentage of Flights and Seating Capacity Remaining When Aircraft Attacked
FlightsCapacity
Type of Aircraft Attacked
Perc
enta
ge R
emai
ning
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How many planes should we allocate at each hub?
Do we need more or less?
Research Questions
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Redesign the Network Model
S THubs
AircraftType
ItineraryFrom Hub
Legs ofthe Flight
Cost Nodes
(0,0,∞) (0,0,1)
(0,0,total number of aircraft)
(0,0,1)
(-profit,0,1)
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Planes Used
Plane Type
A319 B737 B757 B767 B777
Planes Used 11 93 87 28 30
Planes Avail 28 138 87 28 40
Percent 39% 67% 100% 100% 75%
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Things we wish we could have done…◦ The model is running correctly, but we have a
choke point in it limiting the number of flights◦ Time-layering◦ Assigning certain types of planes to certain types
of flights◦ Run a week/month schedule (it is available, but…)
Ways Forward