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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 $7526

B737 144 3050 530 239/138 $8860

B757 164 3900 540 153/5 $12213

B767 209 3850 550 56/8 $14500

B777 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 jProfit

Seat 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 T

Hubs

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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84

86

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90

92

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Percentage of Flights Still Operating with Hub Attacked

Hub Attacked

Perc

enta

ge o

f Flights

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Network Reaction to Attacks to Two Hubs

CLE-L

AX

LAX-S

FO

CLE-S

FO

EWR-L

AX

IAD-L

AX

DEN-L

AX

IAD-S

FO

LAX-O

RD

EWR-S

FO

IAH-L

AX

CLE-E

WR

CLE-IA

D

CLE-D

EN

DEN-S

FO

CLE-O

RD

ORD-SFO

CLE-IA

H

IAH-S

FO

EWR-IA

D

DEN-IA

D

DEN-E

WR

EWR-O

RD

IAD-IA

H

EWR-IA

H

IAD-O

RD

DEN-IA

H

DEN-O

RD

IAH-O

RD

0

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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 Flights

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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

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50

60

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90

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Percentage of Flights and Seating Capacity Remaining When Aircraft Attacked

Flights

Capacity

Type of Aircraft Attacked

Perc

enta

ge R

em

ain

ing

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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 T

HubsAircraftType

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